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## Creator

[Hiroaki HAYASHI](https://orcid.org/0000-0001-7787-9082), [Xun KANG](https://orcid.org/0000-0003-4364-6218), [Alexei BELIK](https://orcid.org/0000-0001-9031-2355), Hiroyuki K. YOSHIDA, [KAZUNARI YAMAURA](https://orcid.org/0000-0003-0390-8244)

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[High-pressure synthesis and magnetic properties of Gd2Rh3Al9 with a distorted honeycomb lattice](https://mdr.nims.go.jp/datasets/2cb79e98-8edc-47ea-993e-6e8c44d64e89)

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1 High-pressure synthesis and magnetic properties of Gd2Rh3Al9 with a distorted honeycomb lattice   Hiroaki HAYASHI,1,2,* Xun KANG,1,2 Alexei BELIK,1 Hiroyuki K. YOSHIDA,3  and  Kazunari YAMAURA 1,2  1 Research Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan 2 Graduate School of Chemical Sciences and Engineering, Hokkaido University, Sapporo, Hokkaido 060-8628, Japan 3 Department of Physics, Faculty of Science, Hokkaido University, Sapporo, Hokkaido 060-0810, Japan           * Corresponding author.  Hiroaki HAYASHI Quantum Solid State Materials Group Research Center for Materials Nanoarchitectonics (MANA) National Institute for Materials Science 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan  E-mail: Hayashi.hiroaki@nims.go.jp   2 Abstract:  This study focuses on exploring new Gd-based intermetallic compounds with honeycomb structures to elucidate intriguing magnetic phenomena, particularly the presence of magnetic skyrmions. The compound Gd2Rh3Al9, synthesized via high-temperature and high-pressure methods, exhibits an orthorhombic structure characterized by a distorted Gd-honeycomb network. Comprehensive investigations of its temperature-dependent behavior in polycrystalline samples reveal sequential antiferromagnetic transitions occurring at T1 = 13.6 K and T2 = 4.1 K. These transitions arise from the antiferromagnetic interaction between the magnetic moments of Gd3+ (S = 7/2) situated within the distorted honeycomb layer. Despite not observing a skyrmion phase in this compound, the data provide valuable insights into the complex behavior of Gd-based intermetallic compounds and their potential as hosts for novel magnetic phases. Further research, particularly using single crystals, is needed to explore the possibility of forming a skyrmion phase in this compound.   Keywords:  Gd2Rh3Al9, Intermetallic compounds, High-pressure synthesis, Magnetic skyrmion    3 1. Introduction  The magnetic properties of 4f electron systems are often attributed to the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, arising from the coupling between localized 4f-electron spins and the spin polarization of conduction electrons. In Gd-based intermetallic compounds, Gd3+ ions possess no orbital moments, leading to the absence of a crystalline electric field, and thus, an expectation of isotropic RKKY interactions. However, these compounds can still exhibit magnetic anisotropy, attributed to either permissible single ion anisotropy or contributions from magnetic dipole interactions [1]. This anisotropy results in a diverse range of magnetic structures, such as helical, spiral, and conical arrangements [2–4]. A particularly intriguing phenomenon is the formation of topologically stable magnetic skyrmions, which are distinguished by their unique spin textures.  Recent theoretical studies have significantly expanded our understanding of magnetic skyrmions. These studies have shown that skyrmions can exist not only in systems lacking inversion symmetry, as predominantly observed previously, but also in systems with inversion symmetry [5–9]. Additionally, a novel stabilization mechanism for magnetic skyrmions in inversion symmetric structures has been proposed [10–12]. This mechanism is distinct from conventional ones as it does not rely on the interplay between ferromagnetic exchange interactions and the Dzyaloshinski-Moriya interaction, which are typically considered in skyrmion formation [13–15].   