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Damian Contant, Sebastian Bette, Robert Dinnebier, [Ivan da Silva](https://orcid.org/0000-0002-4472-9675), [Diana Dragoe](https://orcid.org/0000-0002-8536-1205), Nita Dragoe, Hidenori Takagi, [Tomohiro Takayama](https://orcid.org/0000-0002-3492-2025)

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[Competing Magnetic Ground States in Ilmenite-TypeHigh-Entropy Oxides](https://mdr.nims.go.jp/datasets/7f421c92-9aea-44de-be1e-d7f98f7ce904)

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Competing Magnetic Ground States in Ilmenite-Type High-EntropyOxidesPublished as part of Chemistry of Materials special issue “Celebrating Myung-Hwan Whangbo on the Occasionof his 80th Birthday”.Damian Contant,* Sebastian Bette,* Robert Dinnebier,* Ivan da Silva, Diana Dragoe, Nita Dragoe,Hidenori Takagi,* and Tomohiro Takayama*Cite This: https://doi.org/10.1021/acs.chemmater.6c01899 Read OnlineACCESS Metrics & More Article Recommendations *sı Supporting InformationABSTRACT: High-entropy oxides containing more than five different cations haveemerged as platforms for diverse functionalities, including magnetism. We synthesized ahigh-entropy oxide with an ilmenite-type structure (Mg0.2Mn0.2Co0.2Ni0.2Zn0.2)TiO3 andrevealed that it undergoes long-range antiferromagnetic ordering below TN ∼ 9.5 Kdespite strong cation disorder. Neutron diffraction measurements showed that themagnetic structure comprises ferromagnetic honeycomb planes that stack antiferromag-netically, analogous to those of the parent CoTiO3 and NiTiO3 ilmenites. Derivatives ofthe high-entropy ilmenite were obtained by substituting one of the divalent cations of(Mg0.2Mn0.2Co0.2Ni0.2Zn0.2)TiO3 with an equimolar amount of Li+ ions and trivalentcations. The antiferromagnetic order remains robust against aliovalent doping thatintroduces extra disorder owing to cations with different valence states. In contrast, whenthe cation ratio was tuned to a Mn-rich composition of (Mg0.2Mn0.3Co0.15Ni0.15Zn0.2)-TiO3, spin-glass freezing was observed, most likely because of the enhanced competition between the in-plane magnetic interactions.This suggests that long-range magnetic ordering in high-entropy materials is formed by a subtle balance of competing interactions,and fine-tuning of constituent magnetic ions provides control over their magnetic ground states.1. INTRODUCTIONThe entropy stabilization of complex, multi-componentmaterials was initially proposed for alloys, giving birth to aclass of materials called high-entropy alloys.1,2 The concept ofentropy stabilization was later applied to other classes ofmaterials, such as oxides. A rocksalt-type oxide with more thanfive different cations, (Mg0.2Co0.2Ni0.2Cu0.2Zn0.2)O (denoted as(MgCoNiCuZn)O hereafter), has appeared as the first high-entropy oxide (HEOx).3 The successful synthesis of rocksalt-type HEOx has prompted the search for other complex HEOx,such as perovskite, spinel, and fluorite-type compounds.4 Inparallel with the development of materials, HEOx have beenshown to display unexpected functionalities. For example, therocksalt HEOx exhibits a colossal dielectric constant5 and highionic conductivity upon alkali-metal doping.6 In addition,various properties ranging from high-performance electro-chemical functions,7,8 catalytic activities,9 and thermoelectricproperties10 have been reported for high-entropy oxides andother high-entropy ceramics.As HEOx often contain magnetic cations such as Co2+ andNi2+, they may display unique magnetic properties. At a glance,the strong cation disorder of HEOx would be considered tosimply lead to spin-glass freezing. As opposed to this view, therocksalt-type HEOx (MgCoNiCuZn)O was revealed toundergo long-range antiferromagnetic ordering below ∼120K11,12. The presence of long-range magnetic order in such adisordered material is surprising, and the wide variety ofcompositional spaces in HEOx should enable the fine controlof their magnetic properties and functionalities. Following thediscovery of the long-range magnetic order in the rocksaltHEOx, the magnetic properties and functions of other HEOxhave been extensively investigated.13−16One of the key features of HEOx in terms of magnetism isthe presence of multiple magnetic cations with differentelectronic configurations, which should result in the coex-istence of different magnetic exchange interactions, namely,bond-disorder in magnetic interactions. In the case of therocksalt (MgCoNiCuZn)O, the dominant magnetic exchangecoupling is antiferromagnetic between the second-nearestneighbor cations in the 180° bond.17 This dominant exchangepath is identical to that of binary rocksalt oxides such as CoOReceived: June 30, 2026Revised: August 28, 2026Accepted: August 31, 2026Articlepubs.acs.org/cm© XXXX The Authors. Published byAmerican Chemical SocietyAhttps://doi.org/10.1021/acs.chemmater.6c01899Chem. Mater. XXXX, XXX, XXX−XXXThis article is licensed under CC-BY 4.0Downloaded from pubs.​acs.​org/​cmatex/​article-pdf/​doi/​10.​1021/​acs.​chemmater.​6c01899/​68398719/​acs.​chemmater.​6c01899.​pdf by NATL INST FOR MATLS SCIENCE (NIMS) user on 11 September 2026https://pubs.acs.org/curated-content?journal=cmatex%26ref=featurehttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Damian+Contant"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Sebastian+Bette"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Robert+Dinnebier"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Ivan+da+Silva"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Diana+Dragoe"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Nita+Dragoe"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Hidenori+Takagi"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Hidenori+Takagi"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Tomohiro+Takayama"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/showCitFormats?doi=10.1021/acs.chemmater.6c01899&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c01899?ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c01899?goto=articleMetrics&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c01899?goto=recommendations&?ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c01899?goto=supporting-info&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c01899?fig=agr1&ref=pdfpubs.acs.org/cm?ref=pdfhttps://pubs.acs.org?ref=pdfhttps://pubs.acs.org?ref=pdfhttps://doi.org/10.1021/acs.chemmater.6c01899?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://pubs.acs.org/cm?ref=pdfhttps://pubs.acs.org/cm?ref=pdfhttps://creativecommons.org/licenses/by/4.0/and NiO, which reasonably explains why the high-entropyrocksalt oxides have a similar magnetic structure to the binaryoxides.11,12 To explore potential rich magnetic ground states ofHEOx, complex magnetic interactions, distinct from those ofthe parent compounds containing a single magnetic ion, mayneed to be incorporated.We therefore focused on MTiO3 ilmenite-type oxides(Figure 1a), where M represents a collection of variousdivalent cations. In ilmenite MTiO3, different magneticstructures are observed depending on the nature of the M2+cations; MnTiO3 forms a Neél-type antiferromagnetic order,18whereas the magnetic moments in CoTiO3 and NiTiO3 orderferromagnetically within the honeycomb ab-planes and theferromagnetic planes stack antiferromagnetically along the c-axis,18,19 which is often called A-type antiferromagnetic order.This difference is attributable to the distinct magneticexchange coupling of the M2+ cations. The magnetic momentsof Mn2+ ions with a 3d5 high-spin configuration (S = 5/2)couple antiferromagnetically through the direct exchange of t2gelectrons across the edges of the MnO6 octahedra in thehoneycomb lattice. On the other hand, the ferromagneticinteraction of eg electrons in the 90° M−O−M bonds ispredominant for Co2+ (3d7 high-spin configuration) and Ni2+(3d8) ions. Therefore, by forming a high-entropy configurationat the M-site of the ilmenite MTiO3 phase, competingmagnetic exchange interactions can occur within the M2+honeycomb lattice.W