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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Ferromagnetic Double Perovskite Semiconductors with Tunable Properties

Abstract The authors successfully dope the magnetically silent double perovskite semiconductor Sr 2 GaSbO 6 to induce ferromagnetism and tune its bandgap, with Ga 3+ partially substituted by the magnetic trivalent cation Mn 3+ , in a rigid cation ordering with Sb 5+ . The new ferromagnetic semiconducting Sr 2 Ga 1− x Mn x SbO 6 double perovskite, which crystallizes in tetragonal symmetry (space group I 4/ m ) and has tunable ferromagnetic ordering temperature and bandgap, suggests that magnetic ion doping of double perovskites is a productive avenue toward obtaining materials for application in next‐generation oxide‐based spintronic devices.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Predictive Design of Hybrid Improper Ferroelectric Double Perovskite Oxides

The computational design of suitable multiferroic double perovskite oxides requires finding materials that exhibit sizable polarization, magnetization, and coupling between them. Oxides with the chemical formula of AA'BB'O 6 with building blocks of ABO 3 single perovskite oxides in centrosymmetric Pnma symmetry are strong candidates that have been reported to satisfy such criteria. The system lowers to noncentrosymmetric, polar P2 1 symmetry if A/A' layered and B/B' rocksalt cation orderings are imposed. A detailed compositional search over a variety of chemical spaces followed by evaluating their polarization may lead to the identification of more of these compounds with ferroelectric ordering. The standard density functional theory practices to estimate polarization within the Berry phase formalism require the systems to be perfectly insulating. The number of compounds that can be evaluated using this method is therefore limited. In this work, we introduce a predictive learning strategy based on importance sampling to build a series of machine learning models using results from first-principles simulations to predict polarization and the corresponding switching barrier. The geometry-driven features related to charge states and cationic radii play key roles in predicting the switching barrier with complementary contributions from the key structural mode-based order parameters. These modes become important to draw reasonable predictions of polarization components from machine learning models. In conclusion, our predictive models identify candidates with high polarizations and low switching barriers from a pool of double perovskite oxides, suitable for future investigation for their potential applications in spintronic devices.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Electronic structure and optical properties of halide double perovskites from a Wannier-localized optimally-tuned screened range-separated hybrid functional

Halide double perovskites are a chemically diverse and growing class of compound semiconductors that are promising for optoelectronic applications. However, the prediction of their fundamental gaps and optical properties with density functional theory (DFT) and ab initio many-body perturbation theory has been a significant challenge. Recently, a nonempirical Wannier-localized optimally tuned screened range-separated hybrid (WOT-SRSH) functional has been shown to accurately produce the fundamental band gaps of a wide set of semiconductors and insulators, including lead halide perovskites. Here, in this study, we apply the WOT-SRSH functional to five halide double perovskites and compare the results with those obtained from other known functionals and previous GW calculations. We also use the approach as a starting point for GW calculations and we compute the band structures and optical absorption spectrum for Cs 2 AgBiBr 6 , using both time-dependent DFT and the GW-Bethe-Salpeter equation approach. We show that the WOT-SRSH functional leads to accurate fundamental and optical band gaps, as well as optical absorption spectra, consistent with spectroscopic measurements, thereby establishing WOT-SRSH as a viable method for the accurate prediction of optoelectronic properties of halide double perovskites.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Metamagnetism and kinetic arrest in a long-range ferromagnetically ordered multicaloric double perovskite Y 2 CoMnO 6

