Understanding the Role of Entropy in High Entropy Oxides.

The field of high entropy oxides (HEOs) flips traditional materials science paradigms on their head by seeking to understand what properties arise in the presence of profound configurational disorder. This disorder, which originates from multiple elements sharing a single lattice site, can take on a kaleidoscopic character due to the vast numbers of possible elemental combinations. High configurational disorder appears to imbue some HEOs with functional properties that far surpass their nondisordered analogs. While experimental discoveries abound, efforts to characterize the true magnitude of the configurational entropy and understand its role in stabilizing new phases and generating superior functional properties have lagged behind. Understanding the role of configurational disorder in existing HEOs is the crucial link to unlocking the rational design of new HEOs with targeted properties. In this Perspective, we attempt to establish a framework for articulating and beginning to address these questions in pursuit of a deeper understanding of the true role of entropy in HEOs.

Entropy Engineering and Tunable Magnetic Order in the Spinel High-Entropy Oxide.

Spinel oxides are an ideal setting to explore the interplay between configurational entropy, site selectivity, and magnetism in high-entropy oxides (HEOs). In this work, we characterize the magnetic properties of the spinel (Cr, Mn, Fe, Co, Ni)3O4 and study the evolution of its magnetism as a function of nonmagnetic gallium substitution. Across the range of compositions studied here, from 0 to 40% Ga, magnetic susceptibility and powder neutron diffraction measurements show that ferrimagnetic order is robust in the spinel HEO. However, we also find that the ferrimagnetic order is highly tunable, with the ordering temperature, saturated and sublattice moments, and magnetic hardness all varying significantly as a function of Ga concentration. Through X-ray absorption and magnetic circular dichroism, we are able to correlate this magnetic tunability with strong site selectivity between the various cations and the tetrahedral and octahedral sites in the spinel structure. In particular, we find that while Ni and Cr are largely unaffected by the substitution with Ga, the occupancies of Mn, Co, and Fe are each significantly redistributed. Ga substitution also requires an overall reduction in the transition metal valence, and this is entirely accommodated by Mn. Finally, we show that while site selectivity has an overall suppressing effect on the configurational entropy, over a certain range of compositions, Ga substitution yields a striking increase in the configurational entropy and may confer additional stabilization. Spinel oxides can be tuned seamlessly from the low-entropy to the high-entropy regime, making this an ideal platform for entropy engineering.

Sr(M,Te)2O6 (M = Cr, Mn, Fe, Co, Ni): A Magnetically Dilute Family of Honeycomb Tellurates.

We report the synthesis and characterization of five new honeycomb tellurates with the PbSb2O6 structure type. These materials, SrM2/3Te4/3O6 (M = Cr, Mn, Fe) and SrM1/2Te3/2O6 (M = Co, Ni), are prepared by conventional solid state synthesis. Rietveld refinements of powder X-ray and neutron diffraction data reveal that these materials crystallize in the P3̅1 m space group, in which M and Te are octahedrally coordinated and randomly distributed over the honeycomb sublattice. In three of these materials (M = Cr, Mn, Fe), the transition metal takes a 3+ oxidation state, and hence, charge neutrality necessitates that the honeycomb sublattice is 66% occupied by nonmagnetic Te. In the remaining two of these materials (M = Co, Ni), the transition metal takes a 2+ oxidation state, requiring that 75% of the honeycomb lattice is occupied by nonmagnetic Te. Thus, the honeycomb sublattice is highly diluted, as only 33% or 25% of the sites are occupied by a magnetic ion. These occupation values fall well-below the percolation threshold for the honeycomb lattice, p c = 70%. Accordingly, magnetic susceptibility measurements reveal no magnetic order or spin freezing down to 1.8 K.

Cubic Re6+ (5d1) Double Perovskites, Ba2MgReO6, Ba2ZnReO6, and Ba2Y2/3ReO6: Magnetism, Heat Capacity, µSR, and Neutron Scattering Studies and Comparison with Theory.