e s y n t h e s i z e d a h i g h - e n t r o p y i l m e n i t e(Mg0.2Mn0.2Co0.2Ni0.2Zn0.2)TiO3 (hereafter denoted as(MgMnCoNiZn)TiO3). This high-entropy ilmenite undergoeslong-range antiferromagnetic ordering below 9.5 K, despite thechemical disorder and the resultant bond-disorder in themagnetic interactions. Our neutron diffraction measurementsrevealed that the magnetic structure of (MgMnCoNiZn)TiO3is similar to that of CoTiO3 and NiTiO3, suggesting thatferromagnetic super-exchange interactions are dominant in thehoneycomb planes. Furthermore, a wide variety of high-entropy ilmenites have been synthesized by replacing one ofthe M cations of (MgMnCoNiZn)TiO3 with an equimolaramount of Li+ and a trivalent cation, which retains long-rangemagnetic order, albeit with enhanced chemical disorder. Bycontrast, spin-glass behavior was observed in the non-equimolar sample of (Mg0.2Mn0.3Co0.15Ni0.15Zn0.2)TiO3,where the competition between the in-plane antiferromagneticand ferromagnetic interactions is likely the most pronounced.This suggests a subtle balance of magnetic interactions and thehigh tunability of the magnetic ground states of high-entropymaterials.2. EXPERIMENTAL SECTION2.1. SynthesisThe high-entropy ilmenite (MgMnCoNiZn)TiO3 was synthesized viaa conventional solid-state reaction. Powders of MgO (99.99%, Sigma-Aldrich), MnO (99.99%, Thermo Fisher Scientific), Co3O4 (99.97+%,ChemPUR), NiO (99.99%, Sigma-Aldrich), ZnO (99.999%, ThermoFisher Scientific), and TiO2 (>99.98%, Sigma-Aldrich) were usedwithout further purification. The powders were weighed in the desiredratios and mixed in an agate mortar. The mixture was pelletized andheated at 1100 °C for 24 h in air, and then quenched to roomtemperature. To examine the possible influence of oxygen non-stoichiometry, the (MgMnCoNiZn)TiO3 samples were annealed at1100 °C under different atmospheres, such as air, argon or oxygen gasflow, and then cooled to room temperature using a furnace-coolingprocedure (the cooling rate was approximately 100 °C/hour). For thealiovalent-doped samples, in addition to the chemicals listed above,powder of Li2CO3 (99.995%, ChemPUR), together with Fe2O3(99.995%, Thermo Fisher Scientific), Sc2O3 (99.999%, ThermoFisher Scientific), or In2O3 (99.994%, Thermo Fisher Scientific)powder, was added instead of one of the binary oxides shown above.Figure 1. (a) Crystal structure of high-entropy ilmenites MTiO3. Theright figure depicts the honeycomb lattice composed of MO6octahedra in the ab-plane. The structures were visualized using theVESTA software.48 (b) Powder X-ray diffraction patterns of high-entropy ilmenites MTiO3 collected with Mo−Kα1 radiation, where Mdeno t e s Mg0 . 2Mn 0 . 2Co 0 . 2N i 0 . 2Zn 0 . 2 (MgMnCoNiZn) ,Mg0 . 2Mn0 . 2Co0 . 2N i 0 . 2 (L i 0 . 1 Fe 0 . 1 ) (MgMnCoNi(L iFe)) ,Mn0 . 2Co0 . 2Ni 0 . 2L i 0 . 2Sc 0 . 1 In0 . 1 (MnCoNiLi(ScIn)) , andMg0 . 2Co0 . 2Ni0 . 2Zn0 . 2L i 0 . 1 In0 . 1 (MgCoNiZn(LiIn)) . For(MgMnCoNiZn)TiO3, the selected reflection indices for the spacegroup R3̅ (No. 148) are indicated. (c) Lattice parameters of high-entropy ilmenite-type oxides as a function of the averaged ionic radiiof the M cations, <rM>. The red (blue) markers represent the lengthof the a-axis (c-axis) of the unit cell, which refers to the left (right)vertical axis of the plot. The nominal chemical composition for eachabbreviated sample name is given in Table 1.Chemistry of Materials pubs.acs.org/cm Articlehttps://doi.org/10.1021/acs.chemmater.6c01899Chem. Mater. XXXX, XXX, XXX−XXXBDownloaded from pubs.​acs.​org/​cmatex/​article-pdf/​doi/​10.​1021/​acs.​chemmater.​6c01899/​68398719/​acs.​chemmater.​6c01899.​pdf by NATL INST FOR MATLS SCIENCE (NIMS) user on 11 September 2026https://pubs.acs.org/doi/10.1021/acs.chemmater.6c01899?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c01899?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c01899?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c01899?fig=fig1&ref=pdfpubs.acs.org/cm?ref=pdfhttps://doi.org/10.1021/acs.chemmater.6c01899?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as2.2. Powder X-ray DiffractionThe products were characterized using powder X-ray diffraction(PXRD). The measurements were carried out using a Stoe Stadi-Pdiffractometer with monochromatic Mo−Kα1 radiation from aprimary Ge(111) Johannson-type monochromator or a Bruker D2Phaser diffractometer with Cu−Kα radiation. The measurements withStoe Stadi-P were performed in Debye-Scherrer geometry and thescattered X-rays were collected using a triple array of Mythen 1Kdetectors (Dectris). The samples were sealed in 0.3 mm diameterborosilicate glass capillaries that were spun during the measurements.A scan range from 2θ = 2° to 110° and a total scan time of 3 h wasapplied for every sample. The measurements with Bruker D2 Phaserwere performed in Bragg-Brentano geometry, and the powder sampleswere placed on a flat Si sample holder, which was spun during themeasurements. The lattice parameters were determined by fullyweighted Rietveld refinements using TOPAS v.6.20 The crystalstructure of CoTiO3 was used as the initial model.212.3. Energy-Dispersive X-ray SpectroscopyThe chemical compositions of the samples were examined usingenergy-dispersive X-ray spectroscopy (EDX) equipped with a SEM. ATescan Vega4 LMU SEM instrument equipped with an Oxford X-MaxN 20 was used for the measurements. For each sample, 5−6 EDXspectra were measured at different spots.2.4. X-ray Photoelectron SpectroscopyX-ray photoelectron spectroscopy (XPS) analyses were performedusing a Thermo K-Alpha+ spectrometer equipped with a mono-chromatic Al-Kα X-ray source (1486.7 eV) operated at 12 kV and 6mA (72 W). The angle between the analyzer and the X-ray source was56°. The X-ray spot size was 400 μm, corresponding to an irradiatedarea of approximately 0.1 mm2. The base pressure in the analysischamber was maintained at 2 × 10−9 mbar.The spectrometer was calibrated using metallic reference samplesof Cu, Ag, and Au, with binding energies set at 932.6 eV for Cu 2p3/2,368.2 eV for Ag 3d5/2, and 84.0 eV for Au 4f 7/2. Charge compensationwas achieved using a dual-beam flood gun that provided low-energyelectrons (<5 eV) under a partial argon atmosphere. Binding energyreferencing was performed on the C−C component of the C 1s peakto 284.8 eV. The binding energy accuracy was ±0.2 eV.Survey spectra were acquired at a pass energy of 200 eV with a stepsize of 1 eV and a dwell time of 10 ms per point. High-resolutionspectra were recorded at a pass energy of 50 eV with a step size of 0.1eV and a dwell time of 50 ms per point.2.5. Magnetic and Thermodynamic MeasurementsThe magnetization of the samples was evaluated using a QuantumDesign MPMS3. The data were collected from 2 to 350 K under amagnetic field of 0.1 T in both zero-field and field-cooled procedures.AC magnetic susceptibility measurements were performed using aQuantum Design MPMS-XL. An AC magnetic field of 4 Oe wasapplied in the 1−1000 Hz frequency range. The heat capacity, C(T),was measured using a Quantum Design PPMS. The latticecontribution to C(T) was evaluated by measuring the heat capacityof a non-magnetic (Mg0.5Zn0.5)TiO3 ilmenite sample. All measure-ments were performed on polycrystalline samples.2.6. Powder Neutron DiffractionNeutron diffraction measurements on (MgMnCoNiZn)TiO3 wereconducted at the time-of-flight neutron diffractometer GEM of ISISNeutron and Muon Source, U.K.22 A ∼6.0 g powder sample wasloaded into a thin-wall vanadium can, and the data were collectedfrom 1.85 to 20 K. The magnetic structure was analyzed using theSARAh23 and FullProf Suite24 programs. The chemical compositionwas fixed at the nominal one during the Rietveld refinement withFullProf.3. RESULTS AND DISCUSSION3.1. Long-Range Magnetic Order in High-Entropy Ilmenite(MgMnCoNiZn)TiO3The PXRD pattern of (MgMnCoNiZn)TiO3 synthesized at1100 °C in air is shown in Figure 1b. The observed pattern isconsistent with an ilmenite-type structure (space group R3̅,No. 148), with a minute amount of TiO2 rutile impurities. Thelattice parameters obtained by