Significantly, the majority of magnetic skyrmions recently discovered in material systems with inversion symmetry are found in layered compounds [5,6,13–18]. This is because multiple propagation vectors are energetically equivalent and become degenerate due to rotational operations. For instance, the single-Q magnetic state in Gd2PdSi3 [5,6,13,15,18] and Gd3Ru4Al12 [6,14,16–18] exhibits triple degeneracy on a triangular lattice, which facilitates the formation of triangular skyrmion lattices. Similarly, in GdRu2Si2 [7,8,19–21], square skyrmion lattices emerge due to quadruple degeneracy on the square lattice. Consequently, multi-Q states demonstrate enhanced stability in lattices with high rotational symmetry.    While the high rotational symmetry of layered structures suggests the stabilization of skyrmion lattices, skyrmion lattices have also been observed in distorted lattices. For example, tetragonal EuAl4 exhibits a structural transition to an orthorhombic lattice at low temperatures. This transition results in Eu2+ layers breaking their four-fold rotational symmetry, yet a rhombic skyrmion lattice still emerges [9]. Additionally, theoretical studies have been conducted on the effects of orthorhombic distortion on skyrmion stabilization [22]. Experimental verification is needed to support these theoretical findings.   In this study, our emphasis lies in the quest for intermetallic compounds featuring  distorted crystal structures, aiming to uncover potential magnetic skyrmions. A notably auspicious candidate in this context is a Gd-based intermetallic compound of Y2Co3Ga9-type, wherein Gd takes 4 the place of Y, existing within a subtly distorted honeycomb lattice. This suggests its viability as a host material for magnetic skyrmions [23–25]. As a stride towards this objective, we synthesized Gd2Rh3Al9 by substituting Rh for Co and Al for Ga. This paper provides an account of the synthesis of this Gd2Rh3Al9 compound of Y2Co3Ga9-type, detailing its crystal structure, essential magnetic properties, and electrical conduction behavior. The findings provide insights into the characteristics of this compound and its potential as a platform for investigating distinct magnetic states.   2. Experimental  Polycrystals and single crystals of Gd2Rh3Al9 were synthesized using the Al self-flux method under high-pressure and high-temperature conditions. The raw materials, Gd, Rh, and Al, were combined in a molar ratio of 2:3:9.9 and encapsulated within a BN capsule. This assembly was then enclosed in an outer capsule made of Ta. The entire capsule arrangement was placed within a multi-anvil high-pressure apparatus (CTF-MA1500P; C&T Factory Co., Ltd., Tokyo, Japan) and subjected to heating at 1600 °C for 1 hour. Subsequently, a gradual cooling process occurred over 2 hours, reaching 900 °C, while maintaining a pressure of 6 GPa.   Following the heating steps, rapid cooling procedures brought down the capsule’s temperature to below 100 °C in less than 30 seconds. Subsequently, the pressure was methodically released over a 2-hour period. The resulting product comprised gleaming grey crystals clustered at the lowermost section of the BN capsule, alongside a polycrystalline segment that formed in the major region of the sample. The crystals from the former category underwent physical fragmentation, yielding minute crystals akin to single domains, with dimensions not exceeding 0.2 mm (Fig. 1a). Maintaining high-pressure conditions was essential in this synthesis. Without such conditions, achieving the desired chemical phase would not have been possible.   