# Fileset [DP_review_MTP accepted.pdf](https://mdr.nims.go.jp/filesets/ccce9f55-04c6-403a-98e8-9faef09f3635/download) ## Creator チェン ジェ, フェン ハイ, [山浦 一成](https://orcid.org/0000-0003-0390-8244) ## Rights [Creative Commons BY-NC-ND Attribution-NonCommercial-NoDerivs 4.0 International](https://creativecommons.org/licenses/by-nc-nd/4.0/) ## Other metadata [Review of progress in the materials development of Re, Os, and Ir-based double perovskite oxides](https://mdr.nims.go.jp/datasets/0f211986-68a9-47c6-aaa8-7105f6337288) ## Fulltext 1 Review of progress in the materials development of Re, Os, and Ir-based double perovskite oxides Jie Chen,1,2,* Hai L. Feng,3 Kazunari Yamaura 1,4 1. Research Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science, Namiki 1-1, Tsukuba, Ibaraki 305-0044, Japan 2. Materials Science and Engineering Program, Mechanical Engineering, University of Texas at Austin, Austin, Texas 78712, USA 3. Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, P. R. China 4. Graduate School of Chemical Sciences and Engineering, Hokkaido University, North 10 West 8, Kita-ku, Sapporo, Hokkaido 060-0810, Japan * To whom correspondence should be addressed. Present address: Laboratory for Materials and Structures, Institute of Innovative Research, Tokyo Institute of Technology, Yokohama, Kanagawa 226-8503, Japan Email: is.jiechen@gmail.com 2 Abstract This review explores the experimental advancements in the materials development of three 5d transition metal-based double perovskite oxides (Re, Os, and Ir), which have been predominantly achieved under high pressure. Perovskite oxides have ignited substantial interest due to their remarkable attributes encompassing ferroelectricity, piezoelectricity, catalysis, high-temperature superconductivity, giant magnetoresistance, ionic conduction, and negative thermal expansion. The seminal discovery of copper oxide-based high-temperature superconductors in 1986 marked a pivotal milestone in this field. The creation of double perovskite oxides, accomplished by introducing distinct elements into the B site of a perovskite-type structure, opens new avenues for scientific exploration and practical applications. Notably, double perovskite oxides featuring the 5d element at the B site could unveil significant relativistic effects and distinctive characteristics absent in conventional perovskite-type oxides. A high-pressure and high-temperature synthesis method has played a pivotal role in these studies. The ongoing exploration for new 5d double perovskites and a comprehensive understanding of the physical properties within this compound family remain at the forefront. The flexibility inherent in the double perovskite structure enables variations in A-site and B-site elements, along with the incorporation of 5d elements (Re, Os, and Ir), resulting in a diverse range of physical properties. This review systematically compiles synthesized compounds of Re, Os, and Ir-based double perovskite oxides. It also elucidates the impact of crystal structure on several intriguing properties and explores potential applications across various technological and scientific domains. By providing a comprehensive panorama, it aims to enhance comprehension and drive advancements in oxide materials research. Keywords Double perovskite oxides; 5d-element; Advanced oxide materials; Perovskite-type structures; High-pressure synthesis 3 1. Introduction The exploration of perovskite-type oxides has captivated the materials research community, garnering significant attention for their potential in developing diverse industrial and engineering materials. These materials exhibit remarkable properties, including ferroelectricity, piezoelectricity, catalysis, high-temperature superconductivity, giant magnetoresistance, ionic conduction, and negative thermal expansion, fueling a profound interest in further research and applications. A particularly noteworthy breakthrough was the discovery in 1986 of high-temperature superconductors based on cuprates, propelling research progress to new heights and igniting a wave of enthusiasm in this field. Within the realm of perovskite-type structures, the investigation of double perovskite oxides has emerged as a captivating focus, offering unique opportunities for scientific exploration and practical applications 1-6. By introducing two elements at the B site in a 1:1 ratio (herein defined by the general formula as A2BB’O6), these compounds unveil distinct characteristics, inspiring comprehensive studies on their synthesis and properties. The investigation of double perovskite oxides has unveiled intriguing structural arrangements, with many adopting layered, columnar, or rock-salt configurations. The presence of 5d electrons at the B’ site has sparked significant interest due to the profound influence of relativistic effects, leading to the manifestation of unique properties. This review delves into the captivating world of rock-salt type double perovskite oxides, with a focus on those involving 5d-electron configurations at the B’ site. These materials exhibit extraordinary properties not commonly found in traditional perovskite-type oxides, motivating us to compile a comprehensive list of successfully synthesized compounds. Notably, among these studies, the high-pressure and high-temperature method has proven to be a useful approach for the synthesis of these compounds. The core focus of this paper lies in exploring the captivating properties of 5d-electron double perovskite oxides and their potential implications for various technological fields from an experimental perspective. With attention to detail, our aim is to present a comprehensive overview of the advances made in experimental synthesis and investigation of these compounds, shedding light on their fascinating properties and promising applications. To illustrate the electronic structure evolution from 3d to 5d, we performed calculations on a cubic perovskite lattice (space group: Pm-3m) without structural distortion, specifically focusing on group 8 elements. Notably, all atoms occupy special positions in the crystallographic sense, resulting in an absence of local distortion, ensuring no impact on the electronic state from lattice distortion. The electronic states of the 3d oxide BaFeO3 exhibit a high density of states at the Fermi energy and a relatively narrow d-bandwidth, while the 4d and 5d oxides show progressively wider bandwidths and smaller densities of states (Fig. 1.1). Our nonmagnetic calculations consider the contribution of spin-orbit coupling (SOC). However, for a more comprehensive comparison with actual properties, further investigation involving U (on-site repulsion) and hopping integrals is necessary. It is evident that larger spatial overhang of electron orbitals in elements with larger atomic numbers leads to more pronounced relativistic effects. The results demonstrate that U tends to be smaller in 5d elements compared to 3d elements, exemplifying the significance of these effects. Based on this theoretical calculation, it is evident that 5d oxides distinguish themselves from their 3d and 4d analogues in terms of the nature of the 5d element. This observation motivates further experimental exploration and study of 5d-related oxide compounds. 4 Fig. 1.1: Electronic states of the cubic perovskite (Pm-3m) in BaFeO3 7, BaRuO3 8, and BaOsO3 9 calculated using density functional theory with generalized gradient approximation 10. The consideration of spin-orbit coupling was incorporated in the non-magnetic calculations. The Review comprises four main sections. The Introduction offers an overview of the topic and sets the stage for subsequent sections. The second section delves into the material synthesis and crystal structure of A2BB’O6 double perovskite oxides, laying the groundwork for further exploration. The main section is divided into two subsections, focusing on the properties of 3d-5d double perovskite oxides, with a particular emphasis on Os- and Re-based compounds. In subsection 3.1, we investigate the high-temperature ferrimagnetism of A2FeB’O6 and A2CrB’O6 (B’ = Os, Re), along with the magnetic properties of A2BOsO6 with different A-site elements (A = Ca, Sr, Ba; B = Fe, Co, Ni). Additionally, we explore the properties of Os-based double perovskite oxides with A = Pb and oxides containing Re or Os with nonmagnetic elements in the B site. Section 3.2 outlines properties associated with various B-site elements (nonmagnetic elements, Co, Ni) and various A-site combinations (A = Sr, Ba; B = Ca, Mg, Zn, Cu, Ni), focusing on Ir-based double perovskite oxides. Finally, we discuss the results presented here, including our own work, and provide future prospects for 5d-based double perovskite oxides. Through this comprehensive review, we aim to contribute to a broader understanding of the remarkable properties and potential applications of 5d-based double perovskite oxides, while stimulating further research and innovation in the domain of advanced oxide materials. 2. Material synthesis and crystal structures of A2BB’O6 The early synthesis of 5d double perovskite oxides can be traced back to the 1960s 11,12. However, intensive experimental efforts to synthesize and characterize double-perovskite compounds composed mainly of the 5d element have been made over the past two decades. In general, conventional solid-state reaction methods are used to synthesize double perovskite oxides. This solid-state reaction, performed at ambient pressure, is sufficient to synthesize many members 5 of this compound family. Molten salt-mediated synthetic methods have also been employed in the preparation of this compound family 13. However, for the synthesis of double perovskite compounds, in which the 5d element is the major component, thermal treatment under high-pressure conditions of the gigapascal magnitude has often proven to be effective. Double-perovskite compounds synthesized under high pressure have been reported in the range up to 8 GPa. Various types of high-pressure apparatus have been utilized to achieve pressure conditions in this range, including belt (Fig. 2.1), cubic multi-anvil, and Kawai (also known as Walker) types. For reference, Table 2.1 lists the double perovskite oxides A2BB’O6 synthesized under high pressure that have been reported. Fig. 2.1: Assembled views of a belt-type high-pressure apparatus and sample cell, located at the National Institute for Materials Science (NIMS) in Japan, used for synthesizing a series of compositionally or structurally new osmate double perovskites 14-18. Please note that the view may not accurately represent the relative sizes and shapes of the apparatus, as the anvils are somewhat exaggerated 19. Reprinted from J. Solid State Chem., vol 236, Yamaura, K., Short Review of High-Pressure Crystal Growth and Magnetic and Electrical Properties of Solid-State Osmium Oxides, 45-54, Copyright (2016), with permission from Elsevier. The formula for double perovskite oxides is generally denoted as A2BB’O6. However, compounds with the formula A2BB’O6 can adopt a variety of structures, including rock salt-ordered double perovskite, polytype perovskite, columnar or layered-ordered double perovskite, ilmenite, LiNbO3-type, and corundum-related structures 20-24. It is worth noting that although not classified as a double perovskite, there are also compounds known as antisite disordered perovskites that have a chemical composition of A2BB’O6. For instance, Ca2MnOsO6 crystallizes into an orthorhombic perovskite structure (Pnma) with lattice constants a = 5.50666 Å, b = 7.60562 Å, and c = 5.39317 Å. In this structure, both Mn and Os occupy the same B sites without an ordered arrangement. In this review, the double perovskite structure refers specifically to the rock-salt ordering at the B site and the disorder at the A site. It is important to mention that perovskites with ordered A-site elements also constitute a large family of compounds. Further details on these can be found in other review articles 25,26. Double perovskite oxides with the most symmetric cubic structure and space group Fm-3m can be regarded as the ideal crystal structure representing this category. Similar to simple 6 perovskite-type structures, the tolerance factor of cubic double perovskites is approximately 1 (t = 1). This tolerance factor quantifies the bond mismatch between the A-O and B-O bonds and can be calculated using the formula t = (rA + rO)/(√2(rB + rO)). The cubic double perovskite has approximately twice the unit cell edge size compared to cubic perovskite ABO3. When the tolerance factor is smaller than 1 (t < 1), an octahedral tilt is expected to occur, resulting in a less symmetric structure. P. M. Woodward and C. J. Howard provided a comprehensive description and review of the symmetry lowering of the crystal structure of the ordered double perovskite A2BB’O6 27,28. Based on group theory analysis by Howard et al., a total of 12 different spatial groups were identified for the ordered double perovskite 28. For the 5d double perovskite oxides discussed in this paper, at least five of the predicted space groups have been experimentally identified: Fm-3m (No. 225, a0a0a0), R-3 (No. 148, a-a-a-), I4/m (No. 87, a0a0c-), P21/n (No. 14, a+b-b-) and I2/m (No. 12, a0b-b-) (Fig. 2.2). This means that the double perovskite-type structure with cubic symmetry decreases in symmetry to rhombohedral (R-3), tetragonal (I4/m), and possibly monoclinic (P21/n and I2/m). Conversely, when the tolerance factor is greater than 1 (t > 1), a hexagonal perovskite-type structure is formed. For example, Ba2FeOsO6 (t = 1.0491), Ba2CoOsO6 (t = 1.0416), and Ba2NiOsO6 (t = 1.0461) crystallize into 6L-type perovskite structures (No. 164, P-3m1) 10,11,19. However, it is important to note that these poly-type perovskite oxides do not fall into the category of salt-ordered double perovskites discussed in this paper, and thus will not be further discussed here. Additionally, it should be noted that the lattice and structural parameters discussed in this review are determined through X-ray diffraction (XRD) or neutron diffraction (ND) measurements. Fig. 2.2: Schematic of the most common five B-site ordered double perovskite structure and 6L-type perovskite structure of A2BB’O6; the tilted system described using Glazer’s notation is shown in parentheses. HPHT denotes high-pressure and high-temperature. 