Rietveld refinement were a =5.07544(3) Å and c = 13.96301(9) Å (Figure S1b ofSupporting Information). No noticeable difference was foundin the (MgMnCoNiZn)TiO3 samples annealed under differentconditions (Figure S2 of Supporting Information). The EDXmeasurement of the powder sample indicated a chemicalcomposition close to the nominal ratio of M ions (Table S1 ofSupporting Information), and the XPS measurementssupported that the Mn, Co, and Ni ions at the M-site adoptdivalent ionic states (Figure S4 of Supporting Information).This ilmenite phase is most likely stabilized by its formationenthalpy, rather than by entropy stabilization. To confirmwhether the ilmenite phase was entropy-stabilized, the high-entropy ilmenite sample was annealed at 850 °C in air. Incontrast to the rocksalt (MgCoNiCuZn)O3, the ilmenitesample did not decompose during the low-temperatureannealing. This suggests that the ilmenite phase is predom-inantly stabilized by its formation enthalpy, although its highconfiguration entropy may play some role. We also attemptedto synthesize a high-entropy ilmenite with a combination ofthe divalent cations similar to that used for rocksalt-type HEOx(MgCoNiCuZn)O. However, the product contained severalimpurity phases, such as TiO2 rutile and M2TiO4 inverse spineloxides. Therefore, in contrast to the rocksalt-type structure, itis not easy to fully accommodate the Jahn-Teller active Cu2+ions into the ilmenite-type structure, likely due to the differentbond geometries including face-shared bonds. Attempts toincorporate other divalent cations such as Cd2+ and Fe2+ werealso unsuccessful.The high-entropy ilmenite (MgMnCoNiZn)TiO3 was foundto exhibit long-range magnetic order. Magnetic susceptibility,χ(T), measured at a magnetic field of 0.1 T is shown in Figure2a. A clear cusp was observed at 9.5 K in both the zero-field-cooled and field-cooled processes, indicating the appearance ofantiferromagnetic order. A similar behavior of χ(T) wasobserved in the samples annealed in argon or oxygen gas flow,indicating that the potential influence of oxygen non-stoichiometry is negligible in the magnetic properties (FigureS3 of Supporting Information). The real part of the ACmagnetic susceptibility, χ′(T), shows a sharp cusp near 9.5 Kwithout any frequency dependence. This excludes theformation of a spin-glass state (Figure S5 of SupportingInformation). The inset of Figure 2a shows the inverse of themagnetic susceptibility, χ−1(T). The Curie-Weiss fit of χ−1(T)above 250 K yields an effective moment, μeff, of 3.76 μB/f.u.and a negative Curie-Weiss temperature of θCW = −27 K. Themagnitude of the effective moment agrees well with theexpected value of 3.75 μB/f.u., which was estimated as= × + × + ×0.2 0.2 0.2eff eff,Mn2eff,Co2eff,Ni2 using theeffective moments of the parent compounds such as MnTiO3(μeff,Mn = 5.90 μB/Mn2+),25 CoTiO3 (μeff,Co = 5.02 μB/Co2+),and NiTiO3 (μeff,Ni = 3.21 μB/Ni2+).26 A slight deviation fromthe Curie-Weiss behavior was observed in the χ−1(T) profilebelow ∼100 K, implying the development of short-rangeChemistry of Materials pubs.acs.org/cm Articlehttps://doi.org/10.1021/acs.chemmater.6c01899Chem. Mater. XXXX, XXX, XXX−XXXCDownloaded from pubs.​acs.​org/​cmatex/​article-pdf/​doi/​10.​1021/​acs.​chemmater.​6c01899/​68398719/​acs.​chemmater.​6c01899.​pdf by NATL INST FOR MATLS SCIENCE (NIMS) user on 11 September 2026https://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c01899/suppl_file/cm6c01899_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c01899/suppl_file/cm6c01899_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c01899/suppl_file/cm6c01899_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c01899/suppl_file/cm6c01899_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c01899/suppl_file/cm6c01899_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c01899/suppl_file/cm6c01899_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c01899/suppl_file/cm6c01899_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c01899/suppl_file/cm6c01899_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c01899/suppl_file/cm6c01899_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c01899/suppl_file/cm6c01899_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c01899/suppl_file/cm6c01899_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c01899/suppl_file/cm6c01899_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c01899/suppl_file/cm6c01899_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c01899/suppl_file/cm6c01899_si_001.pdfpubs.acs.org/cm?ref=pdfhttps://doi.org/10.1021/acs.chemmater.6c01899?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asmagnetic correlations above TN. The presence of long-rangemagnetic order was further corroborated by specific heatmeasurements. Figure 2b shows the magnetic specific heat,Cmag(T), where the lattice contribution, Cph(T), to the totalheat capacity was subtracted by using the C(T) of the non-magnetic ilmenite (Mg0.5Zn0.5)TiO3 (Figure S6 of SupportingInformation). Cmag(T) of (MgMnCoNiZn)TiO3 exhibited asharp peak near 9.5 K. This ordering temperature issubstantially lower than that of the parent ilmenite-type oxidessuch as TN = 64 K for MnTiO327 and TN = 38 K for CoTiO3.26A remarkable feature of the specific heat of(MgMnCoNiZn)TiO3 is that Cmag(T) decreases at a moderaterate (Cmag ∼ T1.2) when cooled below TN. Cmag(T) of theparent ilmenites, such as CoTiO3 and NiTiO3, shows a muchsteeper decrease right below TN (Ref. 26 and Figure S7 ofSupporting Information). The behavior of Cmag(T) for(MgMnCoNiZn)TiO3 may be attributed to the presence ofstrong disorder in the magnetic sublattice, which may affect themagnon excitation spectrum, as observed in disorderedantiferromagnets.28,29The magnetic entropy, Smag(T), estimated by integratingCmag(T)/T at zero magnetic field is shown in Figure 2c. Thetotal magnetic entropy expected in (MgMnCoNiZn)TiO3 isapproximately 5.96 J/mol·K from the presence of Mn2+ (S = 5/2 quintet), Co2+ (Jeff = 1/2 doublet),30 and Ni2+ (S = 1 triplet)ions. The magnetic entropy shows a steep increase around TNupon heating and gradually increases further above TN up to∼100 K. This implies that the magnitude of the magneticinteractions is of the order of 100 K and short-range magneticcorrelations develop at temperatures much higher than TN.The smaller magnitude of the Curie-Weiss temperature, |θCW|= 27 K, can be ascribed to the coexistence of ferro- andantiferromagnetic interactions associated with the presence ofmultiple magnetic ions. The magnetic entropy at hightemperatures exceeds the expected value of 5.96 J/mol·K.We suspect that this is caused by the thermal population of theexcited Jeff = 3/2 levels of Co2+ ions.31Cmag(T) shows a strong magnetic-field dependence above 6T. At low fields (up to 3 T), the peak value of Cmag(T) at TNwas only moderately suppressed. Cmag(T) was, however,substantially suppressed near TN above 6 T, and some portionsof the magnetic entropy were transferred to higher temper-atures. This may be attributed to the presence of ferromagneti-cally correlated moments above TN as inferred from the χ−1(T)and Smag(T) data, and the partial alignment of magneticmoments takes place above TN under high magnetic fields.Similarly, the sharp cusp of χ(T) at TN was gradually smearedout by increasing the magnetic field, although no ferromagneticbehavior was seen up to 7 T (Figure S8 of SupportingInformation for the magnetic susceptibility at high fields andthe magnetization curve at 2 K). This suggests thatferromagnetically correlated moments are present at hightemperatures but their long-range ordering may be hamperedby bond-disorder.3.2. Magnetic Structure of (MgMnCoNiZn)TiO3The magnetic structure of the high-entropy ilmenite(MgMnCoNiZn)TiO3 is of particular interest regarding howthe competing magnetic interactions, in the presence of strongchemical disorder, are reconciled. We studied this by powderneutron diffraction measurements at the GEM diffractometerof ISIS Neutron and Muon Source. The neutron diffractionpattern for the Bank 2 detector of the GEM