Crystallographic data were obtained from a carefully selected crystal, which had been polished and cleaned to eliminate any potential residue of Al flux. These data were analyzed using a Rigaku XtaLab mini II diffractometer, which employed Mo Kα radiation. The crystal structure was initially elucidated using the dual-space algorithm approach of SHELXT [26], followed by further refinement through a full-matrix least-squares method using SHELXL. This refinement process was facilitated by the Olex graphical user interface. The detailed results derived from this comprehensive analysis are thoroughly documented in Tables I and II.   Additionally, we conducted Scanning Electron Microscope-Energy Dispersive X-ray Spectroscopy (SEM-EDX) measurements on a polished surface of the selected specimen, mounted on carbon tape. This analysis, performed using a TESCAN Vega-e SBU scanning electron microscope equipped with EDS and operating at an accelerating voltage of 15 kV, yielded the elemental ratio Gd: Rh: Al = 1.73(4): 3.10(4): 9.17(5). These results indicate that the ratio of Gd is 5 slightly lower than the stoichiometry of Gd2Rh3Al9, as further detailed in the Supporting Information. However, we believe this discrepancy is more likely attributable to instrumental precision issues rather than a significant deviation from the intended stoichiometry.   Magnetic susceptibility (χ) and isothermal magnetization (M) measurements were carried out across a temperature range spanning from 2 K to 300 K, employing magnetic fields up to 70 kOe. These analyses were performed using a SQUID magnetometer MPMS3 (Quantum Design, Inc.). To assess specific heat capacity (Cp) and direct current electrical resistivity (ρ), we employed a relaxation method and a four-probe technique, respectively. These experimental procedures were conducted utilizing a PPMS (Quantum Design Inc.).   It is crucial to note that the limited size of the single-domain-like crystals made it infeasible to perform assessments of physical properties along specific crystal directions using our measurement apparatus. Therefore, except for the structural study, all other measurements were conducted on polycrystalline samples. Powder X-ray diffraction (XRD) analysis, the pattern of which is provided in the Supporting Information, identified a small amount of RhO2 as an impurity in the polycrystalline sample. However, given that RhO2 is nonmagnetic and exhibits metallic electrical conductivity within our measurement temperature range, we concluded that the intrinsic properties of Gd2Rh3Al9 are not significantly affected by the presence of RhO2.    Fig. 1: (a) Photograph depicting a Gd2Rh3Al9 sample synthesized under high pressure. The dotted ellipse delineates a clustered area of single crystals formed at the bottom of the BN capsule. Adjacent to the sample are crystal fragments detached from this area. The region above the dotted 5 mmGdGd RhRhAlbacba(a) (b)(c)4.227 Å4.462 Å4.291 Å4.429 Å4.342 Å4.472 Å6 area is polycrystalline. (b) Schematic representation of the crystal structure of Gd2Rh3Al9, displaying its orthorhombic structure (Cmcm). (c) View of the Gd-honeycomb lattice and Rh-triangular lattice from the c-axis direction. The numbers indicate interatomic distances, revealing slight distortions from the ideal lattice.  Table I: Crystallographic parameters and refinement details of a single crystal of Gd2Rh3Al9 Empirical formula  Gd2Rh3Al9 Formula weight  866.05 Temperature  293(2) K Wavelength  0.71073 Å (Mo Kα) Crystal system  Orthorhombic Space group  Cmcm Unit cell dimensions a = 13.0538(4) Å, b = 7.6455(3), c = 9.5117(3) Å Volume 949.29(6) Å3 Z 4 Density (calculated) 6.060 g cm-3 Absorption coefficient 19.649 mm-1 F000 1520 Crystal size 0.066 × 0.056 × 0.024 mm3 2θ for data collection 3.0710 – 30.4550° Index ranges -16 ≤ h ≤ 18, -10 ≤ k ≤ 10, -13 ≤ l ≤ 13 Reflections collected 7294 Independent reflections 793 [R(int) = 0.0313] Completeness to θ = 25.242° 100%  Absorption correction multi-scan Max. and min. transmission 1.000 and 0.738 Data/restraints/parameters 793/0/42 Goodness-of-fit on F2 1.064 Final R indices [I >2σ(I)] R1 = 0.0147, wR2 = 0.0285 R indices (all data) R1 = 0.0178, wR2 = 0.0291 Extinction coefficient 0.00068(3) Largest diff. peak and hole 1.088 and –0.721 e Å-3    7 Table II: Atomic coordinates and equivalent isotropic displacement parameters (Ueq, 10-3 Å2) and anisotropic displacement parameters (Uij; 10-3 Å2) as measured by X-ray diffraction on a single-crystal Gd2Rh3Al9 at 293 K.  