7 High-pressure and high-temperature techniques have often been shown to be effective in stabilizing perovskites and related structures 29. In the case of double perovskites, it is possible to create a salt-ordered double perovskite phase even with a tolerance factor greater than 1 (t > 1). For instance, Ba2NiOsO6 synthesized under 6 GPa pressure exhibits a cubic double-perovskite structure 16, in contrast to the hexagonal phase formed under ambient pressure. This difference may be attributed to the A-O bonds being more compressible than the B-O bonds under pressure. Consequently, the tolerance factor approaches 1 under the stress environment. On the other hand, the rock salt-ordered phase obtained under pressure lacks the face-sharing octahedra present in the hexagonal phase. The redistribution of BO6 octahedra under pressure leads to a rock-salt ordered double perovskite composed solely of corner-sharing octahedra. This structural arrangement effectively reduces electrostatic repulsion, as observed in Pauling’s third law 30. The high-pressure and high-temperature method is also useful in incorporating Mn2+ and Pb2+ ions into the A site of the double perovskite structure. For example, Mn2BReO6 (B = Li, Co, Ni, Mn, Fe) compounds have been synthesized by using the high-pressure and high-temperature method, all of which have monoclinic perovskite-type structures (P21/n) 31-37. This is attributed to the relatively small tolerance factor. On the other hand, the double perovskite Pb2BOsO6 (B = Co, Ni, Zn) possesses a monoclinic perovskite-type structure despite having a tolerance factor larger than 1 18,38,39. This structural distortion is attributed to the hybridization of the lone pair electrons on Pb with the surrounding oxygen ions. Thus, while the tolerance factor serves as a useful guideline for predicting the structural distortion of perovskites, it is important to recognize the contribution of other factors as well. In addition to the lone pair electrons of the A-site ions, the competing covalent nature of the A-O and B-O bonds may influence the symmetry of the perovskite-type structure. The presence of more ionic A-O bonds can lead to the B/B’-O bonds becoming more covalent and thus shorter than the bond lengths predicted by the hard-sphere model with tabulated ionic radii. For instance, Ba2BReO6 (B = Fe, Mn, Co, Ni, Zn) and Ba2BOsO6 (B = Li, Mg, Zn, In, Sc) have tolerance factors greater than 1, but these compounds with rock-salt double-perovskite structures can be synthesized without requiring high pressure 40-43. On the other hand, the development of magnetic ordering can induce structural distortions. In the case of Pb2CoOsO6, the presence of magnetic ordering is accompanied by an abrupt change in the lattice constant 18. Similarly, in Sr2CoOsO6 and Sr2CoReO6, a symmetry reduction from tetragonal to monoclinic is observed upon the onset of magnetic ordering 44,45. Furthermore, spin-lattice interactions can affect the stability of the structure, as evidenced by the contraction of the c-lattice constant with increasing temperature in the tetragonal double perovskites Sr2NiReO6 and Sr2NiOsO6 45,46. The synthesis of certain 5d double perovskite compounds often requires the application of oxygen pressure to effectively stabilize the high oxidation states of the 5d elements and prevent the formation of oxygen vacancies. In ambient pressure synthesis, the desired oxygen pressure can be achieved by using pressurized oxygen or through the thermal decomposition of oxygen sources such as PbO2, Ag2O, and MnO2 in a sealed reaction container 46-49. In high-pressure synthesis, perchlorate salts are commonly used as an in-situ source of oxygen. These salts undergo thermal decomposition to produce chloride salts, thereby providing the necessary oxygen for the synthesis 15,50. 8 Table 2.1: 5d double perovskite oxides obtained by high-pressure and high-temperature conditions. Compounds P (GPa) S. G. a t b GII b Refs 5d0 Mn2LiReO6 8 P21/n 0.8652 0.02871 31 5d1 Mn2CoReO6 8 P21/n 0.8571 0.02701 32 Mn2NiReO6 8 P21/n (150 K) 0.8607 0.02480 33 Pb2CoReO6 8 R-3 0.9926 0.00005 51 5d1-2 Mn2MnReO6 c 5, 8 P21/n 0.8778/ 0.8368 0.01718/0.04379 34,35 5d2 Mn2FeReO6 5 P21/n 0.8780 0.01711 36,37 Pb2NiReO6 6 I2/m 0.9968 0.00101 52 Ca3OsO6 6 P21/n 0.8695 0.04118 14 Ca2MgOsO6 6 P21/n 0.9290 0.00616 53 Sr3OsO6 6 P-1 0.8881 - 49 Sr2MgOsO6 6 I4/m 0.9824 0.02001 53 Ba2NiOsO6 6 Fm-3m 1.0461 0.42842 16 Ba2CuOsO6 6 I4/m 1.0479 0.44848 54 Pb2CaOsO6 d 6 P21/n - - 39 Pb2CoOsO6 6 P21/n 1.0038 0.01937 18 Pb2NiOsO6 6 P21/n 1.0081 0.04611 38 Pb2ZnOsO6 6 P21/n 1.0008 0.00087 39 5d3 Ca2InOsO6 6 P21/n 0.9034 0.01326 55 Pb2FeOsO6 8 Fm-3m 1.0110 0.06712 56 Sr2CuIrO6 4 I4/m 0.9875 0.01441 57 Ba2NiIrO6 8 Fm-3m 1.0450 0.41754 58 5d5 Lu2NiIrO6 6 P21/n 0.8578 0.03420 59 a The structures listed in the table were determined at room temperature or according to the literature. Any structures determined at temperatures other than room temperature are indicated in the table. b Tolerance factor (t) and the global instability index (GII) are calculated by SPuDS version 2.21.05.11. c Mixed valent states of Mn2+/3+ for the B-site and Re6+/5+ for B’-site were suggested in ref. 35. Tolerance factor and GII before the slash was calculated with R0(Mn3+) and R0(Re5+), while the latter was calculated with R0(Mn2+) and R0(Re6+). d Pb2CaOsO6 does not crystallize into a typical double perovskite structure, but rather adopts a highly distorted monoclinic structure (P21/n) with lattice parameters a = 10.0812(3) Å, b = 5.689(1) Å, c = 11.837(4) Å, and β = 125.32(2)° at 2 K. This distorted structure persists at high temperatures. 39 3. Properties of 5d-electron (Re, Os, and Ir) double perovskite oxides 3.1. Re- and Os-based double perovskite oxides The high Curie temperature exhibited by magnetic materials makes them appealing for use in magnetic and spintronic devices. Simple perovskites, however, face challenges in achieving a 9 high Curie temperature, primarily due to the difficulty in establishing a network of orbital ordering that enables three-dimensional ferromagnetic (FM) coupling. In contrast, a group of double perovskite oxides has been discovered to exhibit ferromagnetism or ferrimagnetism (FIM) with remarkably high Curie temperatures (TC). The exploration and investigation of high-TC FM double perovskite oxides can be traced back to the studies of Re-based double perovskite oxides in the 1960s 1,2,52. This early research sparked further interest in exploring other high-TC FM double perovskite oxides, particularly those based on molybdenum and tungsten. The discovery of half-metallic properties in Sr2FeMoO6 in 1998, along with its relatively high TC (410-450 K), has served as a catalyst for exploring these double perovskite materials in the context of their potential applications in spintronics 60. Extending to osmate double perovskite oxides, Sr2CrOsO6, reported in 2007, stands out with the highest known TC of 725 K among FIM double perovskite compounds. The discovery of these double perovskite oxides has laid the foundation for new high-TC FIM materials and has stimulated the understanding of the physics underlying high-TC magnetism. It should be noted that the double perovskite oxide Sr3OsO6 has recently been reported to exhibit a FM transition above 1000 K in its thin film form fabricated on the SrTiO3 substrate 61. However, the corresponding bulk materials of Sr3OsO6 do not exhibit FM features 49. This suggests that there may be a contribution from the interface between the film and the substrate, influencing the magnetic behavior. There is typically no specific temperature criterion for defining a high TC for ferrimagnetic materials. Nevertheless, it is commonly accepted to classify high-TC FIM materials as those demonstrating a net magnetic moment above room temperature. In some reports on double perovskites, materials exhibiting spontaneous magnetization are referred to as FM, distinguishing them from antiferromagnetic (AFM) materials, which do not possess spontaneous magnetization. However, in this review, we emphasize the importance of clearly distinguishing between ferrimagnetism (FIM) and ferromagnetic (FM) based on spin alignment. Specifically, we use the term FIM to describe the antiparallel spin alignment between the B and B’ sites in double perovskites, where the presence of different transition metal elements at these sites results in a non-zero net spin. In this section, our discussion focuses on FIM Re- and Os-based double perovskites that exhibit a net magnetic moment above room temperature. Among the reported Re and Os-based double perovskite oxides, it is commonly observed that compounds with Cr or Fe occupying the B site exhibit high-TC FIM properties, as summarized in Table 3.1. The presence of high-TC ferrimagnetism in A2BB’O6 (B = Cr, Fe; B’ = Re, Os) double perovskite compounds can be attributed to the specific electronic configurations of Cr3+ (3d3) and Fe3+ (3d5). The partially filled orbitals of Cr3+ and Fe3+ are believed to play significant roles in the strong magnetic interactions observed in these materials. It is noteworthy that despite exhibiting high TC ferrimagnetism, the double perovskite compounds listed in the table also demonstrate a diverse range of electron transport properties. Table 3.1: Comparison of the structural parameters and physical properties of double perovskite A2BB’O6 (B = Cr or Fe, B’ = Re or Os) with high-TC ferrimagnetism. Re-based compounds Ca2CrReO6 Sr2CrReO6 Ca2FeReO6 Sr2FeReO6 Ba2FeReO6 Mn2FeReO6 Pb2FeReO6 S.G. P21/n I4/m P21/n I4/m Fm-3m P21/n I4/m Bond length of B-O (Å) 1.966 × 2 1.973 × 2 1.956 × 4 1.956 × 2 2.025 × 2 2.025 × 2 1.985 × 4 2.004 × 2 2.10291 × 6 1.929 × 2 1.962 × 2 1.98 × 4 1.96 × 2 10 1.956 × 2 2.012 × 2 2.060 × 2 Bond length of B’-O (Å) 1.969 × 2 1.972 × 2 1.976 × 2 1.953 × 4 1.949 × 2 1.959 × 2 1.954 × 2 1.940 × 2 1.961 × 4 1.946 × 2 1.92874 × 6 2.036 × 2 2.018 × 2 1.982 × 2 1.99 × 4 2.01 × 2 Bond angle of B-O-B’ (deg.) 154.3 153.1 155.01 179.7 180 151.73 152.24 150.68 170.22 180 180 140.9 139.8 139.7 178.6 180 Tolerance factor (t) a 0.9498 1.0043 0.9414 0.9954 1.0552 0.8780 1.0169 GII 0.00176 0.03352 0.00302 0.00539 0.53261 0.01711 0.10371 Electron transport Insulator Metal 62,63 Semiconductor 64,65 Metal 63 Metal 64 Insulator Semiconductor Semiconductor 13 Metal-insulator transition 62,63 Semiconductor 13 Semiconductor 13 TC (K) 360 635 525 400 315 520 420 Ms (μB/ formula-it) 0.8 0.86 3 3 3.04 5.0 2.4 Ref. 63 13,62,63 62-65 63,66 64,67,68 36,37 69 Os-based compounds Ca2CrOsO6 Sr2CrOsO6 Ca2FeOsO6 S.G. P21/n R-3 (RT) P21/n Bond length of B-O (Å) 1.971 × 2 1.970 × 2 1.972 × 2 1.952 × 6 (500 K) 1.976 × 2 2.020 × 2 2.019 × 2 Bond length of B’-O (Å) 1.959 × 2 1.962 × 2 1.943 × 2 1.958 × 6 (500 K) 1.986 × 2 1.936 × 2 1.946 × 2 Bond angle of B-O-B’ (deg.) 153.4 153.1 154.20 176.5 151.5 154.0 151.7 Tolerance factor (t)a 0.9443 0.9985 0.9359 Electron transport Insulator Insulator Insulator Ms (μB/ formula-nit) 0.2 0.22 ~1.5 TC, TN (K) 490 725 320 Ref. 70 70 15,71 a The tolerance factor (t) and the global instability index (GII) can be calculated using SPuDS version 2.21.05.11. 