diffractometer isdisplayed in Figure 3a, where an additional peak at a d-spacingof ∼9.3 Å was observed clearly at 1.85 K. As shown in theinset, this peak began to grow right below TN (∼9.5 K), whichis suggestive of a magnetic origin. Similar additional peaks wereobserved below TN, as shown in Figure 3b. These peaks can beindexed with a propagation vector k = (0, 0, 3/2), which isidentical to that of CoTiO3 and NiTiO3 forming an A-typeantiferromagnetic order. The temperature dependence of theintegrated intensity of the (0 0 3/2) magnetic Bragg reflection,I(T), shown in Figure 3d, was fitted with a power-law function,I(T) = I0 (1 − T/TN)2β. The fitting yields TN = 10.0(1) K andβ = 0.34(3). This value of β is close to that of the three-dimensional XY model (β = 0.345) and that obtained forNiTiO3, β = 0.35(1),32 suggesting a similar spin anisotropy.From the space group of R3̅ (No. 148) and the propagationvector, we constructed models of the possible magneticstructures with the help of the SARAh program.23 There aresix irreducible representations (Irreps) compatible with thepropagation vector, as listed in Table 2. The Irreps are one-dimensional, and all the components of the basis vectors arereal numbers. Among the Irreps, the Γ3 and Γ5 models areconsistent with the observed magnetic Bragg reflections. Thetwo basis vectors, Ψ3 and Ψ5, represent ferromagnetic orderingwithin the ab-planes, and the ferromagnetic planes stackantiferromagnetically along the c-axis, namely, the A-typeFigure 2. Magnetic and thermodynamic properties of the high-entropy ilmenite (MgMnCoNiZn)TiO3. (a) Temperature depend-ence of magnetic susceptibility, χ(T), measured at a magnetic field of0.1 T. The inset shows the temperature dependence of the inverse ofmagnetic susceptibility, χ−1(T). The red-dotted line delineates theCurie-Weiss fit. (b) Magnetic specific heat, Cmag(T), around theantiferromagnetic transition temperature TN at zero and appliedmagnetic fields. The lattice contribution to the heat capacity wassubtracted using the heat capacity of the non-magnetic ilmenite(Mg0.5Zn0.5)TiO3. (c) Magnetic entropy, Smag, of (MgMnCoNiZn)-TiO3 at zero magnetic field estimated by integrating Cmag(T)/T.Chemistry of Materials pubs.acs.org/cm Articlehttps://doi.org/10.1021/acs.chemmater.6c01899Chem. Mater. XXXX, XXX, XXX−XXXDDownloaded from pubs.​acs.​org/​cmatex/​article-pdf/​doi/​10.​1021/​acs.​chemmater.​6c01899/​68398719/​acs.​chemmater.​6c01899.​pdf by NATL INST FOR MATLS SCIENCE (NIMS) user on 11 September 2026https://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c01899/suppl_file/cm6c01899_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c01899/suppl_file/cm6c01899_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c01899/suppl_file/cm6c01899_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c01899/suppl_file/cm6c01899_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c01899/suppl_file/cm6c01899_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c01899/suppl_file/cm6c01899_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c01899/suppl_file/cm6c01899_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c01899/suppl_file/cm6c01899_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c01899?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c01899?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c01899?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c01899?fig=fig2&ref=pdfpubs.acs.org/cm?ref=pdfhttps://doi.org/10.1021/acs.chemmater.6c01899?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asantiferromagnetic order as in CoTiO3 and NiTiO3. Thedifference between Ψ3 and Ψ5 is only found in the direction ofthe magnetic moments lying in the ab-planes, which cannot bedistinguished by powder neutron diffraction experiments.Thus, we used the Γ3 model for refinement, where themagnetic moments are directed along the a-axis.The result of the Rietveld refinement in the magneticallyordered phase at 1.85 K is shown in Figure 3c. In therefinement of the magnetic structure, for simplicity, weassumed that all M2+ cations possessed the same magneticmoments with a magnetic form factor of the Co2+ ion. Therefined magnetic structure is depicted in Figure 3e. Themagnitude of the ordered moment thus estimated is 0.66(1)μB/M2+, which is much smaller than the average magneticmoments of ∼1.83 μB, based on the 20% contributions fromMn2+ (S = 5/2, 5 μB), Co2+ (Jeff = 1/2 and g = 4.33,33 ∼2.17μB), and Ni2+ (S = 1, 2 μB) ions. Reduced ordered momentshave been observed in magnetic high-entropy compounds,possibly due to strong fluctuations associated with chemicaldisorder and magnetic bond-disorder.11,343.3. High-Entropy Ilmenites with Aliovalent DopingThe high-entropy ilmenite (MgMnCoNiZn)TiO3 turned outto display long-range antiferromagnetic order, and its magneticstructure is identical with that of the parent CoTiO3 andNiTiO3 ilmenites. Meanwhile, the reduced magnitude ofordered magnetic moments suggests the presence of strongfluctuations associated with pronounced disorder. Thus, theenhancement of the chemical disorder may affect the magneticground state. As described above, (MgMnCoNiZn)TiO3 is theonly high-entropy ilmenite obtained by allocating divalentcations to the M-site in an equimolar ratio. Instead, one (ortwo) of the divalent cations was successfully replaced by anequimolar amount of monovalent Li+ ions and a trivalentcation such as Fe3+, Sc3+, or In3+, as in the case of the rocksalt-type high-entropy oxides.5,11 Such aliovalent doping isexpected to introduce extra disorder and local lattice distortionFigure 3. Powder neutron diffraction measurements and refined magnetic structure of (MgMnCoNiZn)TiO3. (a) Powder neutron diffractionpatterns recorded at Bank 2 of GEM diffractometer measured at 1.85, 15, and 20 K. An additional peak was seen at 1.85 K around the d-spacing of9.3 Å. The inset shows the temperature dependence of the additional peak indexed as (0 0 3/2). (b) Powder diffraction patterns recorded at Bank 4of GEM, collected at 1.85 and 15 K. The additional Bragg peaks at 1.85 K were indexed with a propagation vector k = (0, 0, 3/2). (c) Rietveldrefinement of the powder neutron diffraction pattern (Bank 2, GEM) at 1.85 K. The refinement indices are RBragg = 5.38% and RF = 6.38% for thenuclear structure, and the magnetic R-factor is R = 13.3%. (d) Temperature dependence of the integrated intensity of magnetic (0 0 3/2) Braggpeak. The red-dashed line shows a power-law fit, I(T) = I0 (1 − T/TN)2β. (e) Refined magnetic structure of (MgMnCoNiZn)TiO3. For brevity,only the M ions are displayed and they are all assumed to possess the same magnetic moments. The magnetic structure is identical with that ofCoTiO3, namely, an A-type antiferromagnetic order.Table 1. Lattice Parameters of High-Entropy Ilmenites MTiO3aNominal composition Abbrev. name <rM> (Å) σ2 (10−4 Å2) a (Å) c (Å)Mg0.2Co0.2Ni0.2Zn0.2Li0.1Sc0.1TiO3 MgCoNiZn(LiSc) 0.730 5.2 5.06223(4) 13.9195(2)Mg0.2Co0.2Ni0.2Zn0.2Li0.1In0.1TiO3 MgCoNiZn(LiIn) 0.735 9.6 5.07127(3) 13.9604(1)Mg0.2Mn0.2Co0.2Ni0.2Li0.1Fe0.1TiO3 MgMnCoNi(LiFe) 0.738 31.4 5.06694(3) 13.9379(1)Mg0.2Mn0.2Co0.2Ni0.2Zn0.2TiO3 MgMnCoNiZn 0.745 21.8 5.07544(3) 13.96301(9)Mg0.2Mn0.2Co0.2Ni0.2Li0.1Sc0.1TiO3 MgMnCoNi(LiSc) 0.748 21.9 5.07434(3) 13.9925(1)Mg0.2Mn0.2Co0.2Ni0.2Li0.1In0.1TiO3 MgMnCoNi(LiIn) 0.753 24.3 5.08346(3) 14.03105(9)Mn0.2Co0.2Ni0.2Li0.2Sc0.1In0.1TiO3 MnCoNiLi(ScIn) 0.760 21.9 5.08774(3) 14.07867(9)aAbbreviated sample names are used in Figures 1c and 4 and in Table 3. <rM> represents the average of the ionic radii of the M-cations calculatedusing Shannon’s ionic radii for octahedral coordination.47 σ2 indicates the size variance of the M-cation ionic radii, σ2 = Σimi(rM,i − <rM>)2, wheremi represents the molar fraction of cation i.Chemistry of Materials pubs.acs.org/cm Articlehttps://doi.org/10.1021/acs.chemmater.6c01899Chem. Mater. XXXX, XXX, XXX−XXXEDownloaded from pubs.​acs.​org/​cmatex/​article-pdf/​doi/​10.​1021/​acs.​chemmater.​6c01899/​68398719/​acs.​chemmater.​6c01899.