Site WP a Occp. x y z Ueq b Gd 8g 1 0.65998(2) 0.83145(2) 1/4 5.69(6) Rh1 8e 1 0.67087(2) 1/2 1/2 4.55(7) Rh2 4b 1 1/2 0 1/2 4.58(8) Al1 8f 1 1/2 -0.1279(2) 0.0067(3) 6.7(3) Al2 8g 1 0.60687(9) 0.44226(14) 1/4 7.2(2) Al3 16h 1 0.83185(6) 0.66700(11) 0.42572(9) 6.24(16) Al4 8f 1 1/2 0.33228(14) 0.54338(12) 8.6(2) Site U11 U22 U33 U23 U13 U12 Gd 6.00(10)  5.95(9) 5.12(8)  0 0  0.51(7) Rh1 3.76(15)  5.11(14) 4.77(13)  -0.37(11) 0  0 Rh2 4.44(19) 4.56(18) 4.73(16)  0.89(15) 0  0 Al1 4.5(8) 9.1(8) 6.5(7) 0 0 0 Al2 7.5(6) 8.2(5) 5.9(5) 0 0 -1.1(4) Al3 5.2(4) 6.9(4) 6.6(3) -0.5(3) 0.5(3) -0.3(3) Al4 4.2(6) 6.1(5) 15.6(5) 0.1(5) 0 0 a Wyckoff positions b Ueq is defined as one third of the trace of the orthogonalized Uij tensor. The anisotropic displacement factor exponent takes the form -2π2[ h2a*2U11 + ... + 2hka*b*U12].  3. Results and Discussions  The crystal structure of Gd2Rh3Al9 was confirmed by XRD analysis to possess a Y2Co3Ga9-type structure (Cmcm, #63), akin to Gd2Co3Al9 [25]. The Gd-honeycomb layers are aligned along the c-axis (Fig. 1b). Within the intralayer structure, the hexagons constituting the honeycomb network display subtle contractions along the a-axis. These hexagons are comprised of edges with two distinct bond lengths, measuring 4.227 Å and 4.429 Å, respectively (Fig. 1c, left side). Similarly, the triangles formed by Rh in the subsequent layers exhibit distortions, encompassing four isosceles triangles and eight non-equilateral triangles within the unit cell (Fig. 1c, right side). These minor deviations may stem from the overall structure of the orthorhombic crystal, which exhibits a slight departure from trigonal or hexagonal symmetry.  8  Fig. 2: (a) Temperature dependence of χ and 1/χ under H = 1 kOe. The solid red line represents the Curie-Weiss fit for the data above 50 K. (b) χ below 20 K under several magnetic fields ranging from 100 Oe to 70 kOe. Arrows and triangular symbols indicate the anomalies at T1 and T2, respectively.    The temperature-dependent behavior of χ under H = 1 kOe is depicted in Fig. 2a. The inverse of χ conforms well to the Curie-Weiss law, represented by 1/χ = (T - θW)/C, for temperatures exceeding 50 K. The Curie constant, C, is calculated to be 7.973(5) emu K mol⁻¹. The corresponding effective moment, peff = 7.984(2) μB, closely aligns with the anticipated value of 7.94 μB for free Gd³⁺ ions with S = 7/2. The Weiss temperature, θW, is determined to be -32.0(1) K, indicating that the predominant interaction between the magnetic moments of Gd3+ ions is of an antiferromagnetic nature.   Upon lowering the temperature, a magnetic transition manifested at T1 in the χ vs T measurements, followed by another distinctive anomaly indicating an additional magnetic transition at a lower temperature, labeled as T2. Notably, consecutive peaks were discerned at T1 = 13.6 K and T2 = 4.1 K at H = 100 Oe. These transition temperatures exhibited minor shifts towards the lower temperature range with the progressive increase of the magnetic field, extending up to H = 70 kOe, as illustrated in Fig. 2b. Considering T1 as a representative of a long-range antiferromagnetic transition temperature, the corresponding frustration parameter |θW|/T1 was calculated to be 2.34. This value aligns with the range (typically 1-3) often reported for Gd-based intermetallic compounds known to accommodate skyrmions [27–29]. However, the negative θW observed here is in considerable contrast to the positive θW (20-64 K) reported for other Gd-based intermetallic compounds [27–29]. 