Numerous transition-metal oxides have low-temperature antiferromagnetic (AFM) states and high-temperature paramagnetic (PM) phases, where the AFM state is usually insulating while the PM phase can be either insulating or metallic. Without involving strong correlation, we use symmetry-broken density-functional theory (DFT) to obtain the PM phases of insulating NaFeO3 vs the recently discovered metallic NaOsO3. We develop the understanding of insulating and metallic behaviors in paramagnetic oxides by analyzing the interactions between magnetic and positional symmetry breaking: The insulating gap is governed by the competition between the spin disorder that induces a distribution of different magnitudes of local magnetic moments and the polymorphous distribution of off-center atomic displacements. NaFeO3, on the other hand, has large positional displacement with small spin-disorder-induced moments distribution, leading to insulating PM phase, whereas NaOsO3 has a pronounced spin-disorder-induced moments distribution that forces the PM phase to become metallic. Our work identifies this symmetry-breaking competition as a general framework to bridge seemingly disparate metal-insulator behaviors in transition-metal oxides paramagnets without invoking strong correlation.

Materials with interesting physical properties are often designed based on our understanding of the target physical effects. The physical properties can be either explicitly observed (“apparent”) or are concealed by the perceived symmetry (“hidden”) but still exist. Both are enabled by specific symmetries and induced by certain physical interactions. Using the underlying approach of condensed matter theory of real materials (rather than schematic model Hamiltonians), we discuss apparent and hidden physics in real materials focusing on the properties of spin splitting and spin polarization. Depending on the enabling symmetries and underlying physical interactions, we classify spin effects into four categories with each having two subtypes; representative materials are pointed out. We then discuss the electric tunability and switch of apparent and hidden spin splitting and polarization in antiferromagnets. Finally, we extend “hidden effects” to views that are farsighted in the sense of resolving the correct atomistic and reciprocal symmetry and replaced by the incorrect higher symmetry. This framework could guide and enable systematic discovery of such intriguing effects.

Physical properties intermediate between constituents of alloys can be achieved as downward convex positive bowing, upward concave negative bowing, or zero bowing. Such bowing effects are essential for band gap engineering in semiconductor alloys. Upward band gap bowing effects are rather rare, hindering the exploration on half of the available physical property space of alloys. Part of this being a rare event is related to the need to stabilize an alloy with low mixing enthalpy, so it does not phase separate. In this paper we find via density functional theory that one can satisfy the simultaneous conditions of negative mixing enthalpy and upward band gap bowing in four-component ABX3 halide perovskite alloys in the cubic perovskite structure. Such perovskite alloys have the B-site occupied by a mixture of group IVB and IIB elements that have the IVB-s and IIB-s states in the valence bands and conduction bands, respectively, leaving the delocalized s states to strongly repel each other. This s-s repulsion leads to the upward band gap bowing and negative mixing enthalpies simultaneously. Remarkably, we identify a perovskite alloy that has a band gap much larger than all its components. Analogous trends of upward band gap bowing and negative mixing enthalpy also appear in the corresponding three-component and two-component ABX3 halide perovskite alloys. These observations of upward band gap bowing and negative mixing enthalpy will significantly accelerate the design of stable upward band gap bowing alloys in a broad range of material families.