A systematic magnetic study of the double perovskite oxide Y 2 CoMnO 6 (YCMO) has been performed. A monoclinic P21/n phase of YCMO was synthesized using a sol-gel method. Neutron diffraction (ND) measurements evidence the onset of long-range ferromagnetic (FM) ordering at TC ~ 76 K, which persists down to 5 K. The presence of 25% antisite disorder, estimated from the ND data, leads to the appearance of short-range antiferromagnetic (AFM) interactions. The existence of thermal hysteresis due to competing interactions between FM and AFM phases is observed in the M vs. T measurements. The pinning of magnetic domain walls at the Co/Mn antiphase boundaries results in a metamagnetic-like behavior. The field dependence of thermomagnetic irreversibility and the nature of virgin curves indicate the occurrence of a kinetic arrest phenomenon, which is further verified via cooling and heating of the system in an unequal fields (CHUF) protocol. In full agreement with the ND data, a detailed analysis of critical exponents near the paramagnetic (PM)-FM phase transition also establishes YCMO as a long-range interacting mean-field system. A close examination of the temperature- and field-dependent magnetic entropy change yields an in-depth understanding of coexisting magnetically ordered and disordered phases in YCMO, leading to a comprehensive magnetic phase diagram of this multifunctional double perovskite system.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Understanding the evolution of double perovskite band structure upon dimensional reduction

Recent investigations into the effects of dimensional reduction on halide double perovskites have revealed an intriguing change in band structure when the three-dimensional (3D) perovskite is reduced to a two-dimensional (2D) perovskite with inorganic sheets of monolayer thickness (n = 1). The indirect bandgap of 3D Cs 2 AgBiBr 6 becomes direct in the n = 1 perovskite whereas the direct bandgap of 3D Cs 2 AgTlBr 6 becomes indirect at the n = 1 limit. Here, we apply a linear combination of atomic orbitals approach to uncover the orbital basis for this bandgap symmetry transition with dimensional reduction. We adapt our previously established method for predicting band structures of 3D double perovskites for application to their 2D congeners, emphasizing new considerations required for the 2D lattice. In particular, we consider the inequivalence of the terminal and bridging halides and the consequences of applying translational symmetry only along two dimensions. The valence and conduction bands of the layered perovskites can be derived from symmetry adapted linear combinations of halide p orbitals propagated across the 2D lattice. The dispersion of each band is then determined by the bonding and antibonding interactions of the metal and halide orbitals, thus affording predictions of the essential features of the band structure. We demonstrate this analysis for 2D Ag–Bi and Ag–Tl perovskites with sheets of mono- and bilayer thickness, establishing a detailed understanding of their band structures, which enables us to identify the key factors that drive the bandgap symmetry transitions observed at the n = 1 limit. Importantly, these insights also allow us to make the general prediction that direct → indirect or indirect → direct bandgap transitions in the monolayer limit are most likely in double perovskite compositions that involve participation of metal d orbitals at the band edges or that have no metal-orbital contributions to the valence band, laying the groundwork for the targeted realization of this phenomenon.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Structure and properties of the Sr 2 In 1-x Sn x SbO 6 double perovskite

A series of n -type oxide double perovskite semiconductors, Sr 2 In 1-x Sn x SbO 6 (0 ≤ x ≤ 0.3) has been synthesized; Sn 4+ partially substitutes for In 3+ . 121 Sb and 119 Sn Mössbauer spectroscopy are employed to investigate the B-site cation ordering because this issue cannot be resolved by conventional diffraction techniques alone. Rigid ordering between In 3+ /Sn 4+ and Sb 5+ sites is revealed by the spectroscopic method, and hence in combination with the structural parameters extracted from the XRD structural refinements, the crystallographic structure of this series of compounds is depicted. Furthermore, the temperature dependent magnetic susceptibilities, band gaps, and carrier type are characterized, and the calculated band structure is presented.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Dipolar and quadrupolar correlations in the 5⁢𝑑 2 Re-based double perovskites Ba 2 ⁢ YReO 6 and Ba 2 ⁢ ScReO 6

Double perovskites containing heavy transition-metal ions are an important family of compounds for the study of the interplay between electron correlation and spin-orbit coupling. Here, by combining magnetic susceptibility, heat capacity, and neutron scattering measurements, we investigate the dipolar and quadrupolar correlations in two prototypal rhenium-based double perovskite compounds Ba 2 ⁢YReO 6 and Ba 2 ⁢ ScReO 6 . A type-I dipolar antiferromagnetic ground state with a propagation vector 𝐪 = (0,0,1) is observed in both compounds. At temperatures above the magnetic transitions, a quadrupolar ordered phase is identified. Weak spin excitations, which are gapped at low temperatures and softened in the correlated paramagnetic phase, are explained using a minimal model that considers both the dipolar and quadrupolar interactions. In conclusion, at larger wave vectors, we observe dominant phonon excitations that are well described by density functional calculations.