100 Oe1 k10 k30 k50 k   T1T29   Fig. 3: (a) Isothermal M curves below 20 K. The inset shows the differential of M (dM/dH) at each temperature. Arrows within the inset highlight transition points. (b) The magnetic field-temperature phase diagram for Gd2Rh3Al9, which is constructed based on the data from our magnetic measurements.     Figure 3 (a) illustrates the isothermal M curves acquired within the temperature range of 2 K to 20 K. Notably, two distinct anomalies are prominently observed at approximately H1 = 15 kOe and H2 = 30 kOe. These anomalies are clearly depicted in the differential curves of M at 2 K, as showcased in the inset of Fig. 3. The anomaly at H1 materializes below T1, while the anomaly at H2 emerges beneath T2. This observation indicates that the former anomaly is linked to the antiferromagnetic structure formed at T1, while the latter pertains to the magnetic arrangement existing below T2. The M value of 4.2 μB recorded at 70 kOe under 2 K equates to approximately 60% of the saturation moment exhibited by spins with S = 7/2. However, it is noteworthy that no distinctive step-like anomalies accompanied by magnetic hysteresis, commonly observed in skyrmion compounds [18,27–29], were discerned in this case. The complex phase diagram, dependent on magnetic field and temperature, derived from our magnetization-temperature (M-T) and magnetization-field (M-H) measurements, is presented in Fig. 3 (b).     20 K10  Fig. 4: Temperature dependence of Cp/T under H = 0 and 70 kOe. Transition temperatures, T1 and T2, are indicated by an arrow and a triangular symbol, respectively. The inset displays the Cp/T vs. T2 plot, with the blue line denoting the outcome of linear fitting.    The temperature-dependent behavior of Cp is investigated under magnetic fields of 0 and 70 kOe, as depicted in Fig. 4. The Cp/T data at zero-field reveals magnetic transitions corresponding to T1 and T2. Notably, the peak associated with T1 shifts towards lower temperatures with the increment of magnetic fields, extending up to 70 kOe. The inset of Fig. 4 illustrates a plot of Cp/T versus T2, wherein a linear fitting is applied based on the equation Cp/T = γ + βT2. Here, γ represents the electronic specific heat coefficient, and β is a constant associated with the Debye temperature ΘD. The data above T1 are subjected to fitting, effectively circumventing the influence of the magnetic phase transition. The Sommerfeld coefficient γ is ascertained to be 328 mJ mol-1 K-2. While this value surpasses those observed in other Gd-based intermetallic compounds, it remains comparable to the reported value of 500 mJ mol-1 K-2 in Gd2Co3Al9 [25]. The Debye temperature ΘD is calculated to be 168 K based on the estimated β.   11  Fig. 5: Temperature dependence of Cmag/T under H = 0 Oe (black) and 70 kOe (red), and magnetic entropy (blue line). Transition temperatures, T1 and T2, are indicated by an arrow and a triangular symbol, respectively. The inset displays the C-T plot, with the green line denoting the fitting by the Einstein-Debye formula.   The inset of Fig. 5 shows the zero-field (H = 0 Oe) Cp curve and lattice contribution calculated from the Einstein-Debye function, which exhibits great fitting for temperatures exceeding 40 K except in the noisy region (250-300 K) due to the sample-fixing grease. The fitting function is described as follows: Cp = γT + 3𝑛𝑛𝐸𝐸𝑅𝑅𝑥𝑥2𝑒𝑒𝑥𝑥(𝑒𝑒𝑥𝑥−1)2  +  9𝑛𝑛D𝑅𝑅( 𝑇𝑇𝜃𝜃𝐷𝐷)3 ∫ 𝑦𝑦4𝑒𝑒𝑦𝑦(𝑒𝑒𝑦𝑦−1)2𝜃𝜃𝐷𝐷/𝑇𝑇0 d𝑦𝑦 Here, the first term represents a conduction electron contribution, where γ is the Sommerfeld coefficient. The second and third terms correspond to a phonon contribution following Einstein’s and Debye’s models, respectively. In the equations, x = θE/T, y = θD/T, in which θE and θD are the Einstein and Debye temperatures, respectively. The numbers of Einstein models (nE) and Debye oscillations (nD) are constrained by nE + nD = 14 (the number of atoms per formula unit).   