Single-component halide perovskites (HPs) rarely satisfy all the necessary criteria for optoelectronic applications, such as achieving an optimal band gap while maintaining high chemical and structural stability. Alloying halide perovskites has emerged as a promising strategy, not only to enhance stability but also to fine-tune their electronic and optical properties. In this work, we explore multiple degrees of freedom in alloy design, considering different substitution sublattices sites (A, B, or X in ABX3 perovskites), various chemical species (isovalent and hetero-valent elements), and multi-component compositions on a given sublattice. Using first-principles calculations based on density functional theory (DFT), we investigate how compositional variations influence the electronic (band gap) and structural properties (mixing enthalpy) of HP alloys. Our approach employs the polymorphous cell model, allowing full local relaxation which breaks local symmetry while preserving global cubic symmetry-an essential framework for accurately modeling HPs. Our results reveal that X-site mixing (halogen substitution) primarily affects the valence band maximum, allowing target band gap engineering. Additionally, variations in halogen radii introduce internal strain through octahedral distortions, influencing the mixing enthalpy. A-site substitution, while not directly contributing to the band edge states, modifies structural stability via volume effects, indirectly impacting the band gap. B-site alloying plays a dominant role in band gap modulation, leading to either positive or negative band gap bowing. Specifically, isovalent B-site mixing (Sn-Pb) induces strong positive bowing, where the alloy band gap is smaller than the average gap of parent compounds, whereas hetero-valent mixing (Cd-Pb) results in pronounced negative bowing. As an aside, we investigate the competition between the excess energy of disordered alloys vs. that of long-range ordered double perovskites of the same compositions, seeking examples of ordered phases emerging from disordered alloys. Our findings provide fundamental insights into the electronic and structural behavior of HP alloys, offering valuable design principles for the development of stable and efficient materials for next-generation photovoltaic and optoelectronic devices.

Material scientists and condensed matter physicists have long been divided on the issue of choosing the conceptual framework for explaining why open-shell transition-metal oxides tend to be insulators, whereas otherwise successful theories such as DFT often predict them to be (false) metals. Strong correlation becomes the recommended medicine. We point out that strong correlation can be mitigated by allowing DFT to lower the energy by breaking structural, magnetic or dipolar symmetries. Such local motifs are observed experimentally by local probes beyond the 'average structure' determined by X-Ray diffraction. Observed broken symmetries can arise from slow fluctuations that persist over the observation time or longer. The surprising fact is that when symmetry breaking motifs are used as input to electronic structure calculations, false metals are converted into real insulators without the recommended medicine of strong correlation. Consistently, DFT calculations that show energy lowering symmetry breaking correct most cases where DFT, even with advanced exchange-correlation functionals, previously missed the correct metal vs insulator designation. Total energy calculations distinguish systems that support energy-lowering symmetry breaking from those that do not. This approach distinguishes between paramagnetic insulating and metallic phases and shows mass enhancement in Mott metals. The reason is that symmetry breaking removes many of the degeneracies that exist in a symmetry-unbroken system, reducing significantly the need for strong correlation. If one chooses to ignore symmetry breaking, the persistent degeneracies often call for strong correlation treatment. Thus, symmetry breaking transforms strong to normal correlation and false metals to true insulators. This view sheds light on the historic controversy between Mott and Slater that still reverberates today.

The hexagonal antiferromagnet MnTe has attracted enormous interest as a prototypical example of a spin-compensated magnet in which the combination of crystal and spin symmetries lifts the spin degeneracy of the electron bands without the need for spin-orbit coupling, a phenomenon called nonrelativistic spin splitting (NRSS). Subgroups of NRSS are determined by the specific spin-interconverting symmetry that connects the two opposite-spin sublattices. In MnTe, this symmetry is rotation, leading to the subgroup with spin splitting away from the Brillouin zone center, often called altermagnetism. MnTe also has the largest spontaneous magnetovolume effect of any known antiferromagnet, implying strong coupling between the magnetic moment and volume. This magnetostructural coupling offers a potential knob for tuning the spin-splitting properties of MnTe. Here, we use neutron diffraction with in situ applied pressure to determine the effects of pressure on the magnetic properties of MnTe and further explore this magnetostructural coupling. We find that applying pressure significantly increases the N & eacute;el temperature, but decreases the ordered magnetic moment. We explain this as a consequence of strengthened magnetic exchange interactions under pressure, resulting in higher TN, with a simultaneous reduction of the local moment of individual Mn atoms, described here via density functional theory. This reflects the increased orbital hybridization and electron delocalization with pressure. These results shed light on the competition between magnetic exchange interactions and the strength of individual magnetic moments and show that the magnetic properties of MnTe can be controlled by pressure, opening the door to improved properties for spintronic applications through tuning via physical or chemical pressure.