3.1.1 High temperature ferrimagnetism of A2FeB’O6 (B’ = Re, Os) Among Re or Os-based double perovskite oxides, the majority exhibit insulating behavior. However, the electronic properties of A2FeReO6 (A = Ca, Sr, Ba) distinguish them from other members, ranging from insulating to metallic. Ca2FeReO6 has been reported to undergo a metal-insulator transition at 150 K 54,55, while Sr2FeReO6 and Ba2FeReO6 exhibit metallic behavior 63-65. Experimental studies and theoretical simulations suggest that Sr2FeReO6 and Ba2FeReO6 possess half-metallicity, where the conduction electrons are spin-polarized at the Fermi level 68,72-74. The half-metallic FM or FIM nature of these materials has attracted significant interest due to their potential applications in spintronics, such as high tunnel magnetoresistance. However, the electron transport properties of A2FeReO6 (A = Ca, Sr, Ba) reported in different studies are not entirely consistent, as shown in Table 3.1. Resistivity measurements in polycrystalline samples can be influenced by factors such as grain boundary concentration and anti-site disorder, which may contribute to variations in the data. The synthesis method used to prepare these compounds can play 11 a crucial role in minimizing grain boundary effects and anti-site disordering 13,75. The FIM half metals, Sr2FeReO6 and Ba2FeReO6, have attracted significant interest in the field of spintronics due to their similarities to Sr2FeMoO6 60. The half-metallic and FIM ground states observed in Sr2FeReO6 and Ba2FeReO6 can be described using a double-exchange-like model similar to that in Sr2FeMoO6 76. The electronic band crossing the Fermi level in Sr2FeReO6 and Ba2FeReO6 consists of hybridized orbitals involving Fe (t2g orbital of 3d), O (2p orbitals), and Re (t2g orbitals of 5d) 77. This hybridization enables the sharing of conduction electrons between Fe and Re ions, leading to mixed-valent states of Fe2+/Fe3+ and Re6+/Re5+. The coexistence of Fe2+/Fe3+ and Re6+/Re5+ has been investigated through Mössbauer and X-ray absorption spectroscopic studies 77-79. While Re-based and Mo-based double perovskites share certain similarities in their charge configuration and some physical properties, there are also significant differences between the two. Within the framework of a simple ionic model, the distortion of bond angles away from the ideal 180° in double perovskite compounds results in a reduction of effective d-electron hopping or a decrease in the hybridization between the d orbitals of the transition metal ions and the p orbitals of oxygen. In the case of monoclinic Ca2FeReO6, the bond angle of B-O-B’ exhibits severe distortion compared to cubic Ba2FeReO6 or tetragonal Sr2FeReO6. The insulating ground state of Ca2FeReO6 seems to be explained by the reduction of effective d-electron hopping between Fe and Re. Interestingly, Ca2FeMoO6 also exhibits a comparable distorted bond angle of B-O-B’ to Ca2FeReO6. However, unlike Ca2FeReO6, Ca2FeMoO6 maintains a metallic behavior similar to Sr2FeMoO6 80. Therefore, solely attributing the insulating nature of Ca2FeReO6 to the bond-angle distortion becomes challenging. Furthermore, the observed elevated TC in Ca2FeReO6 cannot be adequately explained by this mechanism. The experimental observation of Ca2FeReO6 having the highest TC among A2FeReO6 (A = Ca, Sr, Ba) double perovskites contradicts the expected outcome, as the reduction of hybridization resulting from the bond-angle distortion would typically lead to a lower TC. The angle of Fe-O-Re deviates from 180° disturbs the interaction between the t2g orbitals of Fe and Re, known as pdd-π coupling. Instead, it facilitates the pdd-σ coupling through the eg orbitals of Fe and Re, which has been proposed as the underlying mechanism for the observed increase in ferromagnetic coupling in Ca2FeReO6 74,81. Band structure calculations have indicated that the insulating state of Ca2FeReO6 can be accurately described by incorporating an appropriate on-site Coulomb repulsion term 82. This discovery suggests that Ca2FeReO6 exhibits strong correlation effects, which sets it apart from its electronic analog compounds, Ba2FeReO6 and Sr2FeReO6. The observed metal-insulator transition in Ca2FeReO6 is believed to be associated with a potential orbital transition, which could involve the presence of two competing spin-orbital ordered states 83. Mn2FeReO6 and Pb2FeReO6 are two examples of high-TC FIM double perovskite compounds, where the A-sites are not occupied by alkaline earth ions. The stabilization of the double perovskite forms of Mn2FeReO6 and Pb2FeReO6 requires high-pressure conditions. By introducing Mn2+ at the A-site, a group of transition-metal-only double perovskite materials is formed. Within this family, several Re-based double perovskites have been reported, including Mn2FeReO6, Mn2MnReO6, Mn2CoReO6, and Mn2NiReO6 32-37. However, no osmate double perovskite compound incorporating Mn2+ at the A-site has been identified thus far. The introduction of Mn2+ into the 3d-5d double perovskite leads to more complex magnetic 12 and electronic properties. In Mn2FeReO6, three spin-ordering regimes have been determined from neutron diffraction at different temperatures. At 300 K, the spin structure of Mn2FeReO6 is comparable to other FIM double perovskites, with antiparallel ordering between Fe3+ and Re5+ and no measurable moment from Mn. With cooling, AFM order of Mn2+ appears, and the competition between exchange interactions of Mn-O-Mn, Fe-O-Re, and Mn-O-Fe/Re leads to magnetic frustration at low temperatures. Due to the large spin of Mn2+ ion (S = 5/2), the magnetization in Mn2FeReO6 is significantly higher compared to other members of A2FeReO6 (A = Ca, Sr, Ba, Pb). The high-TC and significant positive magnetoresistance make Mn2FeReO6 a promising material for spintronic applications. The insulating behavior observed in Mn2FeReO6 aligns with the trend observed in A2FeReO6 (A = Ca, Sr, Ba) as the ionic radius of A2+ decreases. In this case, the smaller ionic radius of Mn2+ compared to Ca2+ accentuates the insulating behavior. This correlation suggests that the transition from metal to insulator is influenced by the size of the A-site cation in these double perovskite compounds. The electronic properties observed in Pb2FeReO6 generally follow the trend seen in the A2FeReO6 family regarding the relationship between structural distortion and electron transport. As the temperature decreases, the resistivity of Pb2FeReO6 slightly increases, indicating a semiconducting behavior 69. This contrasts with the metallic behavior observed in A2FeReO6 (A = Sr, Ba), where the A-site ions are larger than Pb2+. The insulating nature of Ca2FeReO6 below its metal-insulator transition temperature (~150 K) has been investigated using photoemission spectroscopy 69,84. 13 Fig. 3.1: Variations of the TC, average bond angle, and bond length in two sets of double perovskite compounds. (a) A2FeReO6 (A = Ca, Sr, Ba, Mn, Pb) compounds. The data are obtained from the references listed in the accompanying table. The plot allows for a comparison of TC among the different compounds. (b) A2FeOsO6 (A = Ca, Sr, Pb) compounds. The data for Sr2FeOsO6 and Pb2FeOsO6 are taken from references 56,85, respectively, and are included for comparison with the high-TC ferrimagnetic compound Ca2FeOsO6. It is noted that Sr2FeOsO6 exhibits two magnetic phase transitions at 140 K and 67 K, and the magnetic transition temperature of 140 K is depicted in the figure. The A2FeReO6 and A2FeOsO6 compounds, sharing the same 3d transition metal but having different 5d transition metals, exhibit variations in their structural characteristics and physical properties. The interplay between the crystal lattice structure, arrangement of transition metal ions, spin states, and electronic states may govern the overall behavior of these high-TC FIM 5d double perovskite oxides. To investigate this statement, we compare the structure, magnetic, and transport properties of the two series of 3d-5d double perovskite oxides, as depicted in Fig. 3.1. When larger A-site ions are present, the double perovskite structures undergo a transition from monoclinic to cubic lattice. The inclusion of data for Sr2FeOsO6 and Pb2FeOsO6 in Fig. 3.1, alongside Ca2FeOsO6, provides insights into the evolution within the Fe-Os double perovskite family, despite these compounds not falling into the high-TC FIM category. This structural transition is evident from the changes in the B-O-B’ bond angle. Interestingly, the bond lengths of B-O and B’-O exhibit distinct evolutions with respect to the ionic radii of A-site cations in A2FeReO6 and A2FeOsO6, despite the similar ionic radii 14 of Re5+ and Os5+. In A2FeReO6, the Fe-O bond length generally increases with larger A-site ions, whereas in A2FeOsO6, the Fe-O bond length decreases with larger A-site ions. The trends for Re-O and Os-O bond lengths show opposite behavior accordingly. Although the tolerance factors, calculated from effective ionic radii, are similar for A2FeReO6 and A2FeOsO6 when the A site is occupied by the same cation, the average bond lengths of B/B’-O exhibit comparable values between these two systems, as indicated by the dashed line in Fig. 3.1. In terms of the magnetic transition temperature, it consistently decreases as the A-site cation size increases for both A2FeReO6 and A2FeOsO6. However, despite the similar magnetic trends, the two series demonstrate different transport properties. The A2FeReO6 compound family exhibits a wider range of electron transport properties, including insulating behavior, metal-insulator transitions, and half-metallic characteristics. In contrast, all three Fe-Os double perovskites exhibit insulating behavior. 3.1.2 High temperature ferrimagnetism of A2CrB’O6 (B’ = Re, Os) The d3 electronic configuration is known to exhibit high magnetic transition temperatures, which is commonly observed in both simple perovskites and double perovskites. For instance, SrTcO3 with a t2g3eg0 configuration in its 4d orbital has the highest Neel temperature (TN) of approximately 1000 K 86. Another example is NaOsO3, a 5d perovskite with a 5d3 electronic configuration, which exhibits a TN of 410 K 87. In the case of the 3d3-5d3 double perovskite Sr2CrOsO6, it demonstrates the highest known TC among bulk double perovskite oxides, reaching up to 725 K. The mechanisms underlying the observed high-TC FIM property and its deference from its counterparts, such as Sr2CrReO6 and Sr2CrWO6, are still being investigated. The specific electronic configurations and the interplay between the 3d and 5d electrons contribute to the unique magnetic properties observed in these systems. Further research is needed to fully understand the factors influencing the high-TC ferrimagnetism in these materials. Replacing Os with Re in Sr2CrReO6 results in a relatively lower TC of 635 K, while an even lower TC of 458 K is found in Sr2CrWO6 88. This suggests that the AFM exchange interaction originating from the Cr3+-O-Os5+ bond is stronger compared to the Cr3+-O-Re5+ and Cr3+-O-W5+ bonds. The electronic analogues of Sr2CrOsO6 and Sr2CrReO6, Ca2CrOsO6 and Ca2CrReO6, crystallize into the monoclinic double perovskite lattice. Similar to Sr2CrOsO6 and Sr2CrReO6, Ca2CrOsO6 exhibits a higher TC compared to Ca2CrReO6. Furthermore, the FIM transition temperature can be influenced by fully or partially substituting Cr3+ with other elements 17,89. These examples highlight the strong correlation between robust high-TC ferrimagnetism and the AFM exchange interaction originating from the Cr3+-O-Os5+ bond. However, the specific reasons for the specialty of d3 electronic configurations and their impact on the magnetic properties require further studies. The antiparallel spin arrangement between Cr3+ and Os5+ in Sr2CrOsO6 and Ca2CrOsO6 is similar to the spin ordering observed in FIM A2FeB’O6 compounds. However, there is a distinction in the electronic configuration between Cr3+ (3d3) and Fe3+ (3d5). While both Cr3+ (3d3) and Os (5d3) have three unpaired electrons, the FIM behavior in Sr2CrOsO6 and Ca2CrOsO6 is influenced by the significant orbital contribution of Os. This non-negligible orbital contribution reduces the magnetic moment on Os, preventing complete compensation between moments of Cr3+ and Os5+ 70,89. 15 This observation challenges the simple assumption that SOC is negligible in 5d3 systems due to the total orbital angular momentum being zero. It has been found that SOC can be present in 4d3 and 5d3-based oxides, as they exist in an intermediate electronic state between L-S and j-j coupling schemes 82,83. The uncompensated magnetic moments on Cr3+ and Os5+ contribute to the saturation magnetization (Ms) of Sr2CrOsO6, which has been determined to be 0.22 μB/formula-unit through neutron diffraction measurements 70. A comparable value of 0.2 μB/formula-unit was found for Ca2CrOsO6. The neutron diffraction measurements also confirm the non-monotonic temperature dependence of magnetic susceptibility observed in Sr2CrOsO6 and exclude the previously proposed canted magnetic structure 90. It is worth noting that the Ms values for Cr-5d double perovskites are significantly lower compared to those observed in high-TC FIM Fe-5d counterparts due to the presence of fewer 3d electrons. However, the magnetic transition temperature is significantly improved in Cr-based analogs. We have highlighted the properties and behavior of double perovskite oxides containing Cr3+, W5+, Re5+, or Os5+ ions. These materials are particularly interesting for investigating the impact of 5d band filling on various physical properties, such as high-temperature ferrimagnetism and electric transport. One notable finding is that the TC for ferrimagnetism significantly increases with increasing bandwidth within the series of Cr-5d double perovskites. Specifically, Sr2CrOsO6 exhibits a TC higher than that of Sr2CrWO6 and Sr2CrReO6 by more than 200 K. This suggests that a wider bandwidth leads to a substantial enhancement of TC. The electronic properties of these materials also demonstrate changes in band filling. While Sr2CrWO6 and Sr2CrReO6 display half-metallic behavior and are positioned on the metallic side of a spin-polarized metal-insulator transition 91, Sr2CrOsO6 is considered to reside at the terminal point of this transition. Despite having low resistivity at room temperature, Sr2CrOsO6 does not exhibit metallic characteristics, indicating that it lies on the boundary of the spin-polarized metal-insulator transition 91. The observed half-metallic behavior in double perovskite oxides containing Cr3+ or Fe3+ can be attributed to kinetic-energy-driven ferrimagnetism. This arises from the hybridization between the 3d orbital of Cr3+ or Fe3+ ions and the 5d orbital of W5+, Re5+, or Os5+ ions. This hybridization causes shifts in the energy levels of W5+, Re5+, or Os5+ ions, resulting in a significant tendency towards half-metallic properties 79,80. The AFM order between the 3d and 5d ions in these double perovskites is facilitated by spin-polarized conduction electrons, as previously described 92-94. This mechanism induces a magnetic moment on the W, Re, and Os sites, consistent with experimental observations 95,96. 