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We analyze the role of local geometry in the spin and orbital interaction in transition metal compounds with orbital degeneracy. We stress that the tendency observed for the most studied case (transition metals in O$_6$ octahedra with one common oxygen -- common corner of neighboring octahedra and with $\sim 180^{\circ}$ metal--oxygen--metal bonds), that ferro-orbital ordering renders antiferro-spin coupling, and, {\it vice versa}, antiferro-orbitals give ferro-spin ordering, is not valid in general case, in particular for octahedra with common edge and with $\sim 90^{\circ}$ M--O--M bonds. Special attention is paid to the ``third case'', neighboring octahedra with common face (three common oxygens) -- the case practically not considered until now, although there are many real systems with this geometry. Interestingly enough, the spin--orbital exchange in this case turns out to be to be simpler and more symmetric than in the first two cases. We also consider, which form the effective exchange takes for different geometries in case of strong spin--orbit coupling., Comment: 31 pages, 9 figures, submitted to JETP

We have synthesized and studied single-crystal Ba5AlIr2O11 that features dimer chains of two inequivalent octahedra occupied by tetravalent and pentavalent ions, respectively. Ba5AlIr2O11 is a Mott insulator that undergoes a subtle structural phase transition near 210 K and a magnetic transition at 4.5 K; the latter transition is surprisingly resistant to applied magnetic fields up to 12 T, but sensitive to modest applied pressure. All results indicate that the phase transition at 210 K signals an enhanced charge order that induces electrical dipoles and strong dielectric response near 210 K. It is clear that the strong covalency and spin-orbit interaction (SOI) suppress double exchange in Ir dimers and stabilize a novel magnetic state. The behavior of Ba5AlIr2O11 therefore provides unique insights into the physics of SOI along with strong covalency in competition with double exchange interactions of comparable strength., Comment: 6 figures, 20 pages. arXiv admin note: text overlap with arXiv:1505.00877

The electronic and magnetic properties of Ba$_5$AlIr$_2$O$_{11}$ containing Ir-Ir dimers are investigated using the GGA and GGA+SOC calculations. We found that strong suppression of the magnetic moment in this compound recently found in [J. Terzic {\it et al.}, Phys. Rev. B {\bf 91}, 235147 (2015)] is not due to charge-ordering, but is related to the joint effect of the spin-orbit interaction and strong covalency, resulting in the formation of metal-metal bonds. They conspire and act against the intra-atomic Hund's rule exchange interaction to reduce total magnetic moment of the dimer. We argue that the same mechanism could be relevant for other $4d$ and $5d$ dimerized transition metal compounds.

An approach to compute exchange parameters of the Heisenberg model in plane-wave-based methods is presented. This calculation scheme is based on the Green's function method and Wannier function projection technique. It was implemented in the framework of the pseudopotential method and tested on such materials as NiO, FeO, Li2MnO3, and KCuF3. The obtained exchange constants are in a good agreement with both the total energy calculations and experimental estimations for NiO and KCuF3. In the case of FeO our calculations explain the pressure dependence of the N\'eel temperature. Li2MnO3 turns out to be a Slater insulator with antiferromagnetic nearest-neighbor exchange defined by the spin splitting. The proposed approach provides a unique way to analyze magnetic interactions, since it allows one to calculate orbital contributions to the total exchange coupling and study the mechanism of the exchange coupling.

Specific features of orbital and spin structure of transition metal compounds in the case of the face-sharing MO$_6$ octahedra are analyzed. In this geometry, we consider the form of the spin--orbital Hamiltonian for transition metal ions with double ($e_g^{\sigma}$) or triple ($t_{2g}$) orbital degeneracy. Trigonal distortions typical of the structures with face-sharing octahedra lead to splitting of $t_{2g}$ orbitals into an $a_{1g}$ singlet and $e_g^{\pi}$ doublet. For both doublets ($e_g^{\sigma}$ and $e_g^{\pi}$), in the case of one electron or hole per site, we arrive at a symmetric model with the orbital and spin interaction of the Heisenberg type and the Hamiltonian of unexpectedly high symmetry: SU(4). Thus, many real materials with this geometry can serve as a testing ground for checking the prediction of this interesting theoretical model. We also compare general trends in spin--orbital ("Kugel--Khomskii") exchange interaction for three typical situations: those of MO$_6$ octahedra with common corner, common edge, and the present case of common face, which has not been considered yet., Comment: 10 pages, 5 figures, RevTeX, in version 2, we took into account the remarks of Referees