Omar, Otkur [University of Science and Technology ↗
DOE OSTI2022

Yttrium-based Double Perovskite Nanorods for Electrocatalysis

In this work, we investigate the effect of chemical composition of double perovskite nanorods on their versatile electrocatalytic activity not only as supports for the oxidation of small organic molecules but also as catalysts for the oxygen evolution reaction. Specifically, Y 2 CoMnO 6 and Y 2 NiMnO 6 nanorods with average diameters of 300 nm were prepared by a two-step hydrothermal method, in which the individual effects of synthetic parameters, such as the pH, annealing temperature, and precursor ratios on both the composition and morphology, were systematically investigated. When used as supports for Pt nanoparticles, Y 2 CoMnO 6 /Pt catalysts exhibited an electrocatalytic activity for the methanol oxidation reaction, which is 2.1 and 1.3 times higher than that measured for commercial Pt/C and Y 2 NiMnO 6 /Pt. Similarly, the Co-based catalyst support material displayed an ethanol oxidation activity, which is 2.3 times higher than both Pt/C and Y 2 NiMnO 6 /Pt. This clear enhancement in the activity for Y 2 CoMnO 6 can largely be attributed to strong metal-support interactions, as evidenced by a downshift in the binding energy of the Pt 4f bands, measured by XPS, which is often correlated not only with a downshift in the d-band center but also to a decreased adsorption of poisoning adsorbates. Moreover, when used as catalysts for the oxygen evolution reaction, Y 2 CoMnO 6 displayed a much greater activity as compared with Y 2 NiMnO 6 . This behavior can largely be attributed not only to a preponderance of comparatively more favorable oxidation states and electronic configurations but also to the formation of an active layer on the surface of the Y 2 CoMnO 6 catalyst, which collectively give rise to improved performance metrics and greater stability as compared with both IrO 2 and Y 2 NiMnO 6 . Overall, these results highlight the importance of both the chemical composition and the electronic structure of double perovskites, especially when utilized in multi-functional roles as either supports or catalysts.

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2020

In Situ Structural and Electrical Conductivity Characterization of Sr2MMoO6-δ Double Perovskite Solid Oxide Fuel Cell Anode Materials

In this study, a series of Sr 2 MMoO 6-δ double perovskite solid oxide fuel cell (SOFC) anode materials (where 0 <= δ <= 0.041 and M = Fe, Co, or Ni) were synthesized, and the changes in their morphologies under relevant SOFC operating conditions were explored. Ultra-small-angle X-ray scattering (USAXS), small-angle X-ray scattering (SAXS), and wide-angle X-ray scattering (WAXS) were used to determine changes in the microstructures and phase compositions of the anode materials at high temperatures and under a reducing atmosphere. The stability of the double perovskite structure was found to be highly dependent on the identity of the cation M, such that when M = Fe, the material remained stable over the course of the experiments. However, when M = Co or Ni, significant changes in the microstructure and phase composition were observed. An in situ study of the M = Co sample, in which electrical conductivity and USAXS/SAXS/WAXS measurements were conducted simultaneously, revealed the structural degradation mechanisms and electrical conductivity changes over a range of temperatures. To conduct these measurements, a cell was developed that allowed for a sample mounted on Pt wires to be placed in the X-ray beam and heated under gas flow comprising 4% mass H 2 and 96% mass N 2 . The resulting measurements allowed for the direct comparison of the electrical and morphological changes occurring in the material under operating conditions, such that increases in conductivity could be attributed to the growth of new phases.