​pdf by NATL INST FOR MATLS SCIENCE (NIMS) user on 11 September 2026https://pubs.acs.org/doi/10.1021/acs.chemmater.6c01899?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c01899?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c01899?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c01899?fig=fig3&ref=pdfpubs.acs.org/cm?ref=pdfhttps://doi.org/10.1021/acs.chemmater.6c01899?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asinduced by cations with different valence states.35 The PXRDpatterns of the aliovalent-doped samples are shown in Figure1b and Figure S1a of Supporting Information. These samplesformed a nearly single-phase of the ilmenite-type structure.The refined lattice parameters are listed in Table 1 and plottedwith respect to the average ionic radii of M-cations, <rM>, inFigure 1c. The lattice parameters scaled nearly linearly with<rM>, suggesting that all the M-cations were successfullyaccommodated in the ilmenite structure.Despite the enhanced chemical disorder, χ(T) of thealiovalent-doped samples showed a sharp cusp, similar tothat of (MgMnCoNiZn)TiO3 as shown in Figure 4a, indicativeof long-range antiferromagnetic order. The presence of long-range magnetic ordering was further confirmed by specific heatmeasurements. The magnetic specific heat, Cmag(T), of(MgMnCoNi(LiFe))TiO3, (MnCoNiLi(ScIn))TiO3 and(MgCoNiZn(LiIn))TiO3 are shown in Figure 4b, where thelattice contributions were subtracted using a procedure similarto that employed for (MgMnCoNiZn)TiO3. Cmag(T) belowTN appears to decrease nearly linearly with temperature, akinto (MgMnCoNiZn)TiO3. The ordering temperature TN andthe Curie-Weiss temperature are summarized in Table 3. TNappears to be solely determined by the contents of magneticions, and is independent of the identity of non-magnetic ions.That is, the average ionic radii or the variance of the ionic radiidoes not affect TN, unlike other high-entropy oxides, where alarge variance in the ionic radii tends to reduce the transitiontemperature.36,37 We suspect that the local structuralmodulation induced by cations with different ionic radii orvalence states may be moderate and its influence on themagnetic exchange paths is negligibly small in the ilmenitestructure comprising a rigid structural network with edge- andface-shared bonds, compared to the corner-shared network ofperovskite or pyrochlore oxides.Interestingly, long-range order was found in (MgCoNiZn-(LiIn))TiO3 that contains only 40% magnetic cations at theM-site. We note that the 40% concentration of magnetic ions isfar below the percolation threshold of a two-dimensionalhoneycomb lattice, which is approximately 69%. We speculatethat the sizable interlayer coupling of the ilmenite structure,together with longer-range interactions within the honeycomblattice, may facilitate long-range magnetic ordering.38,39Longer-range interactions are probably operative in allmagnetic high-entropy ilmenites to stabilize the long-rangeorder despite the presence of non-magnetic M cations, i.e.,“magnetic vacancies”. That is, even though nearest-neighbormagnetic interactions are disrupted by magnetic vacancies,Figure 4. Magnetic properties of aliovalent-doped high-entropyilmenites MTiO3. (a) Magnetic susceptibility, χ(T), measured at 0.1T. The nominal chemical composition of each sample is found inTable 1. (b) Magnetic specific heat, Cmag(T), near the antiferro-magnetic ordering temperature, TN. For all the samples, the behaviorsof Cmag(T) below TN are analogous to that of (MgMnCoNiZn)TiO3.Table 2. Irreducible Representations (Irreps) and BasisVectors (BV) for the M-Site Atom of(MgMnCoNiZn)TiO3aBV componentsIrrep BV M-site ma mb mcΓ1 Ψ1 1 0 0 32 0 0 −3Γ2 Ψ2 1 0 0 32 0 0 3Γ3 Ψ3 1 3 0 02 −3 0 0Γ4 Ψ4 1 3 0 02 3 0 0Γ5 Ψ5 1 −1.732 −3.464 02 1.732 3.464 0Γ6 Ψ6 1 −1.732 −3.464 02 −1.732 −3.464 0a(MgMnCoNiZn)TiO3 crystallizes in a rhombohedral structure withspace group of R3̅ (No. 148) and the M ions occupy the 6c Wyckoffsite, (0, 0, z), with z = 0.3552(3). The propagation vector is k = (0, 0,3/2). There are two distinct M-sites in the unit cell, located at 1: (0, 0,0.3552) and 2: (0, 0, 0.6448). All the imaginary components of thebasis vectors are zero.Table 3. Magnetic Properties of High-Entropy Ilmenite-Type Oxides MTiO3aAbbrev. samplenameRatio ofmagnetic Mions (%)TN(K)μeff(μB/f.u.)Expectedμeff(μB/f.u.)θCW(K)MgMnCoNi(LiFe) 70 13.0 4.95 4.19 −83MgMnCoNiZn 60 9.5 3.76 3.75 −27MgMnCoNi(LiSc) 60 9.5 3.84 3.75 −32MgMnCoNi(LiIn) 60 9.5 3.83 3.75 −32MnCoNiLi(InSc) 60 9.5 3.82 3.75 −30MgCoNiZn(LiIn) 40 7.5 2.84 2.66 −10aThe nominal chemical compositions of the samples are shown inTable 1. The table shows the antiferromagnetic ordering temperatureTN determined by the cusp of χ(T), effective moment μeff, and Curie-Weiss temperature θCW obtained from the Curie-Weiss fit of χ−1(T).The expected μeff was calculated as = mi i ieff eff,2 , where mi is amolar fraction of magnetic ion i and μeff,i is the effective moment ofthe magnetic ion. The reported values for MnTiO3, CoTiO3 andNiTiO3 were used as μeff,i for Mn2+, Co2+ and Ni2+ ions,respectively.25,26 For Fe3+ ions, the value of S = 5/2 with a g-factorof 2, μeff,Fe = 5.92 μB, was used.Chemistry of Materials pubs.acs.org/cm Articlehttps://doi.org/10.1021/acs.chemmater.6c01899Chem. Mater. XXXX, XXX, XXX−XXXFDownloaded from pubs.​acs.​org/​cmatex/​article-pdf/​doi/​10.​1021/​acs.​chemmater.​6c01899/​68398719/​acs.​chemmater.​6c01899.​pdf by NATL INST FOR MATLS SCIENCE (NIMS) user on 11 September 2026https://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c01899/suppl_file/cm6c01899_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c01899/suppl_file/cm6c01899_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c01899?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c01899?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c01899?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c01899?fig=fig4&ref=pdfpubs.acs.org/cm?ref=pdfhttps://doi.org/10.1021/acs.chemmater.6c01899?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asmagnetic correlations develop throughout the crystal vialonger-range magnetic interactions.3.4. Formation of a Spin-Glass State by Changing theCompositional Ratio of Magnetic IonsThe long-range magnetic order of the high-entropy ilmeniteswas found to be robust against aliovalent doping, whichinduces additional chemical disorder. In fact, the high-entropyilmenite (MgMnCoNiZn)TiO3 and those with aliovalentdoping have larger amounts of magnetic ions that prefer in-plane ferromagnetic coupling, that is, Co2+ and Ni2+, comparedto those with dominant antiferromagnetic interactions, such asMn2+ and probably isoelectronic Fe3+. This may promote long-range magnetic order with in-plane ferromagnetic alignments.In an attempt to further enhance the competition of twodifferent magnetic interactions, we synthesized a Mn-rich high-entropy ilmenite (Mg0.2Mn0.3Co0.15Ni0.15Zn0.2)TiO3 with a (Co+ Ni)/Mn ratio of unity (see Figure S9a of SupportingInformation for the PXRD pattern).In contrast to (MgMnCoNiZn)TiO3 with equimolaramounts of the magnetic ions, the magnetic and thermody-namic properties of the Mn-rich sample indicated theformation of a spin-glass state. χ(T) shows a Curie-Weissbehavior at high temperatures as in other high-entropyilmenites (Figure 5a). The Curie-Weiss fit yields an effectivemoment of ∼3.96 μB/f.u. and a Curie-Weiss temperature θCW= −44 K (Figure S9b of Supporting Information). This valueof the effective moment is close to the one expected from thechemical composition, μeff ∼ 3.97 μB/f.u., indicating thesuccessful incorporation of unequal amounts of the magneticions. θCW shifted to a larger negative value compared to that ofthe equimolar (MgMnCoNiZn)TiO3 (θCW = −27 K),reflecting enhanced antiferromagnetic interactions with alarger amount of Mn2+ ions. A closer look at the low-temperature region revealed a bifurcation of χ(T) between thezero-field-cooled (ZFC) and the field-cooled (FC) data below5 K. Additionally, the real part of the AC magneticsusceptibility, χ′(T), measured at zero external magnetic fieldshows a weak frequency dependence below