3.1.3 Evolution of magnetism with different A-site elements in A2BOsO6 (A = Ca, Sr, Ba; B = Fe, Co, Ni) The 3d-5d double perovskite oxides exhibit unique electronic and magnetic properties compared to those containing only 3d elements. This distinction can be primarily attributed to the distinct characteristics of the 5d orbitals. Over the past two decades, there has been rapid progress in the discovery of new 3d-Os double perovskite compounds, with high-pressure synthesis playing a crucial role in stabilizing some of these materials. Most of the reported A2BOsO6 compounds (where A = Ca, Sr, Ba; B = 3d transition metal) exhibit insulating behavior, which is unexpected considering the anticipated stronger hybridization 16 between the extended 5d orbitals and oxygen, which could potentially lead to metallic properties. However, A2BOsO6 compounds display intriguing and unexpected magnetic properties, influenced by various factors such as the large spatial extent of the 5d orbitals, crystal-field splitting effects, and the strong SOC present in these compounds. The magnetic properties of A2BOsO6 compounds have been observed to be effectively altered by substituting A-site cations in osmate double perovskites, often accompanied by structural transitions. In this section, we will review the magnetic properties of several compound families within the A2BOsO6 (A = Ca, Sr, Ba; B = 3d transition metal) family. The objective is to gain insights into how the structure influences the magnetic properties of these osmate double perovskites. Ca2FeOsO6 is a FIM material with a high Curie temperature of 320 K 15. In contrast, the isoelectronic compound Sr2FeOsO6 exhibits AFM properties 85,97. Neutron diffraction studies have determined that Sr2FeOsO6 exhibits two types of AFM spin structures at low temperatures, denoted as AF1 and AF2 (Fig. 3.2) 98,99. In both AF1 and AF2 structures, the magnetic moments of Fe and Os are antiparallel to each other within the ab plane, consistent with the proposed FIM structure of Ca2FeOsO6 15. The main difference between these two AFM spin structures lies in the spin coupling along the c-axis. Morrow et al. propose that in the AF1 phase, the FIM ab planes are coupled to neighboring planes by a 90° AFM Os-O-O-Os interaction on the face-centered cubic-type Os sublattice 71. The AF1 phase emerges at 140 K, while the AF2 phase appears at temperatures below 67 K 71,99. Paul et al. suggest that the change in the dominant AFM spin structure in Sr2FeOsO6 is attributed to a modulation of the Fe-Os distance along the c-axis within the tetragonal lattice as the temperature decreases 99. Morrow et al. propose an alternative explanation for the AF2 magnetic structure, suggesting that a four-bond Fe-O-Os-O-Fe AFM superexchange coupling dominates along the c-axis, leading to antiparallel coupling of Fe spins along these chains 71. Fig. 3.2: Magnetic structures of antiferromagnetic (AF1, AF2), and ferrimagnetic (FIM) phases observed in Sr2FeOsO6 98. Reprinted with permission from [Veiga, L. S. I., et al., Phys. Rev. B, 91 (23), 235135, 2015] Copyright (2015) by the American Physical Society. In comparison to the AF2 phase of Sr2FeOsO6, the magnetic moments of Fe and Os in Ca2FeOsO6 exhibit complete AFM coupling along the c-axis, as opposed to partial AFM coupling. This difference in behavior is attributed to the distinct crystal structures of Ca2FeOsO6 (monoclinic 17 double perovskite) and Sr2FeOsO6 (tetragonal double perovskite), which lead to different magnetic ground states. In the monoclinic lattice of Ca2FeOsO6, the Fe-O-Os bond angles along the c-axis deviate from 180°. Morrow et al. proposed that this c-axis buckling weakens the Fe-O-Os-O-Fe AFM superexchange interaction, resulting in a prevailing antiparallel Fe-O-Os coupling in all three directions and a FIM ground state 71. This hypothesis explains the lower TC observed in SrCaFeOsO6 (TC = 210 K) compared to Ca2FeOsO6 (TC > 300 K) since the Fe-O-Os bond angle is more severely bent in Ca2FeOsO6 71. A2FeOsO6 compounds (A = Ca, Sr) serve as excellent examples to illustrate the intricate competition of superexchange pathways in 3d-5d double perovskite oxides. The enhanced bending of the Fe-O-Os bond angle suppresses the longer-range superexchange interaction of Fe-O-Os-O-Fe, allowing the nearest neighbor Fe-O-Os AFM coupling to dominate. This complexity in the magnetic ground state of 3d-5d double perovskite oxides contrasts with that of 3d perovskite oxides 100. Apart from the degree of collinearity between Fe-O-Os bonds, the exchange interaction between Fe and Os can be influenced by various factors. In the case of Sr2FeOsO6, Veiga et al. reported that the transition from AFM to FIM order can be induced by applying hydrostatic pressure, even without any concurrent symmetric structural changes. The tetragonal lattice of Sr2FeOsO6 is maintained under pressure, indicating the absence of a buckling angle in the high-pressure phase 98,101. Veiga et al. demonstrated that the FIM state of Sr2FeOsO6 is induced by an increase in the difference between Os and Fe crystal-field splitting (10Dq,Os - 10Dq,Fe), rather than by bending the Fe-O-Os bonds under pressure. The decrease in lattice parameters and compression of the Fe-Os distance under pressure result in an increase in crystal fields. This increase in crystal fields stabilizes the AFM coupling between Fe and Os along the c-axis. The transition to fully AFM coupling along the c-axis leads to the emergence of ferrimagnetism in the compressed phase of Sr2FeOsO6 under pressure (Table 3.2). The exchange interactions in Sr2FeOsO6 can be significantly influenced by pressure, a characteristic strongly linked to the unique nature of the 5d element. This distinction stands in stark contrast to systems that lack 5d elements 102. It is noteworthy that the FIM phase induced by high pressure up to 40 GPa in Sr2FeOsO6 is only 40% of that observed in Ca2FeOsO6, as resolved by x-ray magnetic circular dichroism (XMCD) spectroscopy 98. Table 3.2: Comparison of the structural parameters and physical properties of double perovskite oxides A2FeOsO6 (A = Ca, Sr). Ca2FeOsO6 SrCaFeOsO6 Sr2FeOsO6 (AP) Sr2FeOsO6 (HP) S.G. P21/n P21/n (100 K) I4/m I4/m Bond length of Fe-O (Å) 1.976 × 2 2.020 × 2 2.019 × 2 1.967 × 2 1.982 × 2 2.022 × 2 1.939 × 4 1.936 × 2 Bond length of Os-O (Å) 1.986 × 2 1.936 × 2 1.946 × 2 1.997 × 2 1.999 × 2 1.941 × 2 1.985 × 4 2.007 × 2 Bond angle of B-O-Os (deg.) 151.5 154.0 151.7 152.3 150.3 150.7 179.9 180 Physical properties Insulator, FIM FIM Insulator, AFM FIM Tmag (K) 320 15 210 140, 67 Above R.T. 18 350 71 (P > 30 GPa) θWeiss (K) +80 85,97 +24 71 Reference 15,71 71 71,85,97 98,101 Similar to A2FeOsO6 (A = Ca, Sr), the substitution of Ca with Sr in the Co-Os and Ni-Os double perovskite oxides A2BOsO6 (A = Ca, Sr; B = Co, Ni) also leads to a transition from FIM to AFM ordering. Ca2CoOsO6 and Ca2NiOsO6 exhibit insulating and FIM properties with Curie temperatures of 145 K and 175 K, respectively 46,103, which are lower than the observed TC in Ca2FeOsO6. The electronic analogues of these compounds, Sr2CoOsO6 and Sr2NiOsO6, are both AFM insulators 34,36. The structural and physical properties of the Co-Os and Ni-Os double perovskite oxides are presented in Table 3.3. Despite both compounds being insulators, the conductivity of Ca2NiOsO6 is 2-3 orders of magnitude lower than that of Ca2CoOsO6 103. This difference in conductivity can be attributed to the variations in the filling of the 3d orbitals. However, the magnetic ordering in both FIM insulator compounds remains similar. XMCD studies have revealed the FM coupling between Os-Os through the Os-O-O-Os exchange pathway 103. Morrow et al. demonstrated that the primary driving force towards the FIM state in Ca2CoOsO6 and Ca2NiOsO6 is the AFM Os-O-Co/Ni superexchange coupling, which involves virtual hopping between partially filled t2g orbitals of Os and half-filled eg orbitals of Co or Ni. In the case of Sr2CoOsO6 and Sr2NiOsO6, where the bond angle of Os-O-Co/Ni approaches linearity, t2g-eg coupling is forbidden. As a result, both Sr2CoOsO6 and Sr2NiOsO6 exhibit AFM states instead of FIM states 103. The sensitivity of magnetic interactions in Co-Os double perovskite compounds to changes in the Co-O-Os bond angles is further demonstrated by the substitution case of SrCaCoOsO6 104. Regarding the AFM compound Sr2CoOsO6, neutron diffraction studies have revealed different ground states for the magnetic sublattices of Co and Os 44,104,105. Consequently, Sr2CoOsO6 exhibits two magnetic transition temperatures. Below 108 K (TN1), AFM ordering of Os6+ occurs, while high-spin Co2+ orders antiferromagnetically below 70 K (TN2) 44. Yan et al. suggested that in the first AFM state, the magnetic moments of Co2+ and Os6+ dynamically fluctuate, while their average effective moments (μeff) exhibit long-range order 105. Furthermore, below TN2, the magnetic moments of Co2+ become frozen, resulting in a noncollinear spin-canted AFM state 105. In contrast, the moments of Os6+ freeze into a randomly canted state at an even lower temperature, approximately 5 K 105. These observations indicate weak coupling between the Co and Os sublattices in the double perovskite Sr2CoOsO6. Although both Sr2CoOsO6 and Sr2NiOsO6 exhibit AFM ordering, the exchange interactions in these compounds may not be exactly the same. This is evidenced by the different signs of the Weiss temperatures (θWeiss): a negative value for Sr2CoOsO6 and a positive value for Sr2NiOsO6, as shown in Table 3.3. The positive θWeiss suggests a net FM interaction in Sr2NiOsO6 46. The FM interaction is even stronger in the cubic double perovskite Ba2NiOsO6, as indicated by the increase in θWeiss from 27 K to 113 K. This strong FM interaction results in FM ordering above 100 K 16. Fig. 3.3 provides a comparison of the magnetic properties of the three Ni-Os double perovskite oxides. 19 Fig. 3.3: (a) Isothermal magnetization loop of Ba2NiOsO6 at 5 K in comparison with the loops for ferrimagnetic Ca2NiOsO6 and antiferromagnetic Sr2NiOsO6. (b) Magnetic field dependence of the intensity of the magnetic peak of Ba2NiOsO6 , with the inset showing the magnetic order model of the ferromagnetic state of Ba2NiOsO6 based on the neutron diffraction analysis 16. Reprinted with permission from [Feng, H. L., et al., Phys. Rev. B, 94 (23), 235158, 2016] Copyright (2016) by the American Physical Society. The substitution of larger alkaline earth ions at the A-site leads to an increase in the tolerance factor for the double perovskite structure. Ba2NiOsO6, for instance, exhibits a tolerance factor greater than 1. However, the stabilization of the rock-salt double perovskite phase in Ba2NiOsO6 requires high-pressure conditions 16. This cubic double perovskite compound displays intriguing properties, as it is a FM semiconductor and exhibits metamagnetic behavior. At approximately 32 K, the application of a weak external magnetic field induces an antiferromagnetic-like transition in Ba2NiOsO6. Furthermore, around 100 K, it undergoes a transition to a FM insulating state. Neutron diffraction studies have confirmed the transition from a modulated AFM state to a collinear FM state under a magnetic field of 21 kOe at 5 K. Notably, the insulating property persists in both magnetic states 16. Theoretical calculations, as illustrated in Fig. 3.4, suggest that SOC plays a significant role in generating a charge gap and contributing to the insulating nature of Ba2NiOsO6 16. 