25 ENERGY STORAGE↗
DOE OSTI2022

Hybrid Layered Double Perovskite Halides of Transition Metals

Hybrid layered double perovskite (HLDP) halides comprise hexacoordinated 1+ and 3+ metals in the octahedral sites within a perovskite layer and organic amine cations between the layers. Here, progress on such materials has hitherto been limited to compounds containing main group 3+ ions isoelectronic with Pb II (such as Sb III and Bi III ). Furthermore, we report eight HLDP halides from the A 2 M I M III X 8 family, where A = para-phenylenediammonium (PPDA), 1,4-butanediammonium (1,4-BDA), or 1,3-propanediammonium (1,3-PDA); M I = Cu or Ag; M III = Ru or Mo; X = Cl or Br. The optical band gaps, which lie in the range 1.55 to 2.05 eV, are tunable according to the layer composition, but are largely independent of the spacer. Magnetic measurements carried out for (PPDA) 2 Ag I Ru III Cl 8 and (PPDA) 2 Ag I Mo III Cl 8 show no obvious evidence of a magnetic ordering transition. While the t 2g 3 Mo III compound displays Curie–Weiss behavior for a spin-only d 3 ion, the t 2g 5 Ru III compound displays marked deviations from the Kotani theory.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Magnetic ground state of La 2 LiMoO 6 : A comparison with other Mo 5+ ( S=1/2 ) double perovskites

La 2 LiMoO 6 is a double perovskite (DP) with P2 1 /n symmetry based on the Mo5+ ion, 4d1, t2g1, S=1/2. It is isostructural with Sr 2 YMoO 6 , the magnetic ground state of which is apparently a very unusual collective spin singlet or valence-bond glass state as is the case for cubic (Fm-3m) Ba 2 YMoO 6 . Initial studies of La 2 LiMoO 6 suggested a different ground state from the other DPs but no clear conclusions could be drawn. A more detailed study is presented here including magnetic susceptibility, heat capacity, and elastic neutron-scattering results. This DP is now well characterized as an antiferromagnet, T N =18K, via observation of magnetic Bragg peaks in neutron scattering and an anomaly in the magnetic heat capacity. The ordering wave vector is k=( 1/21/2 0), consistent with a type I face-centered-cubic magnetic structure, and the ordered moment on Mo 5+ is 0.32(11)μ B , much reduced from the spin-only value of 1μ B . The index, f=|v c |/T N ~3, indicates a low level of frustration. The heat-capacity data above T N can be interpreted in terms of a one-dimensional spin-correlation model, as can the low-temperature data which follow a T 1 power law. This is consistent with an earlier suggestion. The difference with isostructural Sr 2 YMoO 6 is attributed to differences in the local distortion of the Mo–O octahedron and the resulting orbital ordering.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Lead-Free Cs 4 CuSb 2 Cl 12 Layered Double Perovskite Nanocrystals

Concerns about the toxicity of lead-based perovskites have aroused great interest for the development of alternative lead-free perovskite-type materials. Recently, theoretical calculations predict that Pb 2+ cations can be substituted by a combination of Cu 2+ and Sb 3+ cations to form a vacancy-ordered layered double perovskite structure with superior optoelectronic properties. However, accessibilities to this class of perovskite-type materials remain inadequate, hindering their practical implementations in various applications. Here, we report the first colloidal synthesis of Cs 4 CuSb 2 Cl 12 perovskite-type nanocrystals (NCs). The resulting NCs exhibit a layered double perovskite structure with ordered vacancies and a direct bandgap of 1.79 eV. A composition-structure-property relationship has been established by investigating a series of Cs 4 Cu x Ag 2-2x Sb 2 Cl 12 perovskite-type NCs (0 ≤ x ≤ 1). The composition-induced crystal structure transformation, thus the electronic bandgap evolution has been explored by experimental observations and further confirmed by theoretical calculations. Taking advantages of both the unique electronic structure and solution processability, we demonstrate that the Cs 4 CuSb 2 Cl 12 NCs can be solution-processed as high-speed photodetectors with ultrafast photo-response and narrow bandwidth. We anticipate that our study will prompt future research to design and fabricate novel and high-performance lead-free perovskite-type NCs for a range of applications.