the cusp at ∼5 K(Figure 5b), unlike that of (MgMnCoNiZn)TiO3. Thissuggests the formation of a spin-glass state below 5 K.Cmag(T) of (Mg0.2Mn0.3Co0.15Ni0.15Zn0.2)TiO3 shows a broadhump around 5 K instead of a sharp peak, which was graduallysuppressed by increasing the magnetic fields, in line with aspin-glass state.The (Mg0.2Mn0.3Co0.15Ni0.15Zn0.2)TiO3 sample was there-fore found to form a spin-glass state, unlike other high-entropyilmenites. In mixed ilmenites with two magnetic ions, such asMn1−xNixTiO3, a spin-glass phase has been observed near x =0.5, because of the competition between two distinct magneticstructures of Ne ́el-type and A-type antiferromagneticorder.40,41 Considering that both CoTiO3 and NiTiO3 forman identical in-plane ferromagnetic order, the chemicalcomposition of (Mg0.2Mn0.3Co0.15Ni0.15Zn0.2)TiO3 may beregarded as analogous to that of Mn0.5Ni0.5TiO3 with a spin-glass ground state. The ground state of high-entropy ilmenitesmay be solely controlled by the compositional ratio ofmagnetic ions.Nevertheless, we infer that the magnetic interactions in high-entropy ilmenites should be more subtle because of thepresence of different types of magnetic interactions in thenearest-neighbor bonds, such as Mn−Mn, Mn−Co, Mn−Ni,Co−Co, Co−Ni, and Ni−Ni pairs. The magnetic interactionsin the Co−Co, Co−Ni, and Ni−Ni pairs of the edge-shared90° bonds should be ferromagnetic due to the superexchangeinteractions of eg electrons, whereas the Mn−Mn bond yieldsantiferromagnetic interactions owing to the predominant directhopping of t2g electrons across the edges of the MnO6octahedra. The magnetic interactions in the Mn−Co andMn−Ni pairs are multifaceted because of the existence ofdifferent hopping processes of d-electrons, such as eg − eg or t2g− eg orbitals. In addition, the hopping process between the t2g− t2g orbitals is also active for the Mn−Co pair; the Mn−Coand Mn−Ni magnetic interactions are not thus fully identical,introducing additional competition in the high-entropyilmenites. We suspect that such complex magnetic interactionslead to distinct magnetic properties in high-entropy ilmenites.Indeed, the suppression of ordered moments is much morepronounced in the high-entropy sample, compared to themixed ilmenite Mn1−xNixTiO3,42 pointing to stronger magneticFigure 5. Magnetic and thermodynamic properties of the Mn-richhigh-entropy ilmenite (Mg0.2Mn0.3Co0.15Ni0.15Zn0.2)TiO3. (a) Tem-perature dependence of the magnetic susceptibility, χ(T). The insetshows a magnified view of the cusp at ∼5 K. (b) The real part of theAC magnetic susceptibility, χ′(T), measured at zero external magneticfield. The AC magnetic fields of 4 Oe were applied at the frequency of1, 10, 100, and 1000 Hz. (c) Magnetic heat capacity, Cmag(T), at lowtemperatures. The lattice specific heat was subtracted using the heatcapacity of the non-magnetic (Mg0.5Zn0.5)TiO3. A broad humpcentered at ∼5 K was gradually suppressed by increasing magneticfields, supporting a spin-glass state.Chemistry of Materials pubs.acs.org/cm Articlehttps://doi.org/10.1021/acs.chemmater.6c01899Chem. Mater. XXXX, XXX, XXX−XXXGDownloaded from pubs.​acs.​org/​cmatex/​article-pdf/​doi/​10.​1021/​acs.​chemmater.​6c01899/​68398719/​acs.​chemmater.​6c01899.​pdf by NATL INST FOR MATLS SCIENCE (NIMS) user on 11 September 2026https://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c01899/suppl_file/cm6c01899_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c01899/suppl_file/cm6c01899_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c01899/suppl_file/cm6c01899_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c01899/suppl_file/cm6c01899_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c01899/suppl_file/cm6c01899_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c01899?fig=fig5&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c01899?fig=fig5&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c01899?fig=fig5&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c01899?fig=fig5&ref=pdfpubs.acs.org/cm?ref=pdfhttps://doi.org/10.1021/acs.chemmater.6c01899?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asfluctuations. Since the mixed ilmenite Mn1−xNixTiO3 displaysrich magnetic phases in the intermediate x values, such as spin-reorientation transition,40,42 more complex high-entropyilmenites may potentially exhibit even richer magneticbehaviors via fine adjustment of the ratio of magnetic ions,which are worthy of further exploration.4. CONCLUSIONHigh-entropy ilmenite-type oxides MTiO3 with more than fivedifferent cations at the M-site were successfully synthesized.Despite the presence of strong cation disorder that leads tobond-disorder in magnetic exchange interactions, long-rangeantiferromagnetic order was identified in (MgMnCoNiZn)-TiO3 by the magnetic susceptibility, specific heat, and neutrondiffraction measurements. Long-range magnetic ordering wasretained in the presence of additional disorder introduced byaliovalent doping. We suspect that the robustness of the long-range magnetic order may be attributed to the presence oflonger-range magnetic interactions and the rigid lattice of theilmenite structure evading local distortion potentially inducedby aliovalent doping. On the other hand, by changing the ratioof magnetic ions, spin-glass freezing was observed, likely owingto the enhanced competition of distinct magnetic interactions.This indicates that magnetic ground states of the high-entropyilmenites can be controlled by the ratio of magnetic ions andrich magnetic phases may be realized by fine-tuning ofcompeting magnetic interactions. Furthermore, ilmenitecompounds have been reported to display a variety offunctional properties, including magnetoelectric effect,27,41ferro-axial order,43 toroidicity44 and nontrivial topologicalmagnetic excitations.30,45 Exploring these properties in high-entropy ilmenites can be an intriguing future subject.■ ASSOCIATED CONTENT*sı Supporting InformationThe Supporting Information is available free of charge athttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c01899.Powder X-ray diffraction patterns of all samples;Rietveld refinement; chemical characterization (EDX,XPS); annealing effects; AC magnetic susceptibility;specific heat; magnetization curve; additional character-ization of the Mn-rich sample (PDF)■ AUTHOR INFORMATIONCorresponding AuthorsTomohiro Takayama − Max Planck Institute for Solid StateResearch, Stuttgart 70569, Germany; Institute for FunctionalMatter and Quantum Technologies, University of Stuttgart,Stuttgart 70569, Germany; National Institute for MaterialsScience, Tsukuba, Ibaraki 305-0047, Japan; orcid.org/0000-0002-3492-2025; Email: TAKAYAMA.Tomohiro@nims.go.jpDamian Contant − Max Planck Institute for Solid StateResearch, Stuttgart 70569, Germany; Department ofChemistry, ENS Paris-Saclay, Université Paris-Saclay, Gif-sur-Yvette 91192, France; Present Address: Department ofPhysics, King’s College London, Strand, London, WC2R2LS, U.K; Email: damian.contant@kcl.ac.ukSebastian Bette − Max Planck Institute for Solid StateResearch, Stuttgart 70569, Germany; Email: S.Bette@fkf.mpg.deRobert Dinnebier − Max Planck Institute for Solid StateResearch, Stuttgart 70569, Germany; Email: R.Dinnebier@fkf.mpg.deHidenori Takagi − Max Planck Institute for Solid StateResearch, Stuttgart 70569, Germany; Institute for FunctionalMatter and Quantum Technologies, University of Stuttgart,Stuttgart 70569, Germany; Department of Physics,University of Tokyo, Bunkyo, Tokyo 113-0033, Japan;National Institute for Materials Science, Tsukuba, Ibaraki305-0047, Japan; Email: H.Takagi@fkf.mpg.deAuthorsIvan da Silva − ISIS Neutron and Muon Source, STFCRutherford Appleton Laboratory, Didcot, Oxon OX11 0QX,U.K.; orcid.org/0000-0002-4472-9675Diana Dragoe − Institute of Molecular Chemistry andMaterials of Orsay, UMR 8182 CNRS, Université Paris-Saclay, Orsay 91190, France; orcid.org/0000-0002-8536-1205Nita Dragoe − Institute of Molecular Chemistry and Materialsof Orsay, UMR 8182 CNRS, Université Paris-Saclay, Orsay91190, FranceComplete contact information is available at:https://pubs.acs.org/10.1021/acs.chemmater.6c01899FundingOpen access funding provided by Max Planck Society.NotesThe authors declare no competing financial interest.