20 Fig. 3.4: A schematic representation of the density of states structure of the d-band in the ferromagnetic state of Ba2NiOsO6 16. Reprinted with permission from [Feng, H. L., et al., Phys. Rev. B, 94 (23), 235158, 2016] Copyright (2016) by the American Physical Society. Table 3.3: Comparison of the structural parameters and physical properties of double perovskite A2BOsO6 (A = Ca, Sr, Ba; B = Co, Ni). Ca2CoOsO6 Sr2CoOsO6 Ca2NiOsO6 Sr2NiOsO6 Ba2NiOsO6 S.G. P21/n I4/m P21/n I4/m Fm-3m Bond length of B-O (Å) 2.076 × 2 2.063 × 2 2.031 × 2 2.0379 × 4 2.052 × 2 2.024 × 2 2.058 × 2 2.066 × 2 2.032 × 4 2.055 × 2 2.078 × 6 Bond length of Os-O (Å) 1.934 × 2 1.936 × 2 1.929 × 2 1.9151 × 4 1.927 × 2 1.924 × 2 1.928 × 2 1.922 × 2 1.910 × 4 1.906 × 2 1.943 × 6 Bond angle of B-O-Os (deg.) 149.86 150.97 150.78 165.83 180 150.97 150.59 150.53 165.85 180 180 Tolerance factor a 0.93 0.98 0.93 0.99 1.05 BVS at B site b 2.24 2.33 2.18 2.24 2.02 BVS at Os site b 5.55 5.76 5.68 5.93 5.41 Physical properties Insulator, FIM Insulator, AFM Insulator, FIM Insulator, AFM Insulator, FM Tmag (K) 145 108, 70 175 50 100, 32 θWeiss (K) +5 -51 +27 +113 Reference 104 44,105 46,103 46 16 a Tolerance factor and the global instability index (GII) are calculated by SPuDS version 2.21.05.11. b BVS = ∑ 𝑣𝑣𝑖𝑖𝑁𝑁𝑖𝑖=1 , where 𝑣𝑣𝑖𝑖 = 𝑒𝑒(𝑅𝑅0−𝑙𝑙𝑖𝑖)/𝐵𝐵, N is the coordination number, l is the bond length, B = 0.37. 3.1.4 Properties of Os-based double perovskite oxide with A = Pb The high-pressure synthesis technique allows for the stabilization of various osmate double perovskites with lead (Pb) at the A-site, as summarized in Table 3.4. Despite having tolerance factors close to 1, these compounds do not adopt cubic or tetragonal structures. Instead, they crystallize into a monoclinic lattice structure. The application of high-pressure conditions in these cases likely inhibits the formation of competing phases, such as the pyrochlore Pb2BOsO7-δ. Additionally, a related compound, Pb2CaOsO6, has been synthesized under similar high-pressure conditions. However, it does not crystallize into the standard rock-salt double perovskite structure. Instead, it adopts a highly distorted monoclinic structure characterized by lattice parameters a = 10.0812(3) Å, b = 5.689(1) Å, c = 11.837(4) Å, and β = 125.32(2)° at 2 K. This distorted lattice structure persists even at high temperatures 39. Table 3.4: Comparison of the structural parameters and physical properties of double perovskite Pb2BOsO6 (B = Co, Ni, Zn). Pb2CoOsO6 (Room temp.) Pb2NiOsO6 (Room temp.) Pb2ZnOsO6 (T = 2 K) S.G. P21/n P21/n P21/n Bond length of B-O (Å) 1.9027 × 2 2.1084 × 2 2.2409 × 2 2.01 × 2 1.98 × 2 2.275 × 2 2.022 × 2 2.202 × 2 2.177 × 2 Bond length of Os-O (Å) 1.8258 × 2 1.8857 × 2 1.95 × 2 1.99 × 2 2.007 × 2 1.836 × 2 21 2.1119 × 2 1.841 × 2 1.878 × 2 Bond angle of B-O-Os (deg.) 172.2 168.1 145.4 179.5 175.4 147.1 158.62 159.33 156.88 Tolerance factor a 1.004 1.008 1.000 BVS at B site b 2.19 2.08 1.92 BVS at Os site b 6.05 5.91 6.06 Physical properties Metal, AFM Metal, AFM Metal, paramagnetic TN (K) 45 58 θWeiss (K) -106 -102 +214.4 Reference 18 38 39 a Tolerance factor and the global instability index (GII) are calculated by SPuDS version 2.21.05.11. b BVS = ∑ 𝑣𝑣𝑖𝑖𝑁𝑁𝑖𝑖=1 , where 𝑣𝑣𝑖𝑖 = 𝑒𝑒(𝑅𝑅0−𝑙𝑙𝑖𝑖)/𝐵𝐵, N is the coordination number, l is the bond length, B = 0.37. In most osmate double perovskite oxides, the dominant property is insulating behavior. However, osmate double perovskites with Pb at the A-site exhibit contrasting electronic properties. Compounds such as Pb2BOsO6 (B = Co, Ni, Zn) display metallic behavior down to the lowest temperatures 18,38,39. Pb2CaOsO6 undergoes a metal-insulator transition accompanied by an AFM transition 39. Antiferroelectric-like displacements of Pb from the center of the oxygen polyhedron have been observed in Pb2CaOsO6 39. While it is not uncommon for Pb2+-based perovskite insulators to exhibit lone pair electronic instability, it is rare to observe this phenomenon in a metallic phase. Below 80 K, a metal-to-insulator transition occurs in Pb2CaOsO6, accompanied by the onset of AFM order. Jacobsen et al. proposed that the metal-insulator transition in Pb2CaOsO6, driven by spin ordering, can be attributed to a Slater transition 39. Similar phase transitions with inversion symmetry breaking induced by AFM ordering have been observed in metallic Pb2CoOsO6 and Pb2NiOsO6 18,38. In both compounds, a subtle spin-driven structural transition occurs from centrosymmetry to noncentrosymmetry. This transition is analogous to type-II multiferroics, where the establishment of magnetic order leads to the emergence of ferroelectricity. The coexistence of the polar phase and metallic behavior in Pb2CoOsO6 and Pb2NiOsO6 categorizes them as polar metals. Notably, the first known example of a polar metal was discovered in LiOsO3, an osmate oxide 50. The polar phase in LiOsO3 can be induced by changes in temperature or pressure 106,107. Jiao et al. performed transport measurements on Pb2CoOsO6 under pressures up to 11 GPa and found that the AFM polar metal state observed at ambient pressure can be suppressed with increasing pressure. This suppression leads to the emergence of a new centrosymmetric AFM state above a critical pressure 108. 22 Fig. 3.5: Comparison of the crystal structures between Pb2NiOsO6 and A2NiOsO6 (A = Ca, Sr, and Ba). The structure of Pb2NiOsO6 is compared to its analogues A2NiOsO6 (A = Ca, Sr, Ba), as depicted in Fig. 3.5. As the ionic radius at the A-site of the double perovskite A2BOsO6 (A = Ca, Pb, Sr, Ba) increases, the lattice structure undergoes a transformation from monoclinic to tetragonal and eventually to cubic. With the ionic radius of Pb2+ falling between that of Ca2+ and Sr2+, Pb2NiOsO6 adopts a monoclinic lattice structure that closely resembles the A2NiOsO6 compound family. However, a notable difference in octahedral distortion can be observed when comparing the local distortions of Pb2NiOsO6 with its analogues A2NiOsO6 (A = Ca, Sr, Ba). 23 Fig. 3.6: Variations in lattice parameter, bond length and bond angle in double perovskite A2NiOsO6 (A = Ca, Pb, Sr, Ba). The data are extracted from references 16,38,46. The octahedral distortions (Δ) in the double perovskite structure can be calculated using the formula mentioned in the paper 52: ∆= 𝟏𝟏𝟔𝟔∑ (𝒅𝒅𝒊𝒊−𝒅𝒅𝒂𝒂𝒂𝒂𝒅𝒅𝒂𝒂𝒂𝒂)𝟐𝟐𝟔𝟔𝒊𝒊=𝟏𝟏 . Here, di represents the bond length of B-O and B’-O, and dav is the average bond length. The tilting angle (Φ) can be estimated from the average bond angle (θ) of B-O-B’ using the formula Φ = (180 - θ)/2. The variation of structural parameters with the A-site cation radius is depicted in Fig. 3.6. While the Φ shows a continuous change corresponding to the ionic radius of the A-site cation in the A2NiOsO6 series, there is a notable difference in the bond angles of Ni-O-Os in Pb2NiOsO6. Specifically, the bond angle of Ni-O1-Os, which is nearly aligned with the c-axis as shown in Fig. 3.5, is significantly smaller compared to the other two Ni-O2/O3-Os angles that lie approximately in the ab-plane. Moreover, in Pb2NiOsO6, both the octahedral distortion (Δ) of OsO6 and NiO6 are notably enhanced compared to A2NiOsO6 (A = Ca, Sr, Ba). A similar enhanced octahedral distortion 24 can also be observed in Pb2CoOsO6 when compared to Ca2CoOsO6 and Sr2CoOsO6. The presence of Pb2+ with a lone pair occupying the A-site appears to have a significant influence on the local distortion within the double perovskite structure. Fig. 3.7: Total and projected spin-polarized partial density of states for antiferromagnetic Pb2CoOsO6 calculated using the generalized gradient approximation 18. Reprinted with permission from [Princep, A. J., et al., Phys. Rev. B, 102 (10), 104410, 2020] Copyright (2020) by the American Physical Society. The origin of the metallic properties observed in Pb2BOsO6 (B = Co, Ni, Zn) is still not fully understood. First-principles calculations suggest that the density of states at the Fermi level is predominantly contributed by the d-electrons of the 3d element and Os in both Pb2NiOsO6 and Pb2CoOsO6 (Fig. 3.7) 18,38. This is reminiscent of the metallic phase of perovskite BiNiO3, where the presence of a lone pair on Bi3+ and the dominant contribution of the d-band of Ni at the Fermi level are also observed 109. Pb2NiOsO6 and Pb2CoOsO6, as AFM metallic oxides with a three-dimensional structure, are unique as 3d-5d mixed systems. The application of hydrostatic pressure offers the possibility to tune the bandwidth of simple perovskites, especially those consisting of only one 3d element. By measuring the electron transport and magnetic properties under pressure, valuable information can be obtained regarding the nature of the material. According to Bloch’s rule, there is a relationship between the TN and the cell volume of AFM insulators 110. TN can be enhanced by reducing the cell volume through the application of pressure, as observed in localized-electron systems such as YCrO3 and CaMnO3 111. In contrast, the application of pressure on the AFM metal CaCrO3 leads to a reduction in its TN 112,113. Jiao et al. demonstrated that the AFM metal Pb2CoOsO6 exhibits an increase in TN, as determined from the resistivity anomaly, under applied pressure 108. The behavior of Pb2CoOsO6 under pressure differs from that of AFM insulators like YCrO3 and CaMnO3, as well as the AFM metal CaCrO3. In contrast, Sr2FeOsO6, another osmate double perovskite, exhibits behavior expected for a localized Mott-insulating system, where the magnetic ordering temperature increases with increasing pressure 101. In this regard, the effect of pressure on 3d-5d mixed systems has not been extensively 25 investigated, and it appears that the combination of 3d and 5d elements in the same system poses additional challenges for understanding their behavior under pressure. 3.1.5 Properties of the Re or Os-based double perovskite with B = a non-magnetic element The B-site occupied by non-magnetic cations forms an important group in 5d double perovskite oxides, as listed in Table 3.5. Among them, there is a growing interest in certain cubic 5d double perovskite oxides that incorporate alkali or alkaline earth ions, as well as Y3+ and Zn2+ ions, at the B site. For instance, cubic Re or Os-based double perovskites with the electronic configuration 5d1 or 5d2, such as Ba2NaOsO6, Ba2BOsO6 (B = Zn, Mg, Ca), Ba2MgReO6, and Ba2YReO6, serve as promising platforms for exploring multipolar magnetism. The exploration of multipolar magnetism in these materials can provide valuable insights into the behavior of quantum magnets. On the other hand, an epitaxial film of the double perovskite Sr3OsO6 exhibits ferromagnetism at temperatures exceeding 1000 K 61, while the bulk form of the same composition is dominated by antiferromagnetism 49. The underlying reasons for such a remarkably high magnetic transition temperature observed in the double perovskite film remain a mystery and require further investigation 114. In solid materials, conventional broken symmetry phases typically involve the magnetic dipole moment of electrons. However, in certain solid systems, broken symmetry can arise from higher-order multipolar degrees of freedom. Extensive theoretical and experimental investigations have been conducted on multipolar orders in f-orbital compounds 115,116. In recent years, there has been a growing interest in exploring the occurrence of multipolar orders in 5d oxides that exhibit strong SOC 117-119. Re and Os-based cubic double perovskites are particularly significant in this category due to their high local symmetry, strong SOC, presence of localized electrons, and the weakly correlated nature of 5d metals 120-122. The multipolar order is known as the hidden order since it is generally subtle and hard to detect by traditional experimental probes. Nuclear magnetic resonance studies have experimentally confirmed that Ba2NaOsO6 with a 5d1 configuration exhibits a specific type of canted FM state 123,124. This state is characterized by the presence of two sub-lattice magnetizations, and the magnetic order is accompanied by a structural change. Interestingly, the breaking of cubic symmetry occurs prior to the onset of magnetic order 124. The exotic canted two-sublattice FM state observed in Ba2NaOsO6 is believed to be driven by the staggered quadrupolar order 125. Quadrupolar order has also been observed in another double perovskite with a 5d1 configuration, Ba2MgReO6 126. The first identified candidate for d-orbital octupolar order was found in the cubic osmate double perovskites Ba2BOsO6 (B = Zn, Mg, Ca) 121. These compounds possess a 5d2 electron configuration. In contrast to Ba2NaOsO6 and Ba2MgReO6, where a structural change precedes quadrupolar order, there is no deviation from cubic symmetry observed in Ba2BOsO6 (B = Zn, Mg, Ca) 121. Through magnetic neutron powder diffraction, inelastic neutron scattering, and high angular resolution synchrotron x-ray diffraction measurements performed on Ba2BOsO6 (B = Zn, Mg, Ca) along with theoretical calculations, it has been suggested that these 5d2 cubic perovskites exhibit ferro-octupolar order at low temperature 121,122. The multipolar order observed in cubic double perovskites is distinctively different from their electronic counterparts that crystallize in noncubic structures. For example, Sr2MgOsO6 exhibits conventional AFM ground states 53,127. The comprehensive understanding of multipolar 26 order in Re-based and Os-based cubic double perovskites is still an ongoing