We synthesize and study single crystals of the layered honeycomb lattice Mott insulators Na2RuO3 and Li2RuO3 with magnetic Ru4+(4d4) ions. The newly found Na2RuO3 features a nearly ideal honeycomb lattice and orders antiferromagnetically at 30 K. Single-crystals of Li2RuO3 adopt a honeycomb lattice with either C2/m or more distorted P21/m below 300 K, depending on detailed synthesis conditions. We find that Li2RuO3 in both structures hosts a well-defined magnetic state, in contrast to the singlet ground state found in polycrystalline Li2RuO3. A phase diagram generated based on our results uncovers a new, direct correlation between the magnetic ground state and basal-plane distortions in the honeycomb ruthenates., Comment: 4 figures, accepted for publication in Phys. Rev. B

With the use of the band structure calculations we demonstrate that previously reported [Nat. Materials {\bf 3}, 48 (2004)] experimental crystal and magnetic structures for NaMn$_7$O$_{12}$ are inconsistent with each other. The optimization of the crystal lattice allows us to predict a new crystal structure for the low temperature phase, which is qualitatively different from the one presented before. The AFM-CE type of the magnetic order stabilizes the structure with the elongated, not compressed Mn$^{3+}_B$O$_6$ octahedra, striking NaMn$_7$O$_{12}$ out of the list of the anomalous Jahn-Teller systems. The orbital correlations were shown to exist even in the cubic phase, while the charge order appears only in the low temperature distorted phase., Comment: 5 pages

An antiferromagnetic ordering in Pb3TeCo3V2O14 takes place through formation of short range correlation regime with T* ~ 10.5 K and succession of second order phase transition at TN1 = 8.9 K and first order phase transition at TN2 = 6.3 K. An external magnetic field rapidly destroys magnetic structure at T < TN2 and influences the magnetic order at TN2 < T < TN1 resulting in complex magnetic phase diagram of Pb3TeCo3V2O14 as derived from magnetization and specific heat measurements. The first principles calculations indicate that in variance with layered crystal structure the magnetic subsystem of Pb3TeCo3V2O14 is quasi-one-dimensional and highly unusual consisting of weakly coupled triangular tubes., Comment: 12 pages, 10 figures

Using ab initio band structure and model calculations we studied magnetic properties of one of the Mn$_4$ molecular magnets (Mn4(hmp)6), where two types of the Mn ions exist: Mn3+ and Mn2+. The direct calculation of the exchange constants in the GGA+U approximation shows that in contrast to a common belief the strongest exchange coupling is not between two Mn3+ ions (J_{bb}), but along two out of four exchange paths connecting Mn3+ and Mn2+ ions (J_{wb}). The microscopic analysis performed within the perturbation theory allowed to establish the mechanism for this largest ferromagnetic exchange constant. The charge ordering of the Mn ions results in the situation when the energy of the excited state in the exchange process is defined not by the large on-site Coulomb repulsion U, but by much smaller energy V, which stabilizes the charge ordered state. Together with strong Hund's rule coupling and specific orbital order this leads to a large ferromagnetic exchange interaction for two out of four Mn2+ --Mn3+ pairs., Comment: 12 pages, 10 figures

The exchange interactions and magnetic structure in layered system CuMnO2 (mineral crednerite) and in nonstoichiometric system Cu1.04Mn0.96O2, with triangular layers distorted due to orbital ordering of the Mn3+ ions, are studied by ab-initio band-structure calculations, which were performed within the GGA+U approximation. The exchange interaction parameters for the Heisenberg model within the Mn-planes and between the Mn-planes were estimated. We explain the observed in-plane magnetic structure by the dominant mechanism of the direct d-d exchange between neighboring Mn ions. The superexchange via O ions, with 90 degree Mn-O-Mn bonds, plays less important role for the in-plane exchange. The interlayer coupling is largely dominated by one exchange path between the half-filled 3z^2-r^2 orbitals of Mn3+. The change of interlayer coupling from antiferromagnetic in pure CuMnO2 to ferromagnetic in doped material is also explained by our calculations.