The crystal structure used as an input to electronic structure calculation of conventionally bonded solids consists primarily of the standard crystallographic degrees of freedom. Quantum solids sometimes have additional microscopic degrees of freedom nested within the crystallographic structure. These might include local motifs including positional (Peierls dimers, deformed octahedra, and Jahn-Teller distortions), magnetic (local moment configurations), and dipolar (local ferroelectric configurations). Such motifs can be observed experimentally via local probes that avoid averaging and theoretically as distinct total energy-lowering features relative to more simplified average crystallographic structures. Here, we examine the ability of electronic structure methods independent of strong correlation physics to explain the broad phenomenology of metal-insulator selectivity in quantum oxides by energy-lowering symmetry breaking. We do this by avoiding the restriction of considering only (i) electron-electron interactions in a fixed unresponsive lattice-as done in Mott strong correlation explanations-allowing, however, (ii) local positional and magnetic motifs that coexist within a crystallographic landscape. We find, in a broad range of quantum oxides with different symmetry-breaking modes, the formation of split-off flat bands that can also control metallic vs insulating characteristics. The split-off band effect is common to magnetic and nonmagnetic materials, including both binary and ternary oxides. One finds that, when such local symmetry-breaking motifs are considered in mean-field-like (e.g., density functional theory) electronic structure calculations of quantum oxides, they explain many of the observed trends in metal vs insulator phases discussed otherwise in prior literature via strong correlation in symmetry-unbroken view.

The alpha-phase of the gapped insulator Nb3Cl8 has recently emerged as the long-sought critical testing bed for examining the importance of strong interelectronic correlation vs symmetry breaking in understanding insulation of such Mott compounds. Structural symmetry breaking detected by density functional theory (DFT) energy lowering (such as dimer formation, disproportionation, or Jahn-Teller distortions) explains insulation in both d-electron Mott-like systems and in non-d-electron cases without recourse to strong correlation. Yet, in Nb3Cl8, structural symmetry breaking alone (viz. formation of Nb trimers) fails to explain insulation, leading instead to a partially occupied metallic flat band, in contrast with experimental observations. We examine the role of magnetic symmetry breaking, noting that Nb3Cl8 is an observed paramagnet (not an antiferromagnet), thus potentially carrying also short-range ordered magnetic moments. Describing the latter as a polymorphous distribution of nonzero local moments with total zero net magnetization is demonstrated to lower the DFT total energy, while gapping the system without recourse to strong correlation or long-range magnetic order. This suggests that degeneracy removal by symmetry breaking in mean-field-like approaches-either structural, or magnetic, or both-can reduce or eliminate the need for strong correlation, allowing the use of DFT for such Mott systems.

Antiferromagnets that break both space-time reversal and translation-spin-rotation symmetries were 014422 (2020)] to possess splitting between the otherwise spin-degenerate energy bands even without the relativistic spin-orbit coupling (SOC). Here, we point out that such nonrelativistic spin splitting (NRSS)-in particular, "spin splitting type 4" (SST-4) symmetry-broken antiferromagnets-can be divided into subgroups having distinct patterns of spin splitting and spin textures, depending on additional auxiliary symmetries of spin interconversion and polarity. These SST-4 subgroups include the alpha-type (no spin-interconverting symmetry) having spin splitting at the Brillouin zone center, as well as the /3 subgroup in which a rotation symmetry is applied and determines the alternating spin texture and the gamma subgroup having exclusively reflection spin-interconverting symmetry. Unlike ferrimagnets, the alpha type compounds are shown to have tiny net magnetization at finite temperature and thus avoid the adverse effect of the stray field. The alpha and /3 subgroups can be either polar or nonpolar, whereas the gamma subgroup is polar only, providing a basis for possible switching by external fields. The combination of NRSS-enabling and auxiliary symmetries is used here as a filter for identifying previously synthesized compounds as specific prototypes. Their characteristic splitting and spin polarization are calculated by density functional theory to the benefit of potential future experimental testing. Interesting results are as follows: (i) SOC-independent NRSS can exceed the magnitude of the SOC-induced Rashba and Dresselhaus spin splitting in semiconductors. (ii) Examples of predicted alpha-type insulating compounds include BiCrO3 (nonpolar) and Mn2ScSbO6 (polar), the latter having spin splitting of 158 meV and 160 meV in the valence and conduction bands, respectively. (iii) The /3-type (Cu2Y2O5 and FeF2) and gamma type compounds (Mn4Nb2O9 and FeScO3) are distinguished both by their auxiliary symmetries and polarity. The spin textures of gamma-type compounds are mirror reflected with spin degeneracy of the wave vectors on that mirror. These observations will likely broaden the experimental playing field of NRSS physics significantly.