25 ENERGY STORAGE↗
DOE OSTI2022

Spin-orbit coupling controlled ground states in the double perovskite iridates $\textit{A}_2\textit{B}$IrO$_6$ ($\textit{A}$ = Ba, Sr; $\textit{B}$ = Lu, Sc)

Iridates with the 5$d^4$ electronic configuration have attracted recent interest due to reports of magnetically ordered ground states despite longstanding expectations that their strong spin-orbit coupling would generate a $\textit{J}$ = 0 electronic ground state for each Ir 5+ ion. The major focus of prior research has been on the double perovskite iridates Ba 2 YIrO 6 and Sr 2 YIrO 6 , where the nature of the ground states (i.e., ordered vs nonmagnetic) is still controversial. Here, in this work, we present neutron powder diffraction, high-energy-resolution fluorescence-detected x-ray absorption spectroscopy (HERFD-XAS), resonant inelastic x-ray scattering (RIXS), magnetic susceptibility, and muon spin relaxation data on the related double perovskite iridates Ba 2 LuIrO 6 , Sr 2 LuIrO 6 , Ba 2 ScIrO 6 , and Sr 2 ScIrO 6 that enable us to gain a general understanding of the electronic and magnetic properties for this family of materials. Our HERFD-XAS and RIXS measurements establish $\textit{J}$ = 0 electronic ground states for the Ir 5+ ions in all cases, with similar values for Hund's coupling $J_H$ and the spin-orbit coupling constant $λ_{\text{SOC}}$. Our bulk susceptibility and muon spin relaxation data find no evidence for long-range magnetic order or spin freezing, but they do exhibit weak magnetic signals that are consistent with extrinsic local moments. Our results indicate that the large $λ_{\text{SOC}}$ is the key driving force behind the electronic and magnetic ground states realized in the $5d^4$ double perovskite iridates, which agrees well with conventional wisdom.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Carrier Diffusion Lengths Exceeding 1 μm Despite Trap-Limited Transport in Halide Double Perovskites

In this work we image charge carrier transport over nanometers–micrometers and picoseconds–microseconds in halide double perovskites Cs 2 AgBiBr 6 and Cs 2 AgTlBr 6 single crystals using stroboscopic scattering microscopy. Both materials exhibit long, microsecond carrier lifetimes because of their indirect or symmetry-forbidden direct bandgaps. We extract free-charge and trap-limited mobilities near the surface and in the crystal bulk. The free-charge mobilities for both materials (~10–50 cm 2 /(V s)) can reach those reported for archetypal lead halide perovskites. We measure trap densities exceeding 10 17 cm –3 within ~20 nm of the crystal surface. Measurements on freshly cleaved or thermally annealed crystals suggest the traps are primarily halide vacancies that likely form through surface bromine degassing. Although these traps considerably slow charge transport, they are energetically shallow, enabling thermally induced detrapping and mobile carriers over microseconds at room temperature. This defect tolerance yields carrier diffusion lengths exceeding 1 μm even in the presence of large trap densities and under solar excitation conditions where traps are not saturated. These results suggest that halide double perovskites could rival the best lead-based perovskites for photovoltaic and optoelectronic applications.

36 MATERIALS SCIENCE↗
DOE OSTI2021

A Machine Learning Approach for the Prediction of Formability and Thermodynamic Stability of Single and Double Perovskite Oxides

Perovskite oxides continue to attract huge interest due to their fascinating and wide-ranging properties for diverse applications. The tunability of these properties may be further enhanced by increasing their compositional complexity via double perovskite-ordered configurations containing multiple cations. In this work, we focus on an exhaustive chemical space of single and double oxide perovskites and optimally explore this space to identify novel compositions that are likely to form stable compounds. Critically, we examine the relationship between formability, the practical ability to synthesize a compound, and stability, the thermodynamic preference to form the structure. Our formability and stability training data sets were enumerated from the available experimental literature and in-house density functional theory computations and contained 1505 and 3469 examples, respectively, representing state-of-the-art in the current open literature in perovskite and double perovskite compounds. Subsequently, cross-validated and highly accurate machine learning classification models are built using these training data sets and employed to screen for novel stable oxide perovskites. The study identifies (1) atomic features relevant to prediction of formability and stability in perovskite and double perovskite compounds, (2) the importance of including energy contributions due to local structural relaxations going beyond the high symmetry perovskite phase, and (3) 437,828 double perovskite compounds that are likely to be stable and 891,188 compounds that are likely to be formable. From the intersection of this large chemical space of formable and stable oxide perovskites, 414 compositions are identified as the most promising candidates for future experimental synthesis of novel oxide perovskites. The developed models may be generalized and have implications beyond perovskite discovery if applied to other families of compounds.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Crystal and Electronic Structures of A 2 NaIO 6 Periodate Double Perovskites (A = Sr, Ca, Ba): Candidate Wasteforms for I-129 Immobilization