■ ACKNOWLEDGMENTSWe thank D. Bérardan and F. Orlandi for valuable discussions.We are grateful to V. Duppel and E. Bruecher for theirexperimental support. We acknowledge the provision ofbeamtime on GEM at the ISIS Neutron and Muon Source(Proposal No. RB2300010).46 D.C. acknowledges the ARPEprogram of ENS Paris-Saclay for support during his stay at theMax Planck Institute for Solid State Research. This work wassupported by the Deutsche Forschungsgemeinschaft (DFG),Project No. TA1086/1-1.■ REFERENCES(1) Yeh, J.-W.; Chen, S.-K.; Lin, S.-J.; Gan, J.-Y.; Chin, T.-S.; Shun,T.-T.; Tsau, C.-H.; Chang, S.-Y. Nanostructured high-entropy alloyswith multiple principal elements: Novel alloy design concepts andoutcomes. Adv. Eng. Mater. 2004, 6, 299−303.(2) George, E. P.; Raabe, D.; Ritchie, R. O. High-entropy alloys. Nat.Rev. Mater. 2019, 4, 515−534.(3) Rost, C. M.; Sachet, E.; Borman, T.; Moballegh, A.; Dickey, E.C.; Hou, D.; Jones, J. L.; Curtarolo, S.; Maria, J.-P. Entropy-stabilizedoxides. Nat. Commun. 2015, 6, 8485.(4) Musicó, B. L.; Gilbert, D.; Ward, T. Z.; Page, K.; George, E.;Yan, J.; Mandrus, D.; Keppens, V. The emergent field of high entropyoxides: Design, prospects, challenges, and opportunities for tailoringmaterial properties. APL Mater. 2020, 8, 040912.(5) Bérardan, D.; Franger, S.; Dragoe, D.; Meena, A. K.; Dragoe, N.Colossal dielectric constant in high entropy oxides. Phys. Status SolidiRRL 2016, 10, 328−333.(6) Bérardan, D.; Franger, S.; Meena, A. K.; Dragoe, N. Roomtemperature lithium superionic conductivity in high entropy oxides. J.Mater. Chem. A 2016, 4, 9536−9541.(7) Sarkar, A.; Velasco, L.; Wang, D.; Wang, Q.; Talasila, G.; deBiasi, L.; Kübel, C.; Brezesinski, T.; Bhattacharya, S. S.; Hahn, H.;Chemistry of Materials pubs.acs.org/cm Articlehttps://doi.org/10.1021/acs.chemmater.6c01899Chem. Mater. XXXX, XXX, XXX−XXXHDownloaded from pubs.​acs.​org/​cmatex/​article-pdf/​doi/​10.​1021/​acs.​chemmater.​6c01899/​68398719/​acs.​chemmater.​6c01899.​pdf by NATL INST FOR MATLS SCIENCE (NIMS) user on 11 September 2026https://pubs.acs.org/doi/10.1021/acs.chemmater.6c01899?goto=supporting-infohttps://pubs.acs.org/doi/suppl/10.1021/acs.chemmater.6c01899/suppl_file/cm6c01899_si_001.pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Tomohiro+Takayama"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://orcid.org/0000-0002-3492-2025https://orcid.org/0000-0002-3492-2025mailto:TAKAYAMA.Tomohiro@nims.go.jpmailto:TAKAYAMA.Tomohiro@nims.go.jphttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Damian+Contant"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfmailto:damian.contant@kcl.ac.ukhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Sebastian+Bette"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfmailto:S.Bette@fkf.mpg.demailto:S.Bette@fkf.mpg.dehttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Robert+Dinnebier"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfmailto:R.Dinnebier@fkf.mpg.demailto:R.Dinnebier@fkf.mpg.dehttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Hidenori+Takagi"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfmailto:H.Takagi@fkf.mpg.dehttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Ivan+da+Silva"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://orcid.org/0000-0002-4472-9675https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Diana+Dragoe"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://orcid.org/0000-0002-8536-1205https://orcid.org/0000-0002-8536-1205https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Nita+Dragoe"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.chemmater.6c01899?ref=pdfhttps://doi.org/10.1002/adem.200300567https://doi.org/10.1002/adem.200300567https://doi.org/10.1002/adem.200300567https://doi.org/10.1038/s41578-019-0121-4https://doi.org/10.1038/ncomms9485https://doi.org/10.1038/ncomms9485https://doi.org/10.1063/5.0003149https://doi.org/10.1063/5.0003149https://doi.org/10.1063/5.0003149https://doi.org/10.1002/pssr.201600043https://doi.org/10.1039/C6TA03249Dhttps://doi.org/10.1039/C6TA03249Dpubs.acs.org/cm?ref=pdfhttps://doi.org/10.1021/acs.chemmater.6c01899?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-aset al. High entropy oxides for reversible energy storage. Nat. Commun.2018, 9, 3400.(8) Lun, Z.; Ouyang, B.; Kwon, D.-H.; Ha, Y.; Foley, E. E.; Huang,T.-Y.; Cai, Z.; Kim, H.; Balasubramanian, M.; Sun, Y.; et al. Cation-disordered rocksalt-type high-entropy cathodes for Li-ion batteries.Nat. Mater. 2021, 20, 214−221.(9) Wang, T.; Chen, H.; Yang, Z.; Liang, J.; Dai, S. High-entropyperovskite fluorides: A new platform for oxygen evolution catalysis. J.Am. Chem. Soc. 2020, 142, 4550−4554.(10) Jiang, B.; Yu, Y.; Cui, J.; Liu, X.; Xie, L.; Liao, J.; Zhang, Q.;Huang, Y.; Ning, S.; Jia, B.; et al. High-entropy-stabilizedchalcogenides with high thermoelectric performance. Science 2021,371, 830−834.(11) Jimenez-Segura, M. P.; Takayama, T.; Bérardan, D.; Hoser, A.;Reehuis, M.; Takagi, H.; Dragoe, N. Long-range magnetic ordering inrocksalt-type high-entropy oxides. Appl. Phys. Lett. 2019, 114, 122401.(12) Zhang, J.; Yan, J.; Calder, S.; Zheng, Q.; McGuire, M. A.;Abernathy, D. L.; Ren, Y.; Lapidus, S. H.; Page, K.; Zheng, H.; et al.Long-range antiferromagnetic order in a rocksalt high-entropy oxide.Chem. Mater. 2019, 31, 3705−3711.(13) Witte, R.; Sarkar, A.; Kruk, R.; Eggert, B.; Brand, R. A.; Wende,H.; Hahn, H. High-entropy oxides: An emerging prospect formagnetic rare-earth transition metal perovskites. Phys. Rev. Mater.2019, 3, 034406.(14) Sharma, Y.; Mazza, A. R.; Musico, B. L.; Skoropata, E.; Nepal,R.; Jin, R.; Ievlev, A. V.; Collins, L.; Gai, Z.; Chen, A.; et al. Magnetictexture in insulating single crystal high entropy oxide spinel films. ACSAppl. Mater. Interfaces 2021, 13, 17971−17977.(15) Vayer, F.; Decorse, C.; Bérardan, D.; Dragoe, N. New entropy-s t a b i l i z e d o x i d e w i t h p y r o c h l o r e s t r u c t u r e :Dy2(Ti0.2Zr0.2Hf0.2Ge0.2Sn0.2)2O7. J. Alloys Comp. 2021, 883, 160773.(16) Sarkar, A.; Kruk, R.; Hahn, H. Magnetic properties of highentropy oxides. Dalton Trans. 2021, 50, 1973−1982.(17) Rák, Z.; Brenner, D. W. Exchange interactions and long-rangemagnetic order in the (Mg, Co, Cu, Ni, Zn)O entropy-stabilizedoxide: A theoretical investigation. J. Appl. Phys. 2020, 127, 185108.(18) Shirane, G.; Pickart, S. J.; Ishikawa, Y. Neutron diffraction studyof antiferromagnetic MnTiO3 and NiTiO3. J. Phys. Soc. Jpn. 1959, 14,1352−1360.(19) Newnham, R. E.; Fang, J. H.; Santoro, R. P. Crystal structureand magnetic properties of CoTiO3. Acta Crystallogr. 1964, 17, 240−242.(20) Coelho, A. A. TOPAS and TOPAS-Academic: an optimizationprogram integrating computer algebra and crystallographic objectswritten in C++. J. Appl. Crystallogr. 2018, 51, 210−218.(21) Kidoh, K.; Tanaka, K.; Marumo, F.; Takei, H. Electron densitydistribution in an ilmenite-type crystal of cobalt(II). titanium(IV)trioxide. Acta Crystallogr. 1984, B40, 92−96.(22) Hannon, A. C. Results on disordered materials from theGEneral Materials diffractometer, GEM, at ISIS. Nucl. Instrum.Methods Phys. Res., Sect. A 2005, 551, 88−107.(23) Wills, A. S. A new protocol for the determination of magneticstructures using simulated annealing and representational analysis(SARAh). Phys. B 2000, 276-278, 680−681.(24) Rodríguez-Carvajal, J. Recent advances in magnetic structuredetermination by neutron powder diffraction. Phys. B 1993, 192, 55−69.(25) Yamauchi, H.; Hiroyoshi, H.; Yamada, M.; Watanabe, H.;Takei, H. Spin flopping in MnTiO3. J. Magn. Magn. Mater. 1983, 31-34, 1071−1072.(26) Harada, J. K.; Balhorn, L.; Hazi, J.; Kemei, M. C.; Seshadri, R.Magnetodielectric coupling in the ilmenites MTiO3 (M = Co, Ni).Phys. Rev. B 2016, 93, 104404.(27) Mufti, N.; Blake, G. R.; Mostovoy, M.; Riyadi, S.; Nugroho, A.A.; Palstra, T. T. M. Magnetoelectric coupling in MnTiO3. Phys. Rev.B 2011, 83, 104416.