Ordinary band structure calculations of quantum materials often incorrectly predicted metallic, instead of insulating electronic structure, motivating Mott-Hubbard strong electron correlation as a gapping mechanism. More recently, allowing the formation of local structural symmetry breaking motifs in otherwise ordinary band theory was shown to lower the total energy while predicting insulating gaps when they are observed. An important counter example was recently pointed out whereby the flat band formed in Nb3Cl8 by symmetry breaking is by itself partially occupied, thus failing to account for the observed insulating state. It is shown here that a generalized symmetry breaking involving the cooperative structural and magnetic effects produces in mean-field-like density functional theory an energy lowering insulating phase.

It is well established that theoretical prediction of the stable crystal structure of a compound is essential to calculating its electronic properties. When the theoretically predicted structure conflicts with the experimentally assessed structure, it is natural to assume that theory is wrong. An example is S-Bi2O3-an important functional material associated with its record oxygen transport. The standard first step in theoretical structure prediction involves calculation of the "Convex Hull" diagram C (x, S, T = 0) contrasting the zero temperature energies of all currently imaginable competing phases at different compositions x and structures S, retaining the phases that persist with respect to decomposition into other constituents. Proximity of the energy of a structure to the Convex Hull indicates its expected theoretical stability. Surprisingly, the documented nominal fluorite crystal structure of S-Bi2O3-refined from X-ray diffraction (XRD)-is nowhere near the bottom of the Convex Hull calculated with state-of-the-art density functional theory (DFT). This apparent failure of theory comes with additional puzzles. First, using the measured nominal structure as input to DFT band theory predicts the S phase to be a zero-gap metal, in stark contrast with its known insulating properties. Second, phonon calculations indicate that the nominal fluorite structure is not even dynamically stable, exhibiting imaginary phonons. Third, extending the Convex Hull concept to finite temperatures C(x, S, T) via "Compressive Sensing" machine learning reveals that the documented nominal crystal structure has high free energy above the Convex Hull. Here, we study theoretically the possibility that the refined structure for the S phase was, in fact, an effective average "virtual structure," not to be taken literally. To test this, we retain the global macroscopic crystallographic cell symmetry but increase the unit cell to a supercell, allowing local atomic positions to deviate from the artificially imposed average, seeking minimum calculated total energy. This reveals a macroscopically cubic but locally noncubic distribution of low symmetry local motifs. Importantly, this "polymorphous network" distribution has a lower total energy, it correctly predicts an insulating phase and agrees with the measured pair distribution function much better than the literature average structure. It appears that experimentally determined high-symmetry virtual average structure is not realistic.

Transition metal d-electron oxides with an odd number of electrons per unit cell are expected to form metals with partially occupied energy bands, but exhibit in fact a range of behaviors, being either insulators, or metals, or having insulator-metal transitions. Traditional explanations involved predominantly electron-electron interactions in fixed structural symmetry. The present work focuses instead on the role of symmetry breaking local structural motifs. Viewing the previously observed V-V dimerization in VO2 as a continuous knob, reveals in density functional calculations the splitting of an isolated flat band from the broad conduction band. This leads past a critical percent dimerization to the formation of the insulating phase while lowering the total energy. In VO2 this transition is found to have a rather low energy barrier approaching the thermal energy at room temperature, suggesting energy-efficient switching in neuromorphic computing. Interestingly, sufficient V-V dimerization suppresses magnetism, leading to the nonmagnetic insulating state, whereas magnetism appears when dimerization is reduced, forming a metallic state. This study opens the way to design novel functional quantum materials with symmetry breaking-induced flat bands.