We present the \emph{ab initio} calculation of the electronic structure and magnetic properties of Bi$_2$Fe$_4$O$_9$. This compound crystallizes in the orthorhombic crystal structure with the Fe$^{3+}$ ions forming the Cairo pentagonal lattice implying strong geometric frustration. The neutron diffraction measurements reveal nearly orthogonal magnetic configuration, which at first sight is rather unexpected since it does not minimize the total energy of the pair of magnetic ions coupled by the Heisenberg exchange interaction. Here we calculate the electronic structure and exchange integrals of Bi2Fe4O9 within the LSDA+U method. We obtain three different in-plane (J3=36 K, J4=73 K, J5=23 K) and two interplane (J1=10 K, J2=12 K) exchange parameters. The derived set of exchange integrals shows that the realistic description of Bi2Fe4O9 needs a more complicated model than the ideal Cairo pentagonal lattice with only two exchange parameters in the plane. However, if one takes into account only two largest exchange integrals, then according to the ratio x\equiv J3/J4=0.49<\sqrt{2} (a critical parameter for the ideal Cairo pentagonal lattice, see. Ref.~1) the ground state should be the orthogonal magnetic configuration in agreement with experiment. The microscopic origin of different exchange interactions is also discussed., Comment: 6 pages, 4 figures

An unusual orbital state was recently proposed to explain the magnetic and transport properties of Ba$_3$CoRu$_2$O$_9$ [Phys. Rev. B. {\bf 85}, 041201 (2012)]. We show that this state contradicts to the first Hund's rule and does not realize in the system under consideration because of a too small crystal-field splitting in the $t_{2g}$ shell. A strong suppression of the local magnetic moment in Ba$_3$CoRu$_2$O$_9$ is attributed to a strong hybridization between the Ru 4$d$ and O 2$p$ states., Comment: 5 pages, 5 figures

We study experimentally and theoretically the effect of Eu doping and partial oxygen isotope substitution on the transport and magnetic characteristics and spin-state transitions in (Pr$_{1-y}$Eu$_y$)$_{0.7}$Ca$_{0.3}$CoO$_3$ cobaltites. The Eu doping level $y$ is chosen in the range of the phase diagram near the crossover between the ferromagnetic and spin-state transitions ($0.10 < y < 0.20$). We prepared a series of samples with different degrees of enrichment by the heavy oxygen isotope $^{18}$O, namely, containing 90%, 67%, 43%, 17%, and 0% of $^{18}$O. Based on the measurements of ac magnetic susceptibility $\chi(T)$ and electrical resistivity $\rho(T)$, we analyze the evolution of the sample properties with the change of Eu and $^{18}$O content. It is demonstrated that the effect of increasing $^{18}$O content on the system is similar to that of increasing the Eu content. The band structure calculations of the energy gap between $t_{2g}$ and $e_g$ bands including the renormalization of this gap due to the electron-phonon interaction reveal the physical mechanisms underlying such similarity., Comment: 12 pages, 15 figures, submitted to JETP (the last version incorporates all changes made in the manuscript accepted for publication)

The doping series Eu1-xCaxCoO3-d provides a rather peculiar way to study the spin-state transition in cobalt-based complex oxides since partial substitution of Eu3+ ions by Ca2+ ions does not increase the mean valence state of cobalt but is accompanied by appearance of oxygen vacancies in the ratio d \sim x/2. In the parent compound EuCoO3, the low spin (LS)-high spin (HS) transition takes place at temperatures so high that the chemical decomposition prevents its direct observation. The substitution of Eu3+ for Ca2+ in this system shifts the LS-HS transition to lower temperatures. The energy gap associated with this transition in octahedrally-coordinated Co3+ ions changes from 1940 K in EuCoO3 to 1540 K in Eu0.9Ca0.1CoO2.95 and 1050 K in Eu0.8Ca0.2CoO2.9. Besides, each O2- vacancy reduces the local coordination of two neighboring Co3+ ions from octahedral to pyramidal thereby locally creating magnetically active sites which couple into dimers. These dimers at low temperatures form another gapped magnetic system with very different energy scale, D~3 K, on the background of intrinsically non-magnetic lattice of octahedrally-coordinated low-spin Co3+ ions., Comment: 15 pages

