To gain insight into the mechanism of charge-ordering transitions, which conventionally are pictured as a disproportionation of an ion M as 2M$^{n+}$ $rightarrow$ M$^{(n+1)+}$ + M$^{(n-1)+}$, we (1) review and reconsider the charge state (or oxidatio
n number) picture itself, (2) introduce new results for the putative charge ordering compound AgNiO$_2$ and the dual charge state insulator AgO, and (3) analyze cationic occupations of actual (not formal) charge, and work to reconcile the conundrums that arise. We establish that several of the clearest cases of charge ordering transitions involve no disproportion (no charge transfer between the cations, hence no charge transfer), and that the experimental data used to support charge ordering can be accounted for within density functional based calculations that contain no charge transfer between cations. We propose that the charge state picture retains meaning and importance, at least inn many cases, if one focuses on Wannier functions rather than atomic orbitals. The challenge of modeling charge ordering transitions with model Hamiltonians is discussed.
We study vanadium spinels $A$V$_2$O$_4$ ($A$ = Cd, Mg) in pulsed magnetic fields up to 65 T. A jump in magnetization at $mu_0 H approx$ 40 T is observed in the single-crystal MgV$_2$O$_4$, indicating a field induced quantum phase transition between t
wo distinct magnetic orders. In the multiferroic CdV$_2$O$_4$, the field-induced transition is accompanied by a suppression of the electric polarization. By modeling the magnetic properties in the presence of strong spin-orbit coupling characteristic of vanadium spinels, we show that both features of the field-induced transition can be successfully explained by including the effects of the local trigonal crystal field.
We report a series of electronic structure calculations for CrN using different exchange correlation potentials: PBE, LDA+$U$, the Tran-Blaha modified Becke-Johnson, and hybrid functionals. In every case, our calculations show that the onset of magne
tism in CrN should be accompanied by a gap opening. The experimentally found antiferromagnetic order always leads to an insulating behavior. Our results give further evidence that the Tran-Blaha functional is very useful for treating the electronic structure of correlated semiconductors allowing a parameter free description of the system. Hybrid functionals are also well capable of describing the electronic structure of CrN. The analysis of the system is complemented with our calculations of the thermopower that are in agreement with the experimental data.
It was reported earlier [Phys. Rev. Lett. 106, 056401 (2011)] that the skutterudite structure compound CoSb$_3$ displays a unique band structure with a topological transition versus a symmetry-preserving sublattice (Sb) displacement very near the str
uctural ground state. The transition is through a massless Dirac-Weyl semimetal, point Fermi surface phase which is unique in that (1) it appears in a three dimensional crystal, (2) the band critical point occurs at $k$=0, and (3) linear bands are degenerate with conventional (massive) bands at the critical point (before inclusion of spin-orbit coupling). Further interest arises because the critical point separates a conventional (trivial) phase from a topological phase. In the native cubic structure this is a zero-gap topological semimetal; we show how spin-orbit coupling and uniaxial strain converts the system to a topological insulator (TI). We also analyze the origin of the linear band in this class of materials, which is the characteristic that makes them potentially useful in thermoelectric applications or possibly as transparent conductors. We characterize the formal charge as Co$^{+}$ $d^8$, consistent with the gap, with its $bar{3}$ site symmetry, and with its lack of moment. The Sb states are characterized as $p_x$ (separately, $p_y$) $sigma$-bonded $Sb_4$ ring states occupied and the corresponding antibonding states empty. The remaining (locally) $p_z$ orbitals form molecular orbitals with definite parity centered on the empty $2a$ site in the skutterudite structure. Eight such orbitals must be occupied; the one giving the linear band is an odd orbital singlet $A_{2u}$ at the zone center. We observe that the provocative linearity of the band within the gap is a consequence of the aforementioned near-degeneracy, which is also responsible for the small band gap.
The low and high-temperature phases of V$_4$O$_7$ have been studied by textit{ab initio} calculations. At high temperature, all V atoms are electronically equivalent and the material is metallic. Charge and orbital ordering, associated with the disto
rtions in the V pseudo-rutile chains, occur below the metal-insulator transition. Orbital ordering in the low-temperature phase, different in V$^{3+}$ and V$^{4+}$ chains, allows to explain the distortion pattern in the insulating phase of V$_4$O$_7$. The in-chain magnetic couplings in the low-temperature phase turn out to be antiferromagnetic, but very different in the various V$^{4+}$ and V$^{3+}$ bonds. The V$^{4+}$ dimers formed below the transition temperature form spin singlets, but V$^{3+}$ ions, despite dimerization, apparently participate in magnetic ordering.
Electronic structure calculations on the low dimensional spin-1/2 compound TiOCl were performed at several pressures in the orthorhombic phase, finding that the structure is quasi-one-dimensional. The Ti3+ (d1) ions have one t2g orbital occupied (dyz
) with a large hopping integral along the b direction of the crystal. The most important magnetic coupling is Ti-Ti along the b axis. The transition temperature (Tc) has a linear evolution with pressure, and at about 10 GPa this Tc is close to room temperature, leading to a room temperature spin-Peierls insulator-insulator transition, with an important reduction of the charge gap in agreement with the experiment. On the high-pressure monoclinic phase, TiOCl presents two possible dimerized structures, with a long or short dimerization. Long dimerized state occurs above 15 GPa, and below this pressure the short dimerized structure is the more stable phase.
Electronic structure calculations for spinel vanadate ZnV$_2$O$_4$ show that partial electronic delocalization in this system leads to structural instabilities. These are a consequence of the proximity to the itinerant-electron boundary, not being re
lated to orbital ordering. We discuss how this mechanism naturally couples charge and lattice degrees of freedom in magnetic insulators close to such a crossover. For the case of ZnV$_2$O$_4$, this leads to the formation of V-V dimers along the [011] and [101] directions that readily accounts for the intriguing magnetic structure of ZnV$_2$O$_4$.
On the basis of experimental thermoelectric power results and ab initio calculations, we propose that a metal-insulator transition takes place at high pressure (approximately 6 GPa) in MgV_2O_4.
We report a systematic enhancement of the pressure dependence of TN in A2+[V2]O4 spinels as the V-V separation approaches the critical separation for a transition to itinerant-electron behavior. An intermediate phase between localized and itinerant e
lectron behavior is identified in Zn[V2]O4 and Mg[V2]O4 exhibiting mobile holes as large polarons. In Zn[V2]O4, cooperative ordering of V-V pairs below a Ts=TN does not totally suppress the V3+-ion spins at ambient pressure, but makes TN to decrease with pressure. Our results demonstrate that Zn[V2]O4 and Mg[V2]O4 are less localized than previously thought.
