First principles electronic structure calculations have been carried out on ordered double perovskites Sr_2B'B"O_6 (for B' = Cr or Fe and B" 4d and 5d transition metal elements) with increasing number of valence electrons at the B-sites, and on Ba_2MnReO_6 as well as Ba_2FeMoO_6. The Curie temperatures are estimated ab initio from the electronic structures obtained with the local spin-density functional approximation, full-potential generalized gradient approximation and/or the LDA+U method (U - Hubbard parameter). Frozen spin-spirals are used to model the excited states needed to evaluate the spherical approximation for the Curie temperatures. In cases, where the induced moments on the oxygen was found to be large, the determination of the Curie temperature is improved by additional exchange functions between the oxygen atoms and between oxygen and B' and B" atoms.
A pronounced systematics can be found among the experimental and/or calculated Curie temperatures and the total valence electrons of the transition metal elements.
An accurate prediction of atomic diffusion in Fe alloys is challenging due to thermal magnetic excitations and magnetic transitions. We propose an effcient approach to address these properties via Monte Carlo simulation, using ab-initio based effective interaction models. The temperature evolution of self- and Cu diffusion coeffcients in alpha-iron are successfully predicted, particularly the diffusion acceleration around the Curie point, which requires a quantum treatment of spins. We point out a dominance of magnetic disorder over chemical effects on diffusion in the very dilute systems.
We present a data set of calculated Curie temperatures for the main-phase compounds of rare-earth permanent magnets. We employ ab initio electronic structure calculations for the itinerant ferromagnetism and an effective spin model for the finite-temperature magnetism. Curie temperatures are derived on the basis of a classical Heisenberg model mapped via Liechtenstein's formula for atomic-pair-wise exchange couplings. Relative trends with respect to the species of rare-earth elements in calculated Curie temperatures for R2Fe14B are in agreement with experimental trends. Quantitative comparison…
Ion displacements are the cause of the ferroelectricity in perovskites. By properly shifting ions, ab initio computations have been extensively used to investigate properties of perovsites in various structural phases. In addition to the relatively simple ion displacements, perovskites have another type of structural distortion known as antiferrodistortion or oxygen octahedron tilting. The interplay between these two types of distortions have generated abundant structural phases that can be tedious to prepare for ab initio computation, especially for large supercells. Here, we design and imple…
We present the results of first-principles calculations on two possible terminations of the (001) surfaces of SrTiO3 (STO), BaTiO3 (BTO), and PbTiO3 (PTO) perovskite crystals. Atomic structure and the electronic configurations were calculated for different 2D slabs, both stoichiometric and non-stoichiometric, using hybrid (B3PW) exchange-correlation technique and reoptimized basis sets of atomic (Gaussian) orbitals. Results are compared with previous calculations and available experimental data. The electronic density distribution near the surface and covalency effects are discussed in details…
We have determined the lattice dynamics of MgSiO$_3$ perovskite (bridgmanite) by a combination of single-crystal inelastic x-ray scattering and ab initio calculations. We observe a remarkable agreement between experiment and theory, and provide accurate results for phonon dispersion relations, phonon density of states and the full elasticity tensor. The present work constitutes an important milestone to extend this kind of combined studies to extreme conditions of pressure and temperature, directly relevant for the physics and the chemistry of Earth's lower mantle.
The electronic structure of diluted (Ga,Mn)As magnetic semiconductors in the presence of As-antisites and magnetic disorder is studied within the framework of the local spin density approximation. Both the chemical and magnetic disorders are treated using the coherent potential approximation. A ground state with partial disorder in the local moments and with a reduced total magnetic moment appears in the presence of As-antisites. We first estimate the Curie temperature T_c from total energy differences between the ferromagnetic and the paramagnetic state by identifying these with the correspon…
We present an $\textit{ab initio}$ study of the thermodynamic properties of cubic CaSiO$_3$ perovskite (CaPv) over the pressure and temperature range of the Earth's lower mantle. We compute the anharmonic phonon dispersions throughout the Brillouin zone by utilizing the phonon quasiparticle approach, which characterizes the intrinsic temperature dependence of phonon frequencies and, in principle, captures full anharmonicity. Such temperature-dependent phonon dispersions are used to calculate $\textit{ab initio}$ free energy in the thermodynamic limit ($N \rightarrow \infty$) within the framewo…
We have developed first-principles models, based on a general parametrization of the full potential-energy surface, to investigate the lattice-dynamical properties of perovskite oxides. We discuss the application of our method to prototypic ferroelectric PbTiO3, showing that its properties are drastically affected by a competition between structural instabilities. Indeed, we confirm previous indications that the destructive interaction between the ferroelectric and antiferrodistortive (involving rotations of the O6 octahedra) soft modes shifts PbTiO3's Curie temperature by hundreds of degrees.…
A first-principles derived approach is combined with the inverse Monte Carlo technique to determine the atomic orderings leading to prefixed properties in Pb(Sc_{0.5}Nb_{0.5})O_{3} perovskite alloy. We find that some arrangements between Sc and Nb atoms result in drastic changes with respect to the disordered material, including ground states of new symmetries, large enhancement of electromechanical responses, and considerable shift of the Curie temperature. We discuss the microscopic mechanisms responsible for these unusual effects.