The chain-polymer Cu(II) breathing crystals C21H19CuF12N4O6 were studied using the x-ray diffraction and ab initio band structure calculations. We show that the crystal structure modification at T=146 K, associated with the spin crossover transition, induces the changes of the orbital order in half of the Cu sites. This in turn results in the switch of the magnetic interaction sign in accordance with the Goodenough-Kanamori-Andersen theory of the coupling between the orbital and spin degrees of freedom., Comment: 6 pages, 7 figures

The magnetic and electronic properties of Ba$_4$Ru$_3$O$_{10}$ were investigated by the ab-initio and model calculations. It is shown that nonmagnetic ground state of the one-third Ru$^{4+}$ ions is not due to the correlation effects. It is rather caused by the charge disproportionation between crystallographically different Ru and the molecular orbital formation in the Ru's trimer., Comment: 6 pages, 5 figures

With the use of the density function calculations we show that the actual crystal structure of Cs$_2$CuCl$_2$Br$_2$ should contain elongated in the $ab-$plane CuCl$_4$Br$_2$ octahedra, in contrast to the experimentally observed compression in $c-$direction. We also predict that the spins on Cu$^{2+}$ ions should be ferromagnetically ordered in $ab-$plane, while the exchange interaction along $c-$direction is small and its sign is uncertain., Comment: 4 pages, 3 figures

We report the first systematic measurements of the Raman scattering by electrons in elemental metals of Al, Mo, Nb, Os, Pb, Re, Ta, Ti, V, W and metallic compound La$B_6$. Experimental spectra are modelled on the base of the band structures, calculated within the density functional theory, taking properly into account the effects of electron-phonon scattering. The agreement between our measured and calculated spectra is excellent for the variety of metals, thus providing estimates for the electron-phonon coupling constants and temperature-dependent relaxation rates. The method can be applied for other metallic materials to evaluate an electron-phonon coupling as an alternative to the transport and optical measurements.

Synchrotron X-ray diffraction experiment shows that the metal-insulator transition occurring in a ferromagnetic state of a hollandite K$_2$Cr$_8$O$_{16}$ is accompanied by a structural distortion from the tetragonal $I4/m$ to monoclinic $P112_{1}/a$ phase with a $\sqrt{2}\times\sqrt{2}\times 1$ supercell. Detailed electronic structure calculations demonstrate that the metal-insulator transition is caused by a Peierls instability in the quasi-one-dimensional column structure made of four coupled Cr-O chains running in the $c$-direction, leading to the formation of tetramers of Cr ions below the transition temperature. This furnishes a rare example of the Peierls transition of fully spin-polarized electron systems., Comment: Phys. Rev. Lett., in press, 5 pages, 3 figures

Special features of the crystal field splitting of $d-$levels in the transition metal compounds with the small or negative charge-transfer gap $\Delta_{CT}$ are considered. We show that in this case the Coulomb term and the covalent contribution to the $t_{2g} - e_g$ splitting have different signs. In order to check the theoretical predictions we carried out the ab-initio band structure calculations for Cs$_2$Au$_2$Cl$_6$, in which the charge-transfer gap is negative, so that the $d-$electrons predominantly occupy low-lying bonding states. For these states the $e_g$-levels lie below $t_{2g}$ ones, which demonstrates that at least in this case the influence of the $p-d$ covalency on the total value of the crystal field splitting is stronger than the Coulomb interaction (which would lead to the opposite level order). We also show that the states in conduction band are made predominantly of $p-$states of ligands (Cl), with small admixture of $d-$states of Au.