area of research that continues to attract increasing interest in both experimental and theoretical investigations 120,128-131. Table 3.5: Experimental data and properties of Re-based and Os-based cubic double perovskites with non-magnetic elements at the B site. Electronic configuration, compound synthesis pressure t a GII a Physical properties Tmag (K) θWeiss (K) μeff (μB) Ref. 5d0 Ba2LiReO6 AP c 1.0398 0.35824 - - - - 132 Ba2NaReO6 AP 0.9592 0.32403 - - - - 132 K2NaOsO5.5 b AP 1.0226 0.23158 Diamagnetic - - - 133 5d1 Ba2MgReO6 d AP 1.0298 0.26410 FM 18 20.8 0.496 134 Spin–orbit coupled Mott insulator, quadrupolar order (33 K), dipolar order (18 K) 33, 18 -14.6, -15.2, -11.2 0.678, 0.689, 0.673 126 Canted AFM 18 - - 120 Ba2CaReO6 AP 0.9645 0.27768 AFM 15.4 -38.8 0.744 135 AFM 16 -41.5 0.700 136 Ba2ZnReO6 AP 1.0270 0.23662 FM 11 -66 0.940 134 Insulator, canted FM 16 -3.1 0.7141 41 Ba2CdReO6 e AP 0.9788 0.17659 Insulator, AFM 4 -65.8 1.04 41 Quadrupole order (25 K), canted AFM (12 K) 25, 12 -15.3 0.720 137 Ba2LiOsO6 AP 1.0737 0.72101 AFM 8 -40.48 0.733 138 AFM, spin-flop transition 8 - - 139 AFM - -55.7 0.897 41 Ba2NaOsO6 f AP 0.9879 0.14779 FM-like order 8 -32.45 0.677 138 Mott insulator, FM 6.8 -10, -10, -13 0.602, 0.596, 0.647 140 FM 7.2 - - 139 Canted FM, quadrupolar order ~10 - - 123 Canted FM 7 -41.7 0.844 41 5d2 Ba2YReO6 g AP 0.9912 0.08291 AFM 31 -726 2.32 141 Spin freezing 50, 25 -616 1.93 142 Ordered with reduced dipole moment - - - 128 Sr2CaOsO6 AP 0.9194 0.51124 - - -198 1.68 143 Ba2CaOsO6 AP 0.9746 0.21372 AFM 51 -157 1.61 135 AFM 50 -156.2 1.640 144 Ferro-octupolar order 49 121 Ba2MgOsO6 AP 1.0414 0.37790 AFM 51 -120 1.536 145 Ferro-octupolar order 51 121 Ba2ZnOsO6 AP 1.0385 0.34785 AFM ~30 -149 1.947 145 Ferro-octupolar order 30 121 Ba2CdOsO6 AP 0.9892 0.10348 No magnetic ordering - -117.7 1.972 145 5d3 Ba2InOsO6 AP 1.0127 0.10293 Insulator, AFM 28 -155 42 Ba2ScOsO6 AP 1.0259 0.22664 Insulator, AFM 93 -590 42 Ba2YOsO6 AP 0.9858 0.12196 AFM 69.65 -717 3.93 43 6 GPa AFM 69 -571 3.52 42 27 a Tolerance factor and the global instability index (GII) are calculated by SPuDS version 2.21.05.11. b The reference suggests an oxidation state of +8 for Os in K2NaOsO5.5 133. Due to the lack of an effective ionic radius for Os8+ in a six-coordinate environment, the tolerance factor is calculated using the ionic radius data from Os7+. c AP denotes ambient pressure. d In reference 134, a Weiss temperature of -373 K was obtained by fitting the temperature range of approximately 200 to 300 K. Additionally, applying the Curie-Weiss fitting to a narrower temperature range of approximately 22 to 40 K yielded a θWeiss of 20.8 K and an μeff of 0.496 μB. The table presents three values for μeff and θWeiss for single crystal Ba2MgReO6, which were determined based on data collected with magnetic fields oriented in the [100], [110], and [111] directions 126. e The μeff and θWeiss for Ba2CdReO6 obtained by fitting the data between Tq (quadrupole order) and Tm (magnetic order) are 0.50 μB and 10.3 K 137. f The table presents three values for μeff and θWeiss for single crystal Ba2NaOsO6, which were determined based on data collected with magnetic fields oriented in the [100], [111], and [110] directions 140. The reference 123 deduced the transition temperature of around 10 K into the canted FM phase based on the nuclear magnetic resonance data. g In reference 141, the crystal structure of Ba2YReO6 is reported as a P21/n monoclinic structure. In contrast, other references listed in the table suggest that the crystal structure is a cubic double perovskite structure. 3.1.6 Other Re and Os-based double perovskite oxides In the realm of oxides, the A2BB’O6 double perovskite structure accommodates a wide variety of cations at the A and B sites, making it a large family of compounds. While this section focuses specifically on double perovskites with B’ = Re and Os, it is challenging to encompass all the compounds within this category. In previous sub-sections, several families of Re or Os-based double perovskites have been discussed in more detail due to their extensive study or growing interest in recent years. However, to provide a comprehensive research overview, we have included tables summarizing other experimentally reported Re and Os-based double perovskites in this section. The S.G. of the double perovskites listed in Table 3.6 and Table 3.7 were determined at room temperature, and for those not determined at room temperature, the temperature conditions are noted. The properties for each compound include the electronic and magnetic properties confirmed by experimental studies, excluding those solely suggested by theoretical simulations. Table 3.6: Experimentally reported Re-based double perovskite oxides. Re valence state, compound Pressure of synthesis S. G. a t b GII b Properties Tmag (K) Refs Re5+ (5d2) Sr2ScReO6 AP P21/n 0.9732 0.00012 Insulator, AFM 75 63,146 Sr2YReO6 AP P21/n 0.9350 0.00637 Spin glass 12 147 AFM with weak FM component 6 148 Sr2InReO6 AP P21/n 0.9606 0.00076 Insulator, magnetically frustrated system lacking long-range order - 149 Insulator, nonmagnetic singlet ground state 147 Sr2TbReO6 AP P21/n 0.9311 0.00739 AFM 2.6 148 Sr2DyReO6 P21/n 0.9348 0.00642 FM ordering of Dy moments 5, 93 Sr2HoReO6 P21/n 0.9371 0.00512 paramagnetic - Sr2ErReO6 P21/n 0.9359 0.00589 paramagnetic - Sr2TmReO6 P21/n 0.9382 0.00566 paramagnetic - Sr2YbReO6 P21/n 0.9415 0.00429 AFM dominant 20 Sr2LuReO6 P21/n 0.9447 0.00383 AFM with weak FM component 12 Ba2NdReO6 AP P21/n 0.9751 0.00034 AFM 100 141 28 Ba2SmReO6 P21/n 0.9741 0.00053 AFM 82 Ba2EuReO6 P21/n 0.9922 0.00004 paramagnetic - Ba2GdReO6 P21/n 0.9871 0.00019 AFM 65 Ba2TbReO6 P21/n 0.9870 0.00015 AFM 2.4, 29 Ba2DyReO6 P21/n 0.9909 0.00025 AFM 70 Ba2HoReO6 P21/n 0.9934 0.00021 AFM 27 Ba2ErReO6 P21/n 0.9922 0.00004 paramagnetic - Ba2TmReO6 P21/n 0.9945 0.00016 paramagnetic - Ba2YbReO6 P21/n 0.9981 0.00012 paramagnetic - Ba2LuReO6 P21/n AFM 33 Mn2MnReO6 c 5 GPa P21/n 0.8778/ 0.8368 0.01718/0.04379 Insulator, AFM, canted AFM ~110, ~50 35 8 GPa 109, 99 34 La2LiReO6 AP P21/n 0.9429 0.00280 Spin freezing ~50 142 Pb2MnReO6 c AP P21/n 1.0166/0.9692 0.10205/0.00022 Insulator, FIM ~100 150 C2/m 151 Pb2NiReO6 6 GPa I2/m 0.9968 0.00101 FIM, spin glass 37 52 Re6+ (5d1) Ca2MgReO6 AP P21/n 0.9187 0.00868 Canted AFM ~20 152 Ca3ReO6 AP P21/n 0.8605 0.04400 - - 153 Ca2MnReO6 d AP P21/n 0.8972 0.01689 Insulator, FM 110 63 Noncollinear magnetic structure 121 154 Ca2CoReO6 AP P21/n 0.9189 0.00833 Insulator, FM 130 63 Sr2MgReO6 e AP I4/m 0.9714 0.03071 Insulator, AFM 320 63 I4/mmm Layered AFM ~55 155 Sr2CaReO6 AP P21/n 0.9099 0.01780 Spin glass ~14 156,157 Sr2MnReO6 AP P21/n 0.9487 0.00277 Insulator, FM 120 63 FIM 120 158 canted magnetic structure 120 159 Sr2CoReO6 AP I4/m 0.9717 0.03047 Insulator, AFM 65 63 AFM 60 45 Sr2NiReO6 AP I4/m 0.9758 0.02641 Insulator, FM 18 63 30 45 Sr2ZnReO6 AP I4/m 0.9688 0.03325 Insulator, AFM 20 45,63 Ba2MnReO6 AP Fm-3m 1.0057 0.03994 Insulator, FIM 120 158 FM 113 40 Ba2CoReO6 AP Fm-3m 1.0300 0.26662 AFM 25 40 41 160 Ba2NiReO6 AP Fm-3m 1.0344 0.31028 FIM 32 40 Ba2ZnReO6 AP Fm-3m 1.0270 0.23662 Insulator, canted FM 11 134 16 41 Ba2CdReO6 AP Fm-3m 0.9788 0.17659 Insulator, AFM 4 41 Mn2CoReO6 f 8 GPa P21/n 0.8571 0.02701 Insulator, AFM 94, ~40 32 Mn2NiReO6 8 GPa P21/n (150 K) 0.8607 0.02480 Canted AFM 80, 42 33 Pb2CoReO6 8 GPa R-3 0.9926 0.00005 Insulator, AFM 16 51 Re7+ (5d0) Sr2LiReO6 g AP I4/m 0.9809 0.02180 - - 132,161 Sr2NaReO6 AP P21/n 0.9049 0.02492 - - 132 Mn2LiReO6 8 GPa P21/n 0.8652 0.02871 Weak FM 109 31 a The structures listed in the table were determined at or near room temperature according to the literature. Any structures determined at temperatures other than room temperature are indicated in the table. b Tolerance factor (t) and the global instability index (GII) were calculated using SPuDS version 2.21.05.11. 29 c Mixed valent states of Mn2+/3+ for the B-site and Re6+/5+ for B’-site were suggested in ref. 35,151. Tolerance factor and GII before the slash were calculated with R0(Mn3+) and R0(Re5+), while the latter was calculated with R0(Mn2+) and R0(Re6+). The structure of Pb2MnReO6 at room temperature was determined to be a distorted structure with a monoclinic lattice, and the lattice parameters are a = 18.2309 Å, b = 8.0359 Å, c = 5.7072 Å, and β = 108.288°. It crystallizes into a cubic double perovskite at 523 K 151. d Mixed valent states of Mn and Re were suggested in ref. 162. Tolerance factor and GII was calculated with R0(Mn2+) and R0(Re6+). e The I4/m structure was suggested in the references listed in the table, while an earlier literature reported another tetragonal space group, I4/mmm, for Sr2MgReO6 152. f Mn2CoReO6 exhibits complex magnetic properties at low temperatures, and a robust AFM ordering occurs at 94 K, as suggested by ref. 32. The presence of AFM ordering is indicated in the table. The complex magnetic properties are also observed in Mn2BReO6 (B = Mn, Fe, Ni), which are not described in detail in the table. g A cubic structure is determined by single-crystal analysis as suggested by reference 132. However, two other references conducting structure analysis based on polycrystal indicate a tetragonal structure 132,161. Table 3.7: The experimentally reported Os-based double perovskite oxides. Os valence state, compound Pressure of synthesis S. G. a t b GII b Properties Tmag (K) Refs Os4+ (5d4) - Os5+ (5d3) La2NiOsO6 AP P21/n 0.9480 0.00188 Insulator, FIM 125 163 Os5+ Ca2InOsO6 6 GPa P21/n 0.9034 0.01326 Insulator, AFM 14 55 Ca2ScOsO6 AP P21/n 0.9152 0.00894 AFM ~69 164 Sr2InOsO6 AP P21/n 0.9553 0.00116 Insulator, AFM 26 165 Sr2ScOsO6 AP P21/n 0.9678 0.00032 Insulator, AFM 92 165 Sr2YOsO6 AP P21/n 0.9300 0.00751 Insulator, AFM 53 165 Ba2NdOsO6 AP P21/n 0.9699 0.00020 Insulator, AFM 65, ~20 166 Fm-3m 0.23896 AFM 70 167 Ba2PrOsO6 AP Fm-3m 0.9578 0.32099 AFM 71 167 Ba2SmOsO6 AP Fm-3m 0.9689 0.24623 AFM 65 Ba2EuOsO6 AP Fm-3m 0.9558 0.33370 AFM 67 Ba2GdOsO6 AP Fm-3m 0.9817 0.15304 AFM 67 Ba2TbOsO6 AP Fm-3m 0.9817 0.15362 AFM 2.6 Ba2DyOsO6 AP Fm-3m 0.9856 0.12382 Paramagnetic - Ba2HoOsO6 AP Fm-3m 0.9880 0.10495 AFM 24 Ba2ErOsO6 AP Fm-3m 0.9868 0.11447 Paramagnetic - Ba2TmOsO6 AP Fm-3m 0.9891 0.09613 Paramagnetic - Ba2YbOsO6 AP Fm-3m 0.9927 0.06797 AFM 2.4 Ba2LuOsO6 AP Fm-3m 0.9960 0.04097 AFM 66 Pb2FeOsO6 8 GPa Fm-3m 1.0110 0.06712 Insulator, FIM 280 56 La2LiOsO6 AP P21/n 0.9376 0.00397 AFM 39 168 La2NaOsO6 AP P21/n 0.8662 0.05436 Canted AFM 17 169 Pr2LiOsO6 AP P21/n (150 K) 0.9172 0.01281 AFM 35 168 Pr2NaOsO6 AP P21/n 0.8473 0.07909 AFM, spin-flop transition 7 169 Nd2LiOsO6 AP P21/n 0.9199 0.00778 AFM 23 168 Nd2NaOsO6 AP P21/n 0.8498 0.07015 AFM, spin-flop transition 20, 10 169 Sm2LiOsO6 AP P21/n 0.8999 0.02003 AFM 32 168 Os6+ (5d2) Ca3OsO6 6 GPa P21/n 0.8695 0.04118 insulator, AFM 50 14 Ca2MgOsO6 6 GPa P21/n 0.9290 0.00616 insulator, spin glass 19 53 Ca2CoOsO6 AP P21/n 0.9293 0.00608 insulator, FIM 145 103,104 Sr3OsO6 6 GPa P-1 0.8881 - insulator, AFM 12 49 30 Sr2MgOsO6 6 GPa I4/m 0.9824 0.02001 insulator, AFM 110 53 Sr2CoOsO6 AP I4/m 0.9826 0.01975 insulator, AFM 108, 70 44 Sr2CuOsO6 AP I4/m 0.9885 0.01337 AFM 18 170 Os7+ (5d1) Sr2LiOsO6 6 GPa I4/m 1.0129 0.08397 AFM 12 171 AP I4/m spin glass 30 41 Sr2NaOsO6 AP P21/n 0.9320 0.01364 Insulator, canted AFM ~17 172 a The structures listed in the table were determined at or near room temperature according to the literature. Any structures determined at temperatures other than room temperature are indicated in the table. b Tolerance factor (t) and the global instability index (GII) were calculated using SPuDS version 2.21.05.11. 3.2 Ir-based double perovskite oxides 3.2.1 A2BIr4+O6 (B = a nonmagnetic element) The valence electrons in 3d transition metal oxides typically exhibit strong electron correlations, leading to the formation of the Mott insulating state, primarily characterized by the Hubbard parameter U and bandwidth W. In contrast, 5d transition metal oxides have more spatially extended 5d orbitals, resulting in relatively stronger hybridization with neighboring orbitals. This leads to a broader bandwidth and lower density of states near the Fermi level, weakening the electronic correlations. Consequently, 5d transition metal oxides are less prone to exhibiting the Mott insulator state compared to 3d transition metal oxides. However, in the case of double perovskite oxides with the general formula A2BB’O6, even when the B’ position is occupied by a 5d element, the distance between 5d elements increases when B is a different element. This creates an environment that favors the formation of a Mott insulator due to the increased separation between the 5d orbitals. The double perovskites La2MgIrO6 and La2ZnIrO6, which were first studied in 1993 173, have similar crystal structures and electron configurations. However, La2MgIrO6 exhibits AFM behavior, while La2ZnIrO6 displays weak ferromagnetism. Subsequent neutron scattering experiments have confirmed the presence of long-range AFM ordering in both compounds. Specifically, the magnetic moments in La2ZnIrO6 are canted, which explains the observed weak ferromagnetism 174. In both La2MgIrO6 and La2ZnIrO6, the SOC effect can split the three t2g orbitals in the octahedral crystal field into an upper doublet with j = 1/2 and a lower quadruplet with j = 3/2. Theoretical calculations have suggested that the inclusion of a moderate on-site Coulomb repulsion further splits the half-filled jeff = 1/2 state, resulting in a Mott insulating state with a narrow gap opening. Therefore, both La2ZnIrO6 and La2MgIrO6 are considered Mott insulators in which SOC plays a crucial role 174. Although there are small monoclinic structural distortions at the Ir4+ sites, which deviate from perfect cubic crystal fields 168,169, the face-centered cubic (FCC) Kitaev model can still be approximately applied to these materials 175,176. Similar to La2MgIrO6 and La2ZnIrO6, Ba2CeIrO6 and Sr2CeIrO6 exhibit AFM ordering at low temperatures of 17 K and 21 K, respectively. Neutron scattering results for Sr2CeIrO6 and Ba2CeIrO6 confirm the presence of A-type AFM order in these materials, which was previously observed in La2ZnIrO6 177. These findings suggest that the magnetic ground state in all four double perovskite iridates originates from a significant AFM Kitaev interaction 178, as the classical phase diagram for the FCC Heisenberg-Kitaev model with Jeff = 1/2 moments aligns with the observed A-type AFM ordered states in these compounds. 