In this case, proper fitting is observed with the following parameters: γ = 16.7(17) mJ mol-1 K-2, nE = 3.1(1), θE = 148(3) K, nD = 10.9(1), and θD = 493(3) K. The estimated γ and θD are much smaller and larger, respectively, than those reported for the isostructural compound Gd2Co3Al9 (γ = 500 mJ mol-1 K-2, θD = 187 K) [25]. Previous studies on Gd2Co3Al9 relied solely on the approximate formula Cp/T = γ + βT2 to estimate these values, potentially making it challenging to accurately isolate the contribution from the magnetic transition. This discrepancy underscores the critical role 12 of fitting methods in precisely determining thermodynamic parameters.   To better understand the magnetic properties, the magnetic specific heat divided by T (Cmag/T) and magnetic entropy (Smag), by subtracting lattice contribution from Cp, are shown in Fig. 5. The Cmag/T data at zero-field reveals magnetic transitions corresponding to T1 and T2. Notably, the peak associated with T1 shifts towards lower temperatures with the increment of magnetic fields extending up to 70 kOe. The Smag in zero field estimated by integrating the Cmag/T data with respect to T reaches 96.6 % of the expected value Rln8 for S= 7/2 and saturates to Rln8 at around 50 K.    Fig. 6: Temperature dependence of ρ below 300 K under zero magnetic field. The inset shows the ρ curves under H = 0 and 70 kOe.    Figure 6 presents the temperature-dependent behavior of ρ under zero magnetic field and at 70 kOe for Gd2Rh3Al9. In both scenarios, the curves show a sudden decline just below T1, which is likely due to the influence of the antiferromagnetic ordering process. Notably, while a distinctive hump in the ρ curve, indicative of a transition to a skyrmion phase, has been observed in GdRu2Si2 [30], no analogous anomaly is evident in Gd2Rh3Al9. The residual resistivity ratio (RRR) of the compound is calculated to be 5.1. This suggests that there may be contributions from grain boundary scattering in the polycrystalline sample [31], or it could imply that the sample quality is not at its optimal level.   4. Conclusion  We have achieved a significant milestone in synthesizing the Gd-based intermetallic compound Gd2Rh3Al9 through high-temperature and high-pressure synthesis. Crystal structure 0 Oe70 kOe13 analysis revealed an orthorhombic structure characterized by a distorted Gd-honeycomb network. A comprehensive study of the temperature-dependent behavior of χ, M, Cp, and ρ, in polycrystalline samples revealed sequential antiferromagnetic transitions occurring at T1 = 13.6 K and T2 = 4.1 K. These transitions are ascribed to the antiferromagnetic interactions between the magnetic moments of Gd3+ (S = 7/2) within the distorted honeycomb layers. The magnetic phase diagram derived from these findings exhibits a complex dependence on temperature and magnetic field, suggesting the presence of various magnetically ordered states.  However, our study did not provide evidence for the existence of a skyrmion phase in this compound. This may be attributed, at least in part, to the significantly stronger antiferromagnetic interactions compared to other Gd-based skyrmion materials. Nevertheless, the data on the magnetic and transport properties of Gd2Rh3Al9 obtained in this study offer valuable insights into the intricate behavior of Gd-based intermetallic compounds and their potential as hosts for unique magnetic phases. Furthermore, conducting detailed measurements using single crystals is imperative to further explore the possibility of forming a skyrmion phase in this compound. This remains a subject for future research.   Acknowledgment We thank H. Sakurai and Y. Tsujimoto for helpful discussion. 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