The magnetic properties of Ce in the $\alpha$ and $\gamma$ phase are calculated within the LDA+DMFT approach. The magnetic susceptibility in these two phases shows a similar behavior over a wide temperature range: a Curie-Weiss law at high temperatures, indicating the presence of local moments, followed by a maximum in a crossover regime, and a saturation characteristic of a state with screened local moments at low temperature. The difference in experimentally observable magnetic properties is caused by the shift of the susceptibility to higher temperatures in the $\alpha-$phase compared to the $\gamma-$phase, due to the larger hybridization between localized $4f-$states and conductive $spd-$electrons., Comment: 4 pages, 4 figures

The importance of taking into account inter-site $f-f$ hybridization in electron structure calculations for Ce metal and cerium heavy fermion compounds was studied. We demonstrate that for heavy-fermion systems such as cerium compound CeCu$_2$Si$_2$ $f-f$ hybridization can be neglected and Anderson model application is well justified. On another hand for cerium metal $f-f$ hybridization is strong enough to provide the contribution to hybridization function comparable to hybridization between $4f$ and itinerant electrons. We argue that in the case of Ce only the most general Hamiltonian combining Hubbard and Anderson models should be used., Comment: 5 figures

LDA+DMFT (Local Density Approximation combined with Dynamical Mean-Field Theory) computation scheme has been used to calculate spectral properties of LaFeAsO -- the parent compound for new high-T$_c$ iron oxypnictides. Coulomb repulsion $U$ and Hund's exchange $J$ parameters for iron 3d electrons were calculated using \textit {first principles} constrained density functional theory scheme in Wannier functions formalism. Resulting values strongly depend on the number of states taken into account in calculations: when full set of O-$2p$, As-$4p$, and Fe-3d orbitals with corresponding bands are included, computation results in $U=3\div$4 eV and J=0.8 eV. In contrast to that when the basis set is restricted to Fe-3d orbitals and bands only, computation gives much smaller parameter values $F^0$=0.8 eV, $J$=0.5 eV. However, DMFT calculations with both parameter sets and corresponding to them choice of basis functions result in weakly correlated electronic structure that is in agreement with experimental X-ray and photoemission spectra., Comment: 13 pages, 9 figures

First principles constrained density functional theory scheme in Wannier functions formalism has been used to calculate Coulomb repulsion U and Hund's exchange J parameters for iron 3d electrons in LaFeAsO. Results strongly depend on the basis set used in calculations: when O-2p, As-4p, and Fe-3d orbitals and corresponding bands are included, computation results in U=3-4 eV, however, with the basis set restricted to Fe-3d orbitals and bands only, computation gives parameters corresponding to F^0=0.8 eV, J=0.5 eV. LDA+DMFT (the Local Density Approximation combined with the Dynamical Mean-Field Theory) calculation with this parameters results in weakly correlated electronic structure that is in agreement with X-ray experimental spectra.

The experimental data available up to date in literature corresponding to the paramagnetic - spin density wave transition in nonsuperconducting LaOFeAs are discussed. In particular, we pay attention that upon spin density wave transition there is a relative decrease of the density of states on the Fermi level and a pseudogap formation. The values of these quantities are not properly described in frames of the density functional theory. The agreement of them with experimental estimations becomes more accurate with the use of fixed spin moment procedure when iron spin moment is set to experimental value. Strong electron correlations which are not included into the present calculation scheme may lead both to the decrease of spin moment and renormalization of energy spectrum in the vicinity of the Fermi level for correct description of discussed characteristics.

Effects of Coulomb correlation on LaOFeAs electronic structure have been investigated by LDA+DMFT(QMC) method. The calculation results show that LaOFeAs is in the regime of intermediate correlation strength with significant part of the spectral density moved from the Fermi energy to Hubbard bands. However the system is not on the edge of metal insulator-transition because increase of the Coulomb interaction parameter value from $U$=4.0 eV to $U$=5.0 eV did not result in insulator state. Correlations affect different d-orbitals not in the same way. $t_{2g}$ states ($xz,yz$ and $x^2-y^2$ orbitals) have higher energy due to crystal filed splitting and are nearly half-filled. Their spectral functions have pseudogap with Fermi energy position on the higher sub-band slope. Lower energy $e_g$ set of d-orbitals ($3z^2-r^2$ and $xy$) have significantly larger occupancy values with typically metallic spectral functions., Comment: 4 pages, 4 figures

Combining infrared reflectivity, transport, susceptibility and several diffraction techniques, we find compelling evidence that CaCrO3 is a rare case of a metallic and antiferromagnetic transition-metal oxide with a three-dimensional electronic structure. LSDA calculations correctly describe the metallic behavior as well as the anisotropic magnetic ordering pattern of C type: The high Cr valence state induces via sizeable pd hybridization remarkably strong next-nearest neighbor interactions stabilizing this ordering. The subtle balance of magnetic interactions gives rise to magneto-elastic coupling, explaining pronounced structural anomalies observed at the magnetic ordering transition.