31 Double perovskite oxides, A2BIrO6 (A = Pr, Eu, Sn, Nd, Gd), are examples of double perovskite oxides containing a 4f-element on the A-site in combination with a 5d-element on the B’-site 179. Gd2ZnIrO6 and Eu2ZnIrO6 exhibit weak canted AFM order below their respective TN of 23 K and 12 K, similar to La2ZnIrO6. Sm2ZnIrO6 undergoes AFM ordering at TN = 13 K. Notably, Nd2ZnIrO6 displays complex magnetic properties with indications of magnetic transitions occurring at 16.5 K and 14.5 K, suggesting an intricate interplay between Nd3+ and Ir4+ 179. Table 3.8 presents a list of Ir-based double perovskite oxides introduced in this section. Table 3.8: Summary of space group (S.G.) and magnetic properties of A2BIr4+O6 (A = Sr, Ba, a rare earth element; B = Zn, Mg). Material S.G. Properties Tmag (K) μeff (μB/Ir) θWeiss (K) Refs. La2ZnIrO6 P21/n AFM 7.5 1.42 -3.1 174 Eu2ZnIrO6 P21/n FM-like 12 - - 179 Nd2ZnIrO6 P21/n AFM, FM-like 16.5, 14.5 5.6 -40 179 Sm2ZnIrO6 P21/n AFM 13 1.7 7 179 Gd2ZnIrO6 P21/n FM-like 24 11.3 2 179 La2MgIrO6 P21/n AFM 12 1.71 -24 174 Pr2MgIrO6 P21/n AFM 14 -23 180 Nd2MgIrO6 P21/n AFM 12 -25 180 Sm2MgIrO6 P21/n AFM 15 180 Eu2MgIrO6 P21/n AFM 10 180 Gd2MgIrO6 P21/n AFM 3 180 Sr2CeIrO6 P21/n AFM 21 178 Ba2CeIrO6 Fm-3m AFM 17 178 3.2.2 A2BIr4+O6 (B = Co, Ni) In double perovskite oxides Ln2BIr4+O6 (B = Co, Ni), there are interpenetrating magnetic sublattices consisting of Co2+/Ni2+ and Ir4+. The nearest neighbor interaction path is B-O-Ir (B = Co, Ni), and the next nearest neighbor interaction paths are B-O-O-B and Ir-O-O-Ir. Previous reports have indicated that La2NiIrO6 and La2CoIrO6 exhibit magnetic ordering at temperatures of 110 K and 130 K, respectively 181. Notably, the magnetic ordering temperatures of La2NiIrO6 and La2CoIrO6 are approximately one order of magnitude higher than that of La2ZnIrO6, suggesting that the strength of magnetic interactions in La2NiIrO6 and La2CoIrO6 is significantly stronger than in La2ZnIrO6. In La2ZnIrO6, the dominant magnetic interactions occur through Ir-O-O-Ir. However, in La2NiIrO6 and La2CoIrO6, the dominant interactions likely take place via the B-O-Ir (B = Ni, Co) path, as cation-anion-anion-cation interactions are generally one order of magnitude weaker than cation-anion-cation interactions 182. Neutron diffraction studies on La2NiIrO6 have revealed that both the Ni and Ir sublattices simultaneously undergo magnetic ordering, resulting in a non-collinear AFM structure 183. X-ray magnetic circular dichroism studies on La2CoIrO6 have shown that Ir4+ couples antiferromagnetically to the Co2+ sublattice, leading to a weak FM moment 184. These findings support the notion that the dominant magnetic interactions occur through Ni-O-Ir and Co-O-Ir in La2NiIrO6 and La2CoIrO6, respectively. When a magnetic rare-earth element is located on the A-site in Ln2BIrO6 (Ln = Pr, Nd, Sm, 32 Eu, Gd, Ho; B = Co, Ni) double perovskite oxides, it is common to observe two magnetic transitions. The transitions occurring at high temperatures (above 100 K) correspond to the simultaneous ordering of the Ni/Co and Ir sublattices. On the other hand, the transitions at low temperatures are associated with the ordering of the 4f magnetic moments in the rare-earth sublattices, as these moments have a localized nature. For example, in the case of Nd2NiIrO6, studies have shown that the Ni and Ir sublattices exhibit FIM ordering at 125 K. Upon further cooling, the Nd sublattice orders at 7 K, while the magnetic structure of the Ni and Ir sublattices transitions from FIM to AFM. This observation suggests a coupling between the 4f electrons and d electrons, indicating an interaction between them 183. It is worth noting that the ordering of the rare-earth sublattices takes place independently of the Ni/Co and Ir sublattices, although it can have an influence on the magnetic structures of the latter. Fig. 3.8: Magnetic transition temperatures and Ni‒O‒Ir bond angles of the Ln2NiIrO6 (Ln = La, Pr, Nd, Sm, Eu, Gd, Lu). Fig. 3.8 illustrates the magnetic ordering temperatures for the Ni and Ir sublattices and the Ni-O-Ir bond angles of Ln2NiIrO6 (Ln = La, Pr, Nd, Sm-Gd, Lu) 164,172,176,177. Lu2NiIrO6 exhibits the smallest Ni-O-Ir bond angle (resulting in the largest structural distortions) and the highest ordering temperature. On the other hand, La2NiIrO6 has the largest Ni-O-Ir bond angle (resulting in the least structural distortions) and the lowest ordering temperature. This clearly demonstrates the structure-property relationship for these Ir-based double perovskites: greater structural distortions lead to higher magnetic ordering temperatures. A similar correlation has also been observed in the Os-based double perovskites Ca2-xSrxFeOsO6 185,186. The FIM nature of Lu2NiIrO6 indicates that the Ni2+ and Ir4+ are antiferromagnetically coupled, suggesting that the dominant interactions are AFM via Ni2+-O-Ir4+ bonds. Since the t2g orbitals of Ni2+ are fully filled, the AFM exchange coupling between Ni2+ and Ir4+ can only occur through virtual hopping between the half-filled Ni-eg and partially filled Ir-t2g orbitals. In the cubic 33 double perovskite structure, where the Ni2+-O-Ir4+ pathway is linear, the Ni-eg and Ir-t2g orbitals are orthogonal and hopping between them is not possible. However, in the distorted double perovskites where the Ni2+-O-Ir4+ bond angles deviate significantly from 180°, hopping between Ni-eg and Ir-t2g orbitals becomes feasible 187. As the structural distortion increases, the AFM exchange coupling between the half-filled Ni-eg and partially filled Ir-t2g orbitals is expected to strengthen, which could potentially result in higher magnetic ordering temperatures. Ln2CoIrO6 (Ln = La, Eu, Tb, Ho) 184,188 exhibit a similar structural-property relationship as the Ni series of Ir double perovskites. La2CoIrO6, which has the largest A-site cation, exhibits the lowest magnetic ordering temperature. On the other hand, Ho2CoIrO6, with the smallest A-site cation, shows the highest magnetic ordering temperature (refer to Table 3.9). Table 3.9: Summary of space group (S.G.) and magnetic properties of Ln2BIr4+O6 (Ln = a rare earth element; B = Ni, Co). Material S.G. Properties Tmag (K) μeff (μB/Ir) θWeiss (K) Refs. La2CoIrO6 P21/n FIM 90 4.5 36 184 Eu2CoIrO6 P21/n 105 5.5 -5 188 Tb2CoIrO6 P21/n 117, 10 14.7 -7 188 Ho2CoIrO6 P21/n 123, 13 15.9 -3 188 La2NiIrO6 P21/n AFM 75 3.28 0.35 181 Pr2NiIrO6 P21/n FM 105, 4 4.84 183 Nd2NiIrO6 P21/n FM 125, 7 6.19 183 Sm2NiIrO6 P21/n FM 152 183 Eu2NiIrO6 P21/n FM 162 183 Gd2NiIrO6 P21/n FM 170 11.35 183 Lu2NiIrO6 P21/n FM 207 3.47 -37 189 3.2.3 A2BIr5+O6 (B = a nonmagnetic element) Ir, in its pentavalent state, is characterized by a 5d4 electronic configuration. The strong SOC present in these systems causes the splitting of the three t2g orbitals in the octahedral crystal field into an upper doublet with total angular momentum j = 1/2 and a lower quadruplet with j = 3/2 190. In the case of the tetravalent iridate Sr2IrO4 (Ir4+: 5d5), the ground state is attributed to the SOC-assisted Mott-insulating state with Jeff = 1/2 190. When there are four 5d electrons occupying the lower quadruplet, the ground state for Ir4+ is expected to have j = 0. However, the observation of long-range magnetic orders in Ir5+ (5d4) double perovskite oxides, such as Sr2YIrO6 and Ba2YIrO6, with reported μeff of 0.91 μB/Ir and 1.44 μB/Ir, respectively, raises questions regarding the ground state of these 5d4 oxides 183,184. These findings have been met with challenges from other studies reporting the absence of magnetic order in Ba2YIrO6 191 and Sr2YIrO6 192 down to temperatures as low as ~430 mK. Investigations on A2YIrO6 (A = Sr, Ba) and other Ir5+ double perovskite oxides generally reveal weak paramagnetic behavior with small μeff values ranging from 0.19 μB/Ir to 0.63 μB/Ir (as indicated in Table 3.10). These values are significantly lower than the theoretical spin-only value of μeff = 2.83 μB/Ir, highlighting the dominance of SOC in determining the ground state of these systems. The origin of these finite magnetic moments in Ir5+ oxides remains uncertain. One proposed 34 explanation by Cao et al. is the quenching of the J = 0 state for Ir5+ due to distortion of the IrO6 octahedra in Sr2YIrO6 193. However, this scenario fails to explain the observed paramagnetic moment in the cubic Ba2YIrO6, which lacks structural distortion. Studies on Ba2-xSrxYIrO6 have also found no correlation between the μeff values and the degree of structural distortions 194,195. The presence of magnetic impurities has been suggested in studies on Sr2YIrO6 192 and Ba2YIrO6 196. Fuchs et al. confirmed the existence of Ir4+ and Ir6+ magnetic defects, which are responsible for the magnetism observed in Ba2YIrO6 197. Antisite disorder in double perovskites has also been proposed to play a significant role 198,199. Laguna-Marco et al. suggest that the Ir4+ and Ir6+ magnetic impurities may be located in regions of antisite disorder 199. The condensation of J = 1 triplon excitations of 5d4 oxides is also considered as a possible source for the observed magnetic moments 193,194. Chen et al. propose that the condensation is unlikely in Sr2YIrO6 and Ba2YIrO6 with ideal crystal structures, but the presence of antisite disorder between Y3+ and Ir5+ can break down local nonmagnetic singlets 198. Recent studies on A2BIrO6 (A = Ba, Sr; B = Lu, Sc) also support the J = 0 ground state for these Ir5+ oxides and indicate that the magnetic signals arise from extrinsic sources, such as magnetic impurities and antisite disorder 200. Table 3.10: Summary of space group (S.G.) and magnetic properties of Ir5+ oxides with double perovskite structures. Material S.G. χ0 (10-4 emu mol-1 Oe-1) μeff (μB/Ir) θWeiss (K) Refs. Ba2YIrO6 Fm-3m - 0.3 -10 201 Ba2YIrO6 Fm-3m 4.8 0.63 -5 198 Ba2YIrO6 Fm-3m 5.4 0.52 -4 198 Ba2YIrO6 Fm-3m 5.4 0.50 -8 198 Ba2YIrO6 Fm-3m 5.83 0.44 -8.9 191 Ba2YIrO6 Fm-3m - 0.31 - 196 Ba2YIrO6 Fm-3m - 0.48 -16 197 Ba2YIrO6 Fm-3m -3.9 1.44 -149 202 Ba1.26Sr0.74YIrO6 Fm-3m 4.4 0.64 -18 202 Ba2-xSrxYIrO6 Fm-3m - 0.47 - 194 Sr2YIrO6 P21/n - 0.91 -229 193 Sr2YIrO6 P21/n 5.90 0.21 -2.8 192 Sr2YIrO6 P21/n - 0.3 - 199 Sr1.6Ca0.4YIrO6 P21/n - 0.6 - 199 Sr2LuIrO6 P21/n 5.49 0.27 -2.55 200 Ba2LuIrO6 Fm-3m 4.98 0.42 -13.2 200 Sr2ScIrO6 P21/n 5.43 0.32 -10.7 200 Ba2ScIrO6 Fm-3m 5.10 0.48 -18.7 200 Bi2NaIrO 6 P21/n 6.3 0.19 -6.8 203 LaSrMgIrO6 P21/n 3.5 0.61 7 204 LaSrZnIrO6 P21/n 3.9 0.46 1 204 3.2.4 A2BIr6+O6 (A = Sr, Ba; B = Ca, Mg, Zn, Cu, Ni) 35 Ir6+ (5d3) in an octahedral coordination typically requires high oxygen pressure or high-pressure conditions to stabilize in a perovskite structure (as shown in Table 3.11). This is likely the reason why there are fewer reported Ir6+-based double perovskite oxides compared to their Ir5+ and Ir4+ counterparts. Double perovskite oxides, such as Sr2BIrO6 (B = Ca, Mg, Zn) 205,206, which contain a single Ir6+-magnetic sublattice, exhibit AFM order. This observation is consistent with the behavior observed in double perovskites containing single Os5+-magnetic sublattices, where all of them exhibit AFM ordering 207. Comparing to double perovskites with a single Ir4+ magnetic sublattice (with ordering temperatures TN = 7-12 K), Sr2BIrO6 (B = Ca, Mg, Zn) exhibit significantly higher magnetic ordering temperatures (TN = 46-74 K). Despite the magnetic interactions occurring via the Ir-O-O-Ir pathway, the observed Weiss temperatures in Sr2BIrO6 (B = Ca, Mg, Zn) are relatively large (around -363 to -430 K), indicating a strong AFM coupling between Ir6+-O-O-Ir6+. Double perovskite oxides containing both Ni2+ and Ir6+ ions have generated significant interest in the scientific community. According to the Goodenough-Kanamori rules, double perovskite oxides with d8-d3 electronic configurations are expected to exhibit FM behavior 