The isothermal compression of magnesium perovskite and postperovskite is examined through the F-f plot and the diagnostic plot of Vinet universal model theoretically from the ab initio quantum-mechanical calculations at the hybrid Hartree-Fock / Density Functional Theory level. A purely numerical approach, first time applied in this paper, shows that the discrepancies largely observed between studies on the perovskite and criticized in geophysical applications are due to the inadequate choice of the Birch-Murnaghan equation of state; meanwhile the Vinet model is found utterly appropriate for t…
An ab initio structure optimization technique is newly developed to determine the valley line on a total-energy surface for zone-center distortions of ferroelectric perovskite oxides and is applied to barium titanate BaTiO3 and lead titanate PbTiO3. The proposed technique is an improvement over King-Smith and Vanderbilt's scheme [Phys. Rev. B 49, p.5828 (1994)] of evaluating total energy as a function of the amplitude of atomic displacements. The results of numerical calculations show that total energy can be expressed as a fourth-order function of the amplitude of atomic displacements in BaTi…
The Heusler compounds Mn$_2$TiZ (Z = Al, Ga, In, Si, Ge, Sn, P, As, Sb) are of large interest due to their potential ferrimagnetic properties and high spin polarization. Here, we present calculations of the structural and magnetic properties of these materials. Their magnetic moment follows the Slater-Pauling rule $m = N_V - 24$. None of them is actually a perfect half-metallic ferrimagnet, but some exhibit more than 90% spin polarization and Curie temperatures well above room temperature. The exchange interactions are complex, direct and indirect exchange contributions are identified. The Cur…
Hybrid halide perovskites are currently under intense investigation due to their potential applications in optoelectronics and solar cells. Among them, MAPbI$_3$ where MA stands for the methylammonium cation, exhibits ideal properties for solar cells. In attempt to identify new lead-free halide perovskites we have studied using \textit{ab-initio} electronic structure calculations in conjunction with hybrid functionals a series of MABX$_3$ compounds where B is a divalent cation and X a halogen atom. Our results suggest that the compounds under study exhibit a variety of lattice constants and en…
Double perovskite Bi$_2$FeCrO$_6$, related with BiFeO$_3$, is very interesting because strong ferroelectricity and high magnetic Curie temperature beyond room temperature are observed in it. However, existing density-functional-theory (DFT) studies, using pseudo-potentials, produce metallic ground state under the local density approximation (LDA) and need LDA+U method to yield needed nonmetallic ground state, resulting in low magnetic Curie temperature (below 130 K). Here, we optimize its crystal structure and then investigate its electronic structure and magnetic and optical properties by com…
Halide perovskites are currently under intense investigation due to their potential applications in optoelectronics and solar cells. Among them several crystallize in low symmetry lattice structures like trigonal, hexagonal, orthorhombic and monoclinic. Employing \textit{ab-initio} electronic structure calculations in conjunction with generalized gradient approximation and hybrid functionals we study a series of perovskites with the formula A$_3$B$_2$X$_9$ which have been grown experimentally. A stands for a monovalent cation like Cs, Rb, K or the organic methylammonium molecule (MA), B is Sb …
We have calculated Heisenberg exchange parameters for bcc-Fe, fcc-Co, and fcc-Ni using the scalar-relativistic spin-polarized Green function technique within the tight-binding linear muffin-tin orbital method and by employing the magnetic force theorem to calculate total energy changes associated with a local rotation of magnetization directions. We have also determined spin-wave stiffness constants and found the dispersion curves for metals in question employing the Fourier transform of calculated Heisenberg exchange parameters. Curie temperatures were calculated both in the mean-field approx…
Lattice thermal conductivity ($κ_{lat}$) of MgSiO$_3$ postperovskite (MgPPv) under the Earth's lower mantle high pressure-temperature conditions is studied using the phonon quasiparticle approach by combing \textit{ab initio} molecular dynamics and lattice dynamics simulations. Phonon lifetimes are extracted from the phonon quasiparticle calculations, and the phonon group velocities are computed from the anharmonic phonon dispersions, which in principle capture full anharmonicity. It is found that throughout the lowermost mantle, including the D" region, $κ_{lat}$ of MgPPv is ~25% larger than …