(28) Buyers, W. J. L.; Holden, T. M.; Svensson, E. C.; Cowley, R. A.;Stevenson, R. W. H. Character of excitations in substitutionallydisordered antiferromagnets. Phys. Rev. Lett. 1971, 27, 1442.(29) Cao, Y.; Liu, X.; Xu, W.; Yin, W.-G.; Meyers, D.; Kim, J.; Casa,D.; Upton, M. H.; Gog, T.; Berlijn, T.; et al. Giant spin gap andmagnon localization in the disordered Heisenberg antiferromagnetSr2Ir1‑xRuxO4. Phys. Rev. B 2017, 95, 121103.(30) Yuan, B.; Khait, I.; Shu, G.-J.; Chou, F. C.; Stone, M. B.;Clancy, J. P.; Paramekanti, A.; Kim, Y.-J. Dirac magnons in ahoneycomb lattice quantum XY magnet CoTiO3. Phys. Rev. X 2020,10, 011062.(31) Ferreira-Carvalho, M. M.; Chen, S. H.; Ku, Y. C.; Jose, A.;Morrow, R.; Kuo, C. Y.; Chang, C. F.; Hu, Z.; Haverkort, M. W.;Tjeng, L. H. Direct evidence of a near-ideal Jeff = 1/2 ground state intriangular-lattice Na2BaCo(PO4)2. Phys. Rev. Mater. 2026, 10, 025004.(32) Dey, K.; Sauerland, S.; Ouladdiaf, B.; Beauvois, K.; Wadepohl,H.; Klingeler, R. Magnetostructural coupling in ilmenite-type NiTiO3.Phys. Rev. B 2021, 103, 134438.(33) Abragam, A.; Bleaney, B. Electron Paramagnetic Resonance ofTransition Ions; Clarendon Press, 1970.(34) Shen, Y.; Zhang, G.; Zhang, Q.; Gui, X.; Zhang, Y.; Lee, H.;Kuo, C.-T.; Lee, J.-S.; Sutarto, R.; Ye, F.; et al. Long-range magneticorder with disordered spin orientations in a high-entropy anti-ferromagnet. Nat. Commun. 2026, 17, 3558.(35) Braun, J. L.; Rost, C. M.; Lim, M.; Giri, A.; Olson, D. H.;Kotsonis, G. N.; Stan, G.; Brenner, D. W.; Maria, J.-P.; Hopkins, P. E.Charge-induced disorder controls the thermal conductivity ofentropy-stabilized oxides. Adv. Mater. 2018, 30, 1805004.(36) Mazza, A. R.; Acharya, S. R.; Wąsik, P.; Lapano, J.; Li, J.;Musico, B. L.; Keppens, V.; Nelson, C. T.; May, A. F.; Brahlek, M.;et al. Variance induced decoupling of spin, lattice, and charge orderingin perovskite nickelates. Phys. Rev. Res. 2023, 5, 013008.(37) Contant, D.; McNally, G. M.; Krajewska, A.; Takagi, H.;Takayama, T. Robust electronic phase transition against cationdisorder in high-entropy pyrochlore iridates. AIP Adv. 2024, 14,085316.(38) Hwang, I. Y.; Lee, K. H.; Chung, J.-H.; Ikeuchi, K.; Garlea, V.O.; Yamauchi, H.; Akatsu, M.; Shamoto, S. Spin wave excitations inhoneycomb antiferromagnet MnTiO3. J. Phys. Soc. Jpn. 2021, 90,064708.(39) Das, S.; Voleti, S.; Saha-Dasgupta, T.; Paramekanti, A. XYmagnetism, Kitaev exchange, and long-range frustration in the Jeff = 1/2 honeycomb cobaltates. Phys. Rev. B 2021, 104, 134425.(40) Yoshizawa, H.; Kawano, H.; Mori, H.; Mitsuda, S.; Ito, A. Phasediagram of a Heisenberg-like spin glass NixMn1‑xTiO3. Phys. B 1992,180-181, 94−96.(41) Yamaguchi, Y.; Nakano, T.; Nozue, Y.; Kimura, T. Magneto-electric effect in an XY-like spin glass system NixMn1‑xTiO3. Phys. Rev.Lett. 2012, 108, 057203.(42) Chi, S.; Ye, F.; Zhou, H. D.; Choi, E. S.; Hwang, J.; Cao, H.;Fernandez-Baca, J. A. Magnetoelectric coupling tuned by competinganisotropies in Mn1‑xNixTiO3. Phys. Rev. B 2014, 90, 144429.(43) Hayashida, T.; Kimura, K.; Kimura, T. Electric field−inducedmagnetochiral dichroism in a ferroaxial crystal. Proc. Natl. Acad. Sci. U.S. A. 2023, 120, No. e2303251120.(44) Du, K.; Jo, D.; Xu, X.; Huang, F.-T.; Lee, M.-H.; Chu, M.-W.;Wang, K.; Guo, X.; Zhao, L.; Vanderbilt, D.; et al. Electric toroidalinvariance generates distinct transverse electromagnetic responses.Nat. Phys. 2026, 22, 61−67.(45) Elliot, M.; McClarty, P. A.; Prabhakaran, D.; Johnson, R. D.;Walker, H. C.; Manuel, P.; Coldea, R. Order-by-disorder from bond-dependent exchange and intensity signature of nodal quasiparticles ina honeycomb cobaltate. Nat. Commun. 2021, 12, 3936.(46) Takayama, T.; da Silva, I. Magnetic structure analysis of ilmenite-type high-entropy oxide; STFC ISIS Neutron and Muon Source. 2023.(47) Shannon, R. D. Revised effective ionic radii and systematicstudies of interatomic distances in halides and chalcogenides. ActaCrystallogr. 1976, A32, 751−767.(48) Momma, K.; Izumi, F. VESTA3 for three-dimensionalvisualization of crystal, volumetric and morphology data. J. Appl.Crystallogr. 2011, 44, 1272−1276.Chemistry of Materials pubs.acs.org/cm Articlehttps://doi.org/10.1021/acs.chemmater.6c01899Chem. Mater. XXXX, XXX, XXX−XXXIDownloaded from pubs.​acs.​org/​cmatex/​article-pdf/​doi/​10.​1021/​acs.​chemmater.​6c01899/​68398719/​acs.​chemmater.​6c01899.​pdf by NATL INST FOR MATLS SCIENCE (NIMS) user on 11 September 2026https://doi.org/10.1038/s41467-018-05774-5https://doi.org/10.1038/s41563-020-00816-0https://doi.org/10.1038/s41563-020-00816-0https://doi.org/10.1021/jacs.9b12377?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/jacs.9b12377?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1126/science.abe1292https://doi.org/10.1126/science.abe1292https://doi.org/10.1063/1.5091787https://doi.org/10.1063/1.5091787https://doi.org/10.1021/acs.chemmater.9b00624?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1103/PhysRevMaterials.3.034406https://doi.org/10.1103/PhysRevMaterials.3.034406https://doi.org/10.1021/acsami.1c01344?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acsami.1c01344?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1016/j.jallcom.2021.160773https://doi.org/10.1016/j.jallcom.2021.160773https://doi.org/10.1016/j.jallcom.2021.160773https://doi.org/10.1039/D0DT04154Hhttps://doi.org/10.1039/D0DT04154Hhttps://doi.org/10.1063/5.0008258https://doi.org/10.1063/5.0008258https://doi.org/10.1063/5.0008258https://doi.org/10.1143/JPSJ.14.1352https://doi.org/10.1143/JPSJ.14.1352https://doi.org/10.1107/S0365110X64000615https://doi.org/10.1107/S0365110X64000615https://doi.org/10.1107/S1600576718000183https://doi.org/10.1107/S1600576718000183https://doi.org/10.1107/S1600576718000183https://doi.org/10.1107/S0108768184001804https://doi.org/10.1107/S0108768184001804https://doi.org/10.1107/S0108768184001804https://doi.org/10.1016/j.nima.2005.07.053https://doi.org/10.1016/j.nima.2005.07.053https://doi.org/10.1016/S0921-4526(99)01722-6https://doi.org/10.1016/S0921-4526(99)01722-6https://doi.org/10.1016/S0921-4526(99)01722-6https://doi.org/10.1016/0921-4526(93)90108-Ihttps://doi.org/10.1016/0921-4526(93)90108-Ihttps://doi.org/10.1016/0304-8853(83)90802-8https://doi.org/10.1103/PhysRevB.93.104404https://doi.org/10.1103/PhysRevB.83.104416https://doi.org/10.1103/PhysRevLett.27.1442https://doi.org/10.1103/PhysRevLett.27.1442https://doi.org/10.1103/PhysRevB.95.121103https://doi.org/10.1103/PhysRevB.95.121103https://doi.org/10.1103/PhysRevB.95.121103https://doi.org/10.1103/PhysRevX.10.011062https://doi.org/10.1103/PhysRevX.10.011062https://doi.org/10.1103/65bn-63kjhttps://doi.org/10.1103/65bn-63kjhttps://doi.org/10.1103/PhysRevB.103.134438https://doi.org/10.1038/s41467-026-70184-xhttps://doi.org/10.1038/s41467-026-70184-xhttps://doi.org/10.1038/s41467-026-70184-xhttps://doi.org/10.1002/adma.201805004https://doi.org/10.1002/adma.201805004https://doi.org/10.1103/PhysRevResearch.5.013008https://doi.org/10.1103/PhysRevResearch.5.013008https://doi.org/10.1063/5.0201638https://doi.org/10.1063/5.0201638https://doi.org/10.7566/JPSJ.90.064708https://doi.org/10.7566/JPSJ.90.064708https://doi.org/10.1103/PhysRevB.104.134425https://doi.org/10.1103/PhysRevB.104.134425https://doi.org/10.1103/PhysRevB.104.134425https://doi.org/10.1016/0921-4526(92)90671-Ehttps://doi.org/10.1016/0921-4526(92)90671-Ehttps://doi.org/10.1103/PhysRevLett.108.057203https://doi.org/10.1103/PhysRevLett.108.057203https://doi.org/10.1103/PhysRevB.90.144429https://doi.org/10.1103/PhysRevB.90.144429https://doi.org/10.1073/pnas.2303251120https://doi.org/10.1073/pnas.2303251120https://doi.org/10.1038/s41567-025-03100-7https://doi.org/10.1038/s41567-025-03100-7https://doi.org/10.1038/s41467-021-23851-0https://doi.org/10.1038/s41467-021-23851-0https://doi.org/10.1038/s41467-021-23851-0https://doi.org/10.1107/S0567739476001551https://doi.org/10.1107/S0567739476001551https://doi.org/10.1107/S0021889811038970https://doi.org/10.1107/S0021889811038970pubs.acs.org/cm?ref=pdfhttps://doi.org/10.1021/acs.chemmater.6c01899?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as