182. Consistent with this expectation, the d8-d3 double perovskite oxide La2NiMnO6 does indeed exhibit a FM ground state 208. However, the compounds Sr2NiIrO6 and Ba2NiIrO6 display AFM ground states. In Sr2NiIrO6 and Ba2NiIrO6, there exist nearest neighbor Ni2+−O−Ir6+ interactions, as well as next nearest neighbor Ni2+−O−O−Ni2+ and Ir6+−O−O−Ir6+ interactions. Theoretical calculations on Sr2NiIrO6 suggest that the next nearest neighbor Ir6+−O−O−Ir6+ interactions are AFM and stronger than the next nearest FM Ni2+−O−Ir6+ interactions, leading to an overall AFM ground state 209. This explains the observed AFM behavior in Sr2NiIrO6 and Ba2NiIrO6, which is contrary to the simple expectation based on the Goodenough-Kanamori rules. In contrast to Sr2NiIrO6, the AFM state of Ba2NiIrO6 is not as robust. Despite exhibiting AFM ordering at 51 K, the positive value of θWeiss indicates that FM interactions are dominant in Ba2NiIrO6. At low temperatures, when an external magnetic field is applied, Ba2NiIrO6 undergoes a field-induced spin-flop transition, transitioning from the AFM state to a state that is near FM 210. This suggests that there is a strong competition between FM and AFM interactions in Ba2NiIrO6. Table 3.11: Summary of space group (S.G.), synthetic pressure, and magnetic properties of Ir6+ oxides with double perovskite structures. Material S.G. Synthetic pressure Properties Tmag (K) μeff (μB/Ir) θWeiss (K) Refs. Sr2CaIrO6 P21/n 20 MPa (O2) AFM 58 3.43 -363 205 Sr2MgIrO6 P21/n 20 MPa (O2) AFM 74 2.12 -418 205 Sr2ZnIrO6 P21/n 20 MPa (O2) AFM 46 3.82 -430 206 Ba2CaIrO6 Cubic 6 GPa - 211 Ba2SrIrO6 Rhombohedral 60 MPa - 211 Ba2ZnIrO6 Cubic 7 GPa - 211 BaLaLiIrO6 Cubic 7.5 GPa - 211 Sr2CuIrO6 I4/m 4 GPa AFM 15 4.24 -374 212 Sr2NiIrO6 P21/n 20 MPa (O2) AFM 58 206 Ba2NiIrO6 Fm-3m 8 GPa AFM 51 4.67 80 210 36 4. Discussion and prospects The A2BB’O6 double perovskite oxides constitute a vast family of compounds, facilitated by the inherent flexibility of the double perovskite structure. The presence of 5d electrons at the B’ site has generated substantial interest, driven by the profound influence of relativistic effects. The primary focus of this review paper is on three categories of 5d-electron oxides (Ir, Os, and Re) that crystallize into the rock-salt type double perovskite structure. With respect to synthesis of materials, high-pressure and high-temperature technique has demonstrated its effectiveness in broadening the compound family of A2BB’O6 (B’ = Re, Os, and Ir) double perovskite oxides. On one hand, the elevated pressure conditions contribute to stabilizing rock-salt type double perovskite structures, even when the tolerance factor exceeds 1. Furthermore, it facilitates the incorporation of Mn2+ or Pb2+ into the A site of the double perovskite structure. A list of double perovskite oxides A2BB’O6, synthesized under high pressure, is provided in Table 2.1. The achievement of material preparation provides a solid foundation for delving deeper into the physical properties exhibited by double perovskite oxides involving 5d electrons. This section consolidates various experimentally observed properties of A2BB’O6 (B’ = Re, Os, and Ir) double perovskite oxides and outlines the prospects into the following points. (1) Remarkable high-temperature FIM compounds, characterized by exceptionally high Curie temperatures, have been found within the categories of Re-based and Os-based double perovskite oxides as tabulated in Table 4.1. The specific electronic configurations of Cr3+ (3d3) and Fe3+ (3d5) play pivotal roles in facilitating robust magnetic interactions, resulting in the emergence of high-TC FIM within the A2BB’O6 (B = Cr, Fe; B’ = Re, Os) double perovskite compounds. In addition to their high-TC FIM properties, Re-based and Os-based double perovskite oxides, demonstrate a diverse range of electron transport characteristics. The A2FeReO6 compound exhibits a range of electron transport behaviors, spanning from insulating to metal-insulator transitions and half-metallicity. Strikingly, Sr2CrOsO6 boasts the highest TC among bulk double perovskite oxides, soaring up to 725 K. A comprehensive understanding of electron transport and magnetic mechanisms in Sr2CrOsO6 and its electronic analogues Sr2CrMO6 (M = Ta, W, Re) is crucial to unraveling the metal-insulator transition in Mott-insulating systems. Such understanding necessitates further exploration through both experimental and theoretical approaches. Table 4.1: High-TC ferrimagnetic double perovskite A2BB’O6 (B’ = Re or Os). Cr-Re double perovskite Compound Ca2CrReO6 Sr2CrReO6 TC (K) 360 635 Reference 63 13,62,63 Fe-Re double perovskite Compound Ca2FeReO6 Sr2FeReO6 Ba2FeReO6 Mn2FeReO6 Pb2FeReO6 TC (K) 525 400 315 520 420 Reference 62-65 63,66 64,67,68 36,37 69 Cr-Os and Fe-Os double perovskite Compound Ca2CrOsO6 Sr2CrOsO6 Ca2FeOsO6 TC (K) 490 725 320 Reference 70 70 15,71 (2) The magnetic properties and ordering temperatures of double perovskite oxides are significantly influenced by their crystal structures. The evolution of magnetism in osmate double 37 perovskite oxides, under the influence of structural changes and A-site elements, has been elucidated through a discussion of A2BOsO6 (A = Ca, Sr, Ba; B = Fe, Co, Ni). In these 3d-5d double perovskite oxides as shown in Table 4.2, the competition between the nearest neighbor B-O-Os AFM coupling and the long-range superexchange interaction of B-O-Os-O-B results in the complexity in their magnetic ground state. The bent B-O-Os bonds in monoclinic structure may suppress the long-range superexchange interaction, favoring the dominance of B-O-Os AFM coupling. This could explain why monoclinic Ca2BOsO6 (B = Fe, Co, Ni) exhibit ferrimagnetic properties, while tetragonal Sr2BOsO6 (B = Fe, Co, Ni) are antiferromagnetic. Additionally, the FM interaction also plays a role in the magnetism of Sr2NiOsO6, as evidenced by its positive θWeiss. The FM interaction is even more pronounced in the cubic double perovskite Ba2NiOsO6, as indicated by the increase in θWeiss from 27 K to 113 K. This robust FM interaction leads to FM ordering in Ba2NiOsO6 above 100 K. Ba2NiOsO6 stands out as a ferromagnetic insulator. Table 4.2: The structure and physical properties of double perovskite A2BOsO6 (B = Fe, Co, Ni). Fe-Os double perovskite Compound Ca2FeOsO6 SrCaFeOsO6 Sr2FeOsO6 S.G. P21/n P21/n (100 K) I4/m Physical properties Insulator, FIM FIM Insulator, AFM Tmag (K) 320 210 140, 67 θWeiss (K) +80 or +24 Reference 15,71 71 71,85,97 Co-Os double perovskite Compound Ca2CoOsO6 Sr2CoOsO6 S.G. P21/n I4/m Physical properties Insulator, FIM Insulator, AFM Tmag (K) 145 108, 70 θWeiss (K) +5 -51 Reference 104 44,105 Ni-Os double perovskite Compound Ca2NiOsO6 Sr2NiOsO6 Ba2NiOsO6 S.G. P21/n I4/m Fm-3m Physical properties Insulator, FIM Insulator, AFM Insulator, FM Tmag (K) 175 50 100 and 32 θWeiss (K) +27 +113 Reference 46,103 46 16 A clear correlation emerges between the magnetic ordering temperature and the degree of structural distortion in Ir-based double perovskite oxides. The relationship is demonstrated in compounds Ln2NiIrO6 (Ln = La, Pr, Nd, Sm-Gd) and Ln2CoIrO6, where enhanced structural distortions correspond to higher magnetic ordering temperatures, as illustrated in Fig. 3.8 and Table 3.9. (3) The synthesis of double perovskites with Pb at the A-site is achievable through the application of high-pressure and high-temperature condition. Three osmate double perovskite Pb2BOsO6 (B = Co, Ni, Zn) has been reported. Intriguingly, the inversion symmetry breaking induced by AFM ordering is observed in metallic Pb2CoOsO6 and Pb2NiOsO6. Further investigation is required to elucidate the origin of the metallic properties observed in Pb2BOsO6 (B = Co, Ni, Zn). 38 These Pb2BOsO6 compounds provide an intriguing platform for exploring the concept of a ferroelectric metal, challenging the conventional notion that most ferroelectrics are insulators. Beyond theoretical considerations, the practical applications of polar metals are noteworthy, as they hold the potential for developing nano-scaled capacitors. To comprehend the metallicity in Pb2BOsO6 (B = Co, Ni, Zn), exploring the influence of pressure on the physical properties of these compounds could offer further insights into their intrinsic nature. However, the incorporation of both 3d and 5d elements within the same system adds additional complexities when examining their behavior under pressure. This emphasizes the necessity for ongoing future investigations to elucidate these intricate phenomena. (4) The increasing interest in cubic 5d double perovskite oxides, which incorporate non-magnetic elements at the B site, is triggered by the quest to explore multipolar magnetism— a promising candidate for advancing quantum magnets. The potential for multipolar magnetism in these compounds arises from their distinctive features, such as robust SOC, significant separation between magnetic octahedra, and cubic symmetry. A thorough exploration of the multipolar characteristics of 5d cubic double perovskite oxides is still ongoing and necessitates additional dedicated research efforts. Table 4.3: Re-based and Os-based cubic double perovskite with potential for multipolar magnetism Compound Magnetism Tmag (K) θWeiss (K) μeff (μB) Ref. Ba2CdReO6 Quadrupole order (25 K), canted AFM (12 K) 25, 12 -15.3 0.720 137 Ba2NaOsO6 Canted FM, quadrupolar order ~10 123 Ba2CaOsO6 Ferro-octupolar order 49 121 Ba2MgOsO6 Ferro-octupolar order 51 121 Ba2ZnOsO6 Ferro-octupolar order 30 121 The fundamental research on the bulk form of 5d double perovskite, encompassing synthesis, crystal structure, and physical properties, lays the groundwork for advancing potential applications within this category of materials. Due to the diverse magnetic and electrical features inherent in 5d double perovskite oxides, numerous promising applications are anticipated to emerge, including spintronic devices, nonvolatile data memory devices, electrocatalysts, magnetic field sensors, nano-scaled capacitors, and field-effect transistors. The FIM double perovskite with a high magnetic transition temperature shows promise for utilization in spintronic devices as electrodes within magnetic tunnel junctions (MTJ). This potential stems from its advantageous low-field tunneling magnetoresistance effect. The fabrication of MTJ devices based on double perovskite Sr2FeMoO6 has been reported 213-215. However, further exploration of devices based on 5d double perovskites, exemplified by A2FeReO6, is still needed. FM or FIM insulators represent another category of materials with promising applications in spintronic devices. For instance, spin-filtering devices require FM or FIM insulators as tunnel barriers 216. The rock-salt double perovskite Ba2NiOsO6 is identified as a FM insulator, while a range of FIM insulators has been extensively discovered in Re, Os, Ir-based double perovskite oxides. These compounds offer potential materials for the future development of spin-filtering devices. Additionally, Ir-based double perovskite oxides, such as Ba2LnIrO6 (Ln = Y, La, Ce, Pr, Nd, Tb), have been reported for their efficacy as highly active oxygen-evolving catalysts in acid media. Notably, these Ir-based double perovskite 39 oxides demonstrate a more cost-effective alternative compared to conventional catalyst IrO2 217. In conclusion, the 5d transition metal oxides differ from their 3d or 4d by featuring more spatially extended 5d orbitals, resulting in relatively stronger hybridization with neighboring orbitals. Consequently, they possess a broader bandwidth and lower density of states near the Fermi level, leading to a reduction in electronic correlations. This unique characteristic of 5d transition metal elements, coupled with the inter-element spacing in the double perovskite structure, distinguishes 5d double perovskite oxides from their 3d counterparts. A notable example that highlights the disparity between 3d and 5d oxides is the analysis of magnetic properties using the Goodenough-Kanamori rules. La2NiMnO6, a 3d8-3d3 double perovskite oxide, demonstrates a FM ground state in line with the expectations of Goodenough-Kanamori rules. Conversely, Sr2NiIrO6 and Ba2NiIrO6, featuring a 3d8-5d3 configuration, exhibit an AFM ground state. In the solid solution Sr2Cr0.5Ni0.5OsO6, the FM exchange interaction of the 3d8-5d3 configuration (Ni2+-O-Os5+) is more robust than that of the 3d8-3d3 configuration (Ni2+-O-Cr3+). These findings collectively indicate the pivotal role of the 5d orbital in determining the competition of different virtual hopping routes. The question of how to deduce magnetic ground states from the classical Goodenough-Kanamori rules for 5d transition metal oxides remains intriguing and holds significance for the scientific community. In terms of practical applications, the 5d double perovskite oxides exhibit a wide range of physical properties, including high-TC FIM, half-metallicity, high-TC FIM, insulating FM, polar ferroelectrics, and multipolar magnetism. These properties hold great promise for spintronic device and advancing quantum materials. 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