Magnetic insulators have been intensively studied for over 100 years, and they, in particular ferrites, are considered to be the cradle of magnetic exchange interactions in solids. Their wide range of applications include microwave devices and permanent magnets . They are also suitable for spintronic devices owing to their high resistivity, low magnetic damping, and spin-dependent tunneling probabilities. The Curie temperature is the crucial factor determining the temperature range in which any ferri/ferromagnetic system remains stable. However, the record Curie temperature has stood for over …
In the present paper, the electronic, structural, thermodynamic, and elastic properties of cubic $PbGeO_{3}$ perovskite oxide are presented and computed using the WIEN2K code. The structural properties have been evaluated and they are in good agreement with the theoretical and experimental data. A phonon dispersion is made and it reveals that the cubic $PbGeO_{3}$ perovskite is dynamically stable. In addition, the electronic properties of $PbGeO_{3}$ shows an opening gap energy, meaning a semiconductor behavior with an indirect band gap equal to $1.67 eV$. Moreover, the obtained elastic consta…
Double perovskites Sr$_2$FeMO$_6$ (M=Mo and Re) exhibit significant colossal magnetoresistance even at room temperature due to the high Curie Temperature (419K and 401K). However, such a high Curie Temperature is puzzling, given the large separation between magnetic elements (Fe). Moreover, with M=W, the electronic and magnetic properties suddenly change to insulating and antiferromagnetic with the N{é}el temperature of only 16$\sim$37 K. Based on detailed electronic structure calculations, a new mechanism is proposed which stabilizes the strong ferromagnetic state for M=Mo and Re and is passi…
Halide perovskites consist a class of materials under intense investigation due to their potential technological applications like solar cells, optoelectronic devices and catalysis. Recently we have studied using electronic band structure calculations from first principles, the cubic MABX$_3$ compounds [A. Koliogiorgos et al., Comput. Mater. Sci. \textbf{138}, 92 (2017)], where MA stands for the methylammonium cation, B is a divalent cation and X a halogen. We expand our study in the case where Cs stands in place of the MA cation. Our results suggest that the Cs-based compounds exhibit also a …
The high efficiency of lead organo-metal-halide perovskite solar cells has raised many questions about the role of the methylammonium (MA) molecules in the Pb-I framework. Experiments indicate that the MA molecules are able to 'freely' spin around at room temperature even though they carry an intrinsic dipole moment. We have performed large supercell (2592 atoms) finite temperature ab-initio molecular dynamics calculations to study the correlation between the molecules in the framework. An underlying long range anti-ferroelectric ordering of the molecular dipoles is observed. The dynamical cor…
In the development of highly efficient photovoltaic cells, solid perovskite systems have demonstrated unprecedented promise, with the figure of merit exceeding nineteen percent of efficiency. In this paper, we investigate the optical and vibrational properties of organometallic cubic perovskite CH3NH3PbI3 using first-principles calculations. For accurate theoretical description, we go beyond conventional density functional theory (DFT), and calculated optical conductivity using relativist quasi-particle (GW) correction. Incorporating these many-body effects, we further solve Bethe-Salpeter equ…
A little addition of Cl to \ce{MAPbI3} has been reported to improve the material stability as well as light harvesting and carrier conducting properties of organometal trihalide perovskites, the key component of perovskite solar cell (PSC). However, the mechanism of performance enhancement of PSC by Cl addition is still unclear. Here, we apply the efficient virtual crystal approximation method to revealing the effects of Cl addition on the structural, electronic, optical properties and material stability of \ce{MAPb(I_{1-x}Cl_x)3}. Our {\it ab initio} calculations present that as the increase …