The synthesis, structure, and thermal stability of the periodate double perovskites A 2 NaIO 6 (A= Ba, Sr, Ca) were investigated in the context of potential application for the immobilization of radioiodine. A combination of X-ray diffraction and neutron diffraction, Raman spectroscopy, and DFT simulations were applied to determine accurate crystal structures of these compounds and understand their relative stability. The compounds were found to exhibit rock-salt ordering of Na and I on the perovskite B-site; Ba 2 NaIO 6 was found to adopt the Fm- 3 m aristotype structure, whereas Sr 2 NaIO 6 and Ca 2 NaIO 6 adopt the P 2 1 / n hettotype structure, characterized by cooperative octahedral tilting. DFT simulations determined the Fm- 3 m and P 2 1 / n structures of Ba 2 NaIO 6 to be energetically degenerate at room temperature, whereas diffraction and spectroscopy data evidence only the presence of the Fm- 3 m phase at room temperature, which may imply an incipient phase transition for this compound. The periodate double perovskites were found to exhibit remarkable thermal stability, with Ba 2 NaIO 6 only decomposing above 1050 °C in air, which is apparently the highest recorded decomposition temperature so far recorded for any iodine bearing compound. As such, these compounds offer some potential for application in the immobilization of iodine-129, from nuclear fuel reprocessing, with an iodine incorporation rate of 25–40 wt%. The synthesis of these compounds, elaborated here, is also compatible with both current conventional and future advanced processes for iodine recovery from the dissolver off-gas.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Colloidal synthesis and charge carrier dynamics of Cs 4 Cd 1-x Cu x Sb 2 Cl 12 (0 ≤ x ≤ 1) layered double perovskite nanocrystals

The toxicity and instability of lead-based metal halide perovskites are the two main obstacles that prevent perovskite materials from implementation in applications. Recently, layered double perovskites (LDPs) emerge as a new family of perovskite materials which provide a new route to solve these problems by lead-component replacement and reduction of crystal structure dimensionality. However, LDP nanocrystals (NCs) have been rarely studied, limiting the further property exploration and application realization. In this work, we report the colloidal synthesis of a series of Cs 4 Cd 1-x Cu x Sb 2 Cl 12 (0 ≤ x ≤ 1) LDP NCs by tuning the stoichiometry of metal precursors. The composition-structure-property relationships of the resulting LDP NCs are studied through materials characterizations, density functional theory calculations, and transient-absorption spectroscopy. In addition, we demonstrate that high-performance high-speed photodetectors can be fabricated using the colloidal LDP NCs through solution-processing. This work premises further expansion of such LDP-based materials for both fundamental studies and application integrations.

25 ENERGY STORAGE↗
DOE OSTI2020

Octupolar versus Néel Order in Cubic 5d 2 Double Perovskites

We report time-of-flight neutron spectroscopy and neutron and x-ray diffraction studies of the 5 d 2 double perovskite magnets, Ba 2 M OsO 6 ( M = Zn , Mg , Ca ). We find that these materials host antiferromagnetically coupled 5 d 2 Os 6 + ions decorating a face-centered cubic (fcc) lattice and are found to remain cubic down to the lowest temperatures. They all exhibit thermodynamic anomalies consistent with a single phase transition at a temperature T * , and a gapped magnetic excitation spectrum with spectral weight concentrated at wave vectors typical of type-I antiferromagnetic orders. However, while muon spin resonance experiments show clear evidence for time-reversal symmetry breaking below T * , we observe no corresponding magnetic Bragg scattering signal. These results are shown to be consistent with ferro-octupolar symmetry breaking below T * , and are discussed in the context of other 5 d double perovskite magnets and theories of exotic orders driven by multipolar interactions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