Halide perovskite (HP) materials have recently emerged as a class of semiconductors with immense promise for various optoelectronic applications, ranging from solar cells to light-emitting diodes. One of the unique attributes of HPs is their tunable band gaps with different factors governing their value. The first factor is related to relativistic corrections ["mass-Darwin," connected to the ns2 lone pairs, and spin-orbit coupling (SOC)] that induce an orbital shift or degeneracy splitting, resulting in a band-gap reduction. The second factor involves the structural configuration: in HPs the local symmetry of each Wyckoff position tends to be broken, inducing an opening of the band gap. Based on high-throughput density functional theory calculations, this paper systematically studies a possible self-cancelation on the band-gap correction for HPs when the polymorphous configuration-structural effects-and the SOC-electronic effects-are included. Our results indicate that the nature of interplay between SOC and symmetry breaking (SB) is that they are independent decoupling effects to describe the band-gap magnitude in halide perovskites. As a result of that, we observe a transitivity of the band-gap description; i.e., if we know the band gap of halide perovskites without SB and SOC, we can independently add the effects of band-gap reduction due to SOC and band-gap opening due to SB, regardless of the order in which these effects are considered.

Energy bands in antiferromagnets are supposed to be spin degenerate in the absence of spin-orbit coupling (SOC). Recent studies have identified formal symmetry conditions for antiferromagnetic crystals in which this degeneracy can be lifted, spin splitting,even in the vanishing SOC (i.e., non-relativistic) limit. Materials having such symmetries could enable spin-split antiferromagnetic spintronics without the burden of using heavy-atom compounds. However, the symmetry conditions that involve spin and magnetic symmetry are not always effective as practical material selection filters. Furthermore, these symmetry conditions do not readily disclose trends in the magnitude and momentum dependence of the spin-splitting energy. Here, it is shown that the formal symmetry conditions enabling spin-split antiferromagnets can be interpreted in terms of local motif pairs, such as octahedra or tetrahedra, each carrying opposite magnetic moments. Collinear antiferromagnets with such a spin-structure motif pair, whose components interconvert by neither translation nor spatial inversion, will show spin splitting. Such a real-space motif-based approach enables an easy way to identify and design materials (illustrated in real example materials) having spin splitting without the need for SOC, and offers insights into the momentum dependence and magnitude of the spin splitting.

Alloys of ABX 3 halide perovskites (HP) exhibit unique phase behavior compared to traditional III‐V and II‐VI semiconductor alloys used in solar cells. While the latter typically have good mutual miscibility when their mixed components are size matched, and phase‐segregate when size mismatched, HP alloys show good miscibility in the dark but can phase‐segregate under light. Quantum mechanical calculations described herein reveal light‐induced defect formation and migration hold the key. Specifically, the interaction between a halogen vacancy V X with halogen interstitial X i forming together a Frenkel‐pair defect emerges as the enabler for phase‐segregation in HP alloys. At a threshold bromine composition in the Br‐I alloys, the photogenerated holes in the valence band localize, creating thereby a doubly‐charged iodine Frenkel‐pair (V I + I i ) 2+ . Faster migration of iodine over bromine interstitial into the vacant iodine V I site leads to the formation of iodine‐rich and iodine‐depleted regions, establishing phase‐segregation. Removal of the mobile defects–the agent of segregation–by dark thermal annealing, supplies the opposing force, leading to reversal of phase‐segregation. This atomistic understanding can enable some control of the phase‐segregation by selecting substituting elements on the B site–such as replacing some Pb by Sn–that are unable to form stable Frenkel defects.