The phonon spectra of calcium, strontium, barium, radium, cadmium, zinc, magnesium, germanium, tin, and lead titanates with the perovskite structure are calculated from first principles within the density functional theory. By analyzing the unstable modes in the phonon spectra, the possible lattice distortions are determined and the energies of the corresponding phases are calculated. From analyzing the phonon spectra, force constants, and eigenvectors of TO phonons, a conclusion is drawn on the origin of the ferroelectricity in considered crystals. It is shown that the main factors determinin…
We present a first-principles investigation of ferroelectricity in layered perovskite oxide La2Ti2O7 (LTO), one of the compounds with highest Curie temperature known (1770 K). Our calculations reveal that LTO's ferroelectric transition results from the condensation of two soft modes that have the same symmetry and are strongly coupled anharmonically. Further, the leading instability mode essentially consists of rotations of the oxygen octahedra that are the basic building block of the perovskite structure; remarkably, because of the particular topology of the lattice, such O6 rotations give ra…
Employing first-principles electronic structure calculations in conjunction with the frozen-magnon method we study the effective exchange interactions and spin waves in local moment ferromagnets. As prototypes we have chosen three L2$_1$-type full Heusler alloys Cu$_2$MnAl, Ni$_2$MnSn and Pd$_2$MnSn, and the L1$_2$-type XPt$_3$ compounds with X= V, Cr and Mn. We have also included CoPt$_3$ which is a usual ferromagnet. In all compounds due to the large spatial separation ($\sim 4$ Å) of the magnetic transition metal atoms, the 3\textit{d} states belonging to different atoms overlap weakly and …
Exploring epitaxial structures for electrically pumped perovskite lasers: a study of CsPb(Br,I)$_3$ based on the \textit{ab initio} Bethe-Salpeter equation
La1-xSrxCo0.25Fe0.75O3-delta is known as one of the best cathode materials for permeation membranes and solid oxide fuel cells. Optimization of its chemical composition is a challenging problem. One of the key properties is concentration of oxygen vacancies, controlled by their formation energies. Ab initio calculations were employed in order to study the formation of oxygen vacancies in La1-xSrxCo0.25Fe0.75O3-delta perovskites by varying the Sr content from x = 12.5% to 50%. The formation energies were obtained for different stoichiometries as functions of temperature and oxygen partial press…
The exchange interactions of Cr4N, Mn4N, Fe4N, Co4N, and Ni4N compounds with perovskite structure were calculated to obtain the Curie temperatures for these compounds from Monte Carlo calculations. Contrary to naive expectation, the exchange interactions vary markedly among these five compounds. In Fe4N, the intra-sublattice interaction of the Fe 3c atoms is strongly negative, leading to a significant reduction of the Curie temperature. The calculated Curie temperatures are 291K (Cr4N), 710K (Mn4N), 668K (Fe4N), 827K (Co4N), and 121K (Ni4N), in good agreement with experimental observations whe…
In this work we performed a detailed investigation about ordering in \bcn perovskite. The sintering temperature and time were changed to obtain samples with different ordering. The order parameters were probed by Raman spectroscopy based on a partial disordered model. To use the partial disordered model correctly we performed {\it ab initio} calculations in \bcn to assign the optical phonons. The results showed that sintering temperature improves order while sintering time is not so efficient to promote order.
In recent experiments the irradiation of insulators of perovskite type with swift heavy ions under glancing incidence has been shown to provide a unique means to generate periodically arranged nanodots at the surface. The physical origin of these patterns has been suggested to stem from a highly anisotropic electron density distribution within the bulk. In order to show the relevance of the electron density distribution of the target we present a model calculation for the system Xe$^{+23}$ $\to$ SrTiO$_{3}$ that is known to produce the aforementioned surface modifications. On the basis of the …
The effects of annealing conditions upon the microstructure and the magnetic properties of the colossal magnetoresistive manganite La0.75Sr0.25MnO3 have been investigated. Increasing the annealing temperature and time of annealing is seen to increase the size of crystallites within the samples. The spontaneous magnetic moment per formula unit and the Curie temperature, as obtained from Arrott plot analysis, are observed to depend upon the average size of crystallites.