Double perovskites (DP) of the general formula Ba2MReO6, where M = Mg, Zn, and Y2/3, all based on Re6+ (5d1, t2g1), were synthesized and studied using magnetization, heat capacity, muon spin relaxation, and neutron-scattering techniques. All are cubic, Fm3̅m, at ambient temperature to within the resolution of the X-ray and neutron diffraction data, although the muon data suggest the possibility of a local distortion for M = Mg. The M = Mg DP is a ferromagnet, Tc = 18 K, with a saturation moment ∼0.3 bohr magnetons at 3 K. There are two anomalies in the heat capacity: a sharp feature at 18 K and a broad maximum centered near 33 K. The total entropy loss below 45 K is 9.68 e.u., which approaches R ln 4 (11.52 e.u.) supporting a j = 3/2 ground state. The unit cell constants of Ba2MgReO6 and the isostructural, isoelectronic analogue, Ba2LiOsO6, differ by only 0.1%, yet the latter is an anti-ferromagnet. The M = Zn DP also appears to be a ferromagnet, Tc = 11 K, µsat(Re) = 0.1 µB. In this case the heat capacity shows a somewhat broad peak near 10 K and a broader maximum at ∼33 K, behavior that can be traced to a smaller particle size, ∼30 nm, for this sample. For both M = Mg and Zn, the low-temperature magnetic heat capacity follows a T3/2 behavior, consistent with a ferromagnetic spin wave. An attempt to attribute the broad 33 K heat capacity anomalies to a splitting of the j = 3/2 state by a crystal distortion is not supported by inelastic neutron scattering, which shows no transition at the expected energy of ∼7 meV nor any transition up to 100 meV. However, the results for the two ferromagnets are compared to the theory of Chen, Pereira, and Balents, and the computed heat capacity predicts the two maxima observed experimentally. The M = Y2/3 DP, with a significantly larger cell constant (3%) than the ferromagnets, shows predominantly anti-ferromagnetic correlations, and the ground state is complex with a spin frozen component Tg = 16 K from both direct current and alternating current susceptibility and µSR data but with a persistent dynamic component. The low-temperature heat capacity shows a T1 power law. The unit cell constant of B = Y2/3 is less than 1% larger than that of the ferromagnetic Os7+ (5d1) DP, Ba2NaOsO6.

Volume-wise destruction of the antiferromagnetic Mott insulating state through quantum tuning.

RENiO3 (RE=rare-earth element) and V2O3 are archetypal Mott insulator systems. When tuned by chemical substitution (RENiO3) or pressure (V2O3), they exhibit a quantum phase transition (QPT) between an antiferromagnetic Mott insulating state and a paramagnetic metallic state. Because novel physics often appears near a Mott QPT, the details of this transition, such as whether it is first or second order, are important. Here, we demonstrate through muon spin relaxation/rotation (µSR) experiments that the QPT in RENiO3 and V2O3 is first order: the magnetically ordered volume fraction decreases to zero at the QPT, resulting in a broad region of intrinsic phase separation, while the ordered magnetic moment retains its full value until it is suddenly destroyed at the QPT. These findings bring to light a surprising universality of the pressure-driven Mott transition, revealing the importance of phase separation and calling for further investigation into the nature of quantum fluctuations underlying the transition.

Synthesis, structure, and magnetic properties of novel B-site ordered double perovskites, SrLaMReO6 (M = Mg, Mn, Co and Ni).

Four new double perovskites, SrLaMReO(6) (M = Mg, Mn, Co, Ni) in which Re(5+) (5d(2)) is present, were prepared via conventional solid state reactions and characterized by X-ray and neutron powder diffraction, XANES, SQUID magnetometry, and muon spin relaxation (µSR). Synchrotron X-ray and neutron diffraction experiments confirmed that all compounds crystallize in the monoclinic P2(1)/n structure type, which consists of alternately corner-shared octahedra of MO(6) and ReO(6). Rietveld refinement results indicated anti-site mixing of less than 7% on the M/Re sites. Bond valence sum calculations (BVS) suggest all M and Re ions are 2+ and 5+, respectively, and for the Mn-containing phase this is also supported by XANES measurements. All of the materials are paramagnetic at room-temperature and their Curie-Weiss temperatures are positive (except for Mg) indicating net ferromagnetic interactions. No evidence for long-range magnetic order is evident in the dc magnetic susceptibility and µSR measurements for SrLaMgReO(6) to 2 K. The Mn-phase shows long-range order at T(C) = 190 K and neutron diffraction revealed a ferromagnetic structure with a refined net moment of ∼3.7µ(B). Both Co- and Ni-containing phases exhibit spin glass behavior at T(G) = 23 and 30 K, respectively, which is supported by neutron diffraction and a.c. susceptibility data. The structure and physical properties of these four new rhenium based ordered double perovskites are compared to the closely related "pillared perovskites", La(5)Re(3)MO(16), the isoelectronic Os(6+) (5d(2)) double perovskite Sr(2)CoOsO(6), and the Re(6+) (5d(1)) double perovskites, Sr(2)MReO(6), (M = Mg, Ca, Mn, Co, Ni).