Compounds having an odd number of electrons with the same orbital character in occupied and unoccupied band edge states would be expected to have band degeneracy at the Fermi energy, making such reference system metals. Yet, many ABO3 oxide perovskites with a magnetic 3d B-atom are, in fact, insulators both below and above the Neel temperature. These inconsistencies between experimental observation and expectation have been traditionally resolved by invoking degeneracy-breaking physics based largely on high-order electron effects, such as strong interelectronic correlation (the Mott mechanism). Such explanations generally utilize the highest symmetry structure, considering microscopic degrees of freedom (m-DOF) as largely passive spectators. Yet, it has long been known that ABO3 perovskites can manifest an arrangement of m-DOFs in the form of octahedral tilting, bond dimerization, Jahn-Teller distortions, and ordering of local magnetic moments as part of the stabilizing intrinsic symmetry. Such m-DOFs are seen both by local experimental probes and theoretically in total energy minimization of its Born-Oppenheimer state. While such local structural and magnetic symmetry breaking motifs were often considered to be the reason for gapping of the reference system below the transition into Para phases, it was also often thought that above the transition those local motifs might vanish, requiring a different mechanism for gapping - such as strong correlation. Here we examine if such intrinsic structural and magnetic symmetry breaking might systematically explain the formation of insulating band gaps both below and above the magnetic transition and account at the same time for specific and non-accidental exceptions of the absence of gaping in some compounds, such as SrVO3.

Metal $d$-electron oxides having an odd number of electrons per cell should exhibit band degeneracy at the Fermi energy, making them, in band theory, formally metallic. In many cases, however, these are false metals, as evidenced by the observation that many $\mathrm{AB}{\mathrm{O}}_{3}$ oxide perovskites with a magnetic $3d$ B atom are observed to be insulators both below and above the N\'eel temperature. These inconsistencies between experimental observation and expectation have historically been resolved by invoking degeneracy-breaking physics, based largely on pure electron effects, such as strong interelectronic correlation for $d$-electron compounds (the Mott mechanism). Such explanations generally consider the microscopic lattice or magnetic degrees of freedom (m-DOFs) as largely passive spectators, not causes of the formal metal being an insulator. However, it has long been known that $\mathrm{AB}{\mathrm{O}}_{3}$ perovskites can manifest an arrangement of m-DOFs in the form of octahedral tilting, bond dimerization, Jahn-Teller distortions, and ordering of local magnetic moments. It appears reasonable that such structural and magnetic local degrees of freedom need to be allowed to compete with purely electronic strong correlation. To answer this question, we explored a range of $d$-electron oxide perovskites exemplified by the archetypes $\mathrm{LaTi}{\mathrm{O}}_{3}$, $\mathrm{LaV}{\mathrm{O}}_{3}$, $\mathrm{SrMn}{\mathrm{O}}_{3}$, and $\mathrm{LaMn}{\mathrm{O}}_{3}$ with 1, 2, 3, or 4 $d$ electrons, respectively. Using a mean-field-like electronic structure method (here, density functional theory), we find that a combination of magnetic symmetry breaking (SB) with structural distortions can account for insulating band gaps in this series while correctly predicting for the control case, an intrinsic paramagnetic metal in $\mathrm{SrV}{\mathrm{O}}_{3}$, as SB is insufficiently strong to remove the degeneracy. This indicates that calculating quantitatively local magnetic and positional SB motifs in unit cells that avoid averaging at the outset over the low-symmetry motifs can provide consistent trends in a Mott transition without Mott U.

Many textbook physical effects in crystals are enabled by some specific symmetries. In contrast to such "apparent effects", "hidden effect X" refers to the general condition where the nominal global system symmetry would disallow the effect X, whereas the symmetry of local sectors within the crystal would enable effect X. Known examples include the hidden Rashba and/or hidden Dresselhaus spin polarization that require spin orbit coupling, but (unlike the apparent Rashba and Dresselhaus counterparts) can exist even in inversion-symmetric non-magnetic crystals. Here we point out that the spin splitting effect that does not require spin-orbit coupling (SOC) can have a hidden spin polarization counterpart in antiferromagnets. We show that such hidden, SOC-independent effects reflect intrinsic properties of the perfect crystal rather than an effect due to imperfections, opening the possibility for experimental realization, and offering a potential way to switch antiferromagnetic ordering.