Mixed-anion mixed-cation perovskites with (FAPbI$_3$)$_{1-x}$(MAPbBr$_3$)$_x$ composition have allowed record efficiencies in photovoltaic solar cells, but their atomic-scale behaviour is not well understood yet, in part because their theoretical modelling requires consideration of complex and interrelated dynamic and disordering effects. We present here an ab initio molecular dynamics investigation of the structural, thermodynamic, and electronic properties of the (FAPbI$_3$)$_{0.875}$(MAPbBr$_3$)$_{0.125}$ perovskite. A special quasi-random structure is proposed to mimic the disorder of both…
Density-functional simulations are used to calculate structural properties and high-symmetry phonons of the hypothetical cubic phase, the stable orthorhombic phase and an intermediate tetragonal phase of magnesium silicate perovskite. We show that the structure of the stable phase is well described by freezing in a small number of unstable phonons into the cubic phase. We use the frequencies of these unstable modes to estimate transition temperatures for cubic--tetragonal and tetragonal--orthorhombic phase transitions. These are investigated further to find that the coupling with the strain su…
Hybrid organic-inorganic halide perovskites for photovoltaics have attracted research interest due to their unique material properties, but suffered from poor material stability. In this work, we investigated the surface phase diagrams of PbI$_2$ and cubic CH$_3$NH$_3$PbI$_3$ (MAPbI$_3$) for a better understanding of precursor effect on perovskite synthesis via solid-gas reaction, by density functional theory calculations combined with thermodynamics. Using the devised slab models of PbI$_2$(001) and MAPbI$_3$(100), (110) and (111) surfaces with perfect and various vacant defect terminations, …
We determine from first-principles the Curie temperature Tc for bulk Co in the hcp, fcc, bcc, and tetragonalized bct phases, for FeCo alloys, and for bcc and bct Fe. For bcc-Co, Tc=1420 K is predicted. This would be the highest Curie temperature among the Co phases, suggesting that bcc-Co/MgO/bcc-Co tunnel junctions offer high magnetoresistance ratios even at room temperature. The Curie temperatures are calculated by mapping ab initio results to a Heisenberg model, which is solved by a Monte Carlo method.
Here we perform $ab-initio$ study of Curie temperature $T_C$ under hydrostatic pressure for intermetallic compound GdFe$_2$. To calculate $T_C$ for GdFe$_2$ we applied mean-field solution of the Heisenberg model for several magnetic sublattices with DFT/LDA calculated values of necessary exchange interaction integrals and local magnetic moments. To compare with available experimental data pressure values were taken from zero up to about 70 Kbar. It corresponds to 2\% compression of the volume of the unit cell. In agreement with experimental data $T_C$ grows under pressure. It was shown that Fe…
We discovered an unprecedented magnitude of the 1/f noise near the Curie temperature Tc in low-Tc manganites. The scaling behavior of the 1/f noise and the resistance provides strong evidence of the percolation nature of the ferromagnetic transition in the polycrystalline samples. The step-like changes of the resistance with temperature, observed for single crystals, suggest that the size of the ferromagnetic domains depends on the size of crystallites.
Single crystals of a new twinned hexagonal perovskite compound Sr8Os6.3O24 have been synthesized, and structural and magnetic properties have been determined. The compound crystallizes in a hexagonal cell with lattice parameters a = 9.6988(3) Å and c = 18.1657(5) Å. The structure is an eight-layered hexagonal B-site deficient perovskite with the layer sequence (ccch)2 and represents the first example of a hexagonal structure among 5d oxides adopting a twin option. The sample shows spontaneous ferromagnetic magnetization below 430 K with a small saturation moment of 0.11 μB/Os ion. This is the …
Hybrid organic/inorganic perovskites have emerged as efficient semiconductor materials for applications in photovoltaic solar cells with conversion efficiency above 20 \%. Recent experiments have synthesized ultra-thin two-dimensional (2D) organic perovskites with optical properties similar to those of 2D materials like monolayer MoS$_2$: large exciton binding energy and excitonic effects at room temperature. In addition, 2D perovskites are synthesized with a simple fabrication process with potential low-cost and large-scale manufacture. Up to now, state-of-the-art simulations of the excitonic…
We predict through our first-principles calculations that four double perovskite oxides of Bi2ABO6 (AB = FeMo, MnMo, MnOs, CrOs) are half-metallic ferrimagnets. Our calculated results shows that the four optimized structures have negative formation energy, from -0.42 to -0.26 eV per formula unit, which implies that they could probably be realized. In the case of Bi2FeMoO6, the half-metallic gap and Curie temperature are predicted to reach to 0.71 eV and 650 K, respectively, which indicates that high spin polarization could be kept at high temperatures far beyond room temperature. It is believe…
The impact of ordered vacancies on the dynamic stability of perovskites is investigated under the $\textit{ab initio}$ framework with a focus on cubic BaFeO$_{3}$ ($Pm\bar{3}m$) and vacancy-ordered monoclinic BaFeO$_{2.67}$ ($P2_{1}/m$). The harmonic approximation shows that both structures are dynamically unstable at 0 K. For the monoclinic structure, the instability is related to rotational distortions of the Fe coordination tetrahedra near the ordered vacancies. $\textit{Ab initio}$ molecular dynamics simulations in combination with the introduced structural descriptor demonstrate that both…
The temperature dependence of the O K-edge pre-edge structure in the x-ray absorption spectra of the perovskites La(1-x)A(x)MnO(3), (A = Ca, Sr; x = 0.3, 0.4) reveals a correlation between the disappearance of the splitting in the pre-edge region and the presence of Jahn-Teller distortions. The different magnitudes of the distortions for different compounds is proposed to explain some dissimilarity in the line shape of the spectra taken above the Curie temperature.
We predict high thermoelectric efficiency in the layered perovskite La$_2$Ti$_2$O$_7$, based on calculations (mostly ab-initio) of the electronic structure, transport coefficients, and thermal conductivity in a wide temperature range. The figure of merit $ZT$ computed with a temperature-dependent relaxation time increases monotonically from just above 1 at room temperature to over 2.5 at 1200 K, at an optimal carrier density of around 10$^{20}$ cm$^{-3}$. The Seebeck thermopower coefficient is between 200 and 300 $μ$V/K at optimal doping, but can reach nearly 1 mV/K at low doping. Much of the …
Newly synthesized perovskite NaOsO3 shows Curie-Weiss metallic nature at high temperature and suddenly goes into an antiferromagnetically insulating state at 410 K on cooling. Electronic specific heat at the low temperature limit is absent, indicating that the band gap fully opens. In situ observation in electron microscopy undetected any lattice anomalies in the vicinity of the transition temperature. It is most likely that the antiferromagnetic correlation plays an essential role of the gap opening.
Recently, direct bandgap double perovskites are becoming more popular among photovoltaic research community owing to their potential to address issues of lead (Pb) toxicity and structural instability inherent in lead halide (simple) perovskites. In this study, In-Ag based direct bandgap double perovskite, Cs2AgInCl6 (CAIC), is treated with transition metal doping to improve the optoelectronic properties of the material. Investigations of structural and optoelectronic properties of Cu-doped CAIC, Cs2Ag(1-x)CuxInCl6, are done using ab-initio calculations with density functional theory (DFT) and …
Relaxor ferrolectrics are important in technological applications due to a strong electromechanical response, energy storage capacity, electrocaloric effect, and pyroelectric energy conversion properties. Current efforts to discover and design new materials in this class generally rely on substitutional doping of known ferroelectrics, as slight changes to local compositional order can significantly affect the Curie temperature, morphotropic phase boundary, and electromechanical responses. In this work, we demonstrate that moving to the strong limit of compositional complexity in an ABO3 perovs…
We present a powder inelastic neutron scattering study of magnetic excitations in Ba$_2$FeReO$_6$, a member of the double perovskite family of materials which exhibit half-metallic behavior and high Curie temperatures. We find clear evidence of two well-defined dispersing magnetic modes in its low temperature ferrimagnetic state. We develop a local moment model, which incorporates the interaction of Fe spins with spin-orbit locked magnetic moments on Re, and show that this captures our experimental observations. Our study further opens up double perovskites as model systems to explore the inte…
We study a selection of Cu-containing magnetic quadruple perovskites (CaCu$_{3}$Ti$_{4}$O$_{12}$, LaCu$_{3}$Fe$_{4}$O$_{12}$, and YCu$_{3}$Co$_{4}$O$_{12}$) by ab initio calculations, and show that Cu is in an effective divalent Cu(II)-like state or a trivalent Cu(III) state depending on the choice of octahedral cation. Based on the electronic structure, we also discuss the role of Mott and Zhang-Rice physics in this materials class.