The results of the LSDA+U calculations for pyroxenes with diverse magnetic properties (Li,Na)TM(Si,Ge)$_2$O$_6$, where TM is the transition metal ion (Ti,V,Cr,Mn,Fe), are presented. We show that the anisotropic orbital ordering results in the spin-gap formation in NaTiSi$_2$O$_6$. The detailed analysis of different contributions to the intrachain exchange interactions for pyroxenes is performed both analytically using perturbation theory and basing on the results of the band structure calculations. The antiferromagnetic $t_{2g}-t_{2g}$ exchange is found to decrease gradually in going from Ti to Fe. It turns out to be nearly compensated by ferromagnetic interaction between half-filled $t_{2g}$ and empty $e_g$ orbitals in Cr-based pyroxenes. The fine-tuning of the interaction parameters by the crystal structure results in the ferromagnetism for NaCrGe$_2$O$_6$. Further increase of the total number of electrons and occupation of $e_g$ sub-shell makes the $t_{2g}-e_g$ contribution and total exchange interaction antiferromagnetic for Mn- and Fe-based pyroxenes. Strong oxygen polarization was found in Fe-based pyroxenes. It is shown that this effect leads to a considerable reduction of antiferromagnetic intrachain exchange. The obtained results may serve as a basis for the analysis of diverse magnetic properties of pyroxenes, including those with recently discovered multiferroic behavior., Comment: 11 pages, 10 figures

Pyroxenes with the general formula $AM$Si$_2$O$_6$ ($A$ = mono- or divalent metal, $M$ = di- or trivalent metal) are shown to be a new class of multiferroic materials. In particular, we have found so far that NaFeSi$_2$O$_6$ becomes ferroelectric in a magnetically ordered state below $\simeq 6$ K. Similarly, magnetically driven ferroelectricity is also detected in the Li homologues, LiFeSi$_2$O$_6$ ($T_C \simeq 18$ K) and LiCrSi$_2$O$_6$ ($T_C \simeq 11$ K). In all these monoclinic systems the electric polarization can be strongly modified by magnetic fields. Measurements of magnetic susceptibility, pyroelectric current and dielectric constants (and their dependence on magnetic field) are performed using a natural crystal of aegirine (NaFeSi$_2$O$_6$) and synthetic crystals of LiFeSi$_2$O$_6$ and LiCrSi$_2$O$_6$ grown from melt solution. For NaFeSi$_2$O$_6$ a temperature versus magnetic field phase diagram for NaFeSi$_2$O$_6$ is proposed. Exchange constants are computed on the basis of {\it ab initio} band structure calculations. The possibility of a spiral magnetic structure caused by frustration as origin of the multiferroic behaviour is discussed. We propose that other pyroxenes may also be multiferroic, and that the versatility of this family offers an exceptional opportunity to study general conditions for and mechanisms of magnetically driven ferroelectricity., Comment: 10 pages, 4 figures; calculated excange constants have been updated

Magnetic and electronic properties of NaTiSi$_2$O$_6$ in low temperature phase were studied in the framework of the LDA+U approximation. We stress that neglecting correlation effects in LSDA calculations one obtains not only several times smaller value of the band gap, but also fails to describe magnetic properties of NaTiSi$_2$O$_6$. Our LDA+U results confirm formation of singlet Ti-Ti dimers in low temperature phase of NaTiSi$_2$O$_6$ driven by corresponding orbital ordering [J. Phys. Soc. Jpn. 71, 1423 (2002)], but strongly disagree with the LSDA results and interpretations of Phys. Rev. Lett. 93, 036401 (2004)., Comment: 1 table. Submitted to Phys. Rev. Lett. as a Comment

We found direct experimental evidence for an orbital switching in the V 3d states across the metal-insulator transition in VO$_{2}$. We have used soft-x-ray absorption spectroscopy at the V $L_{2,3}$ edges as a sensitive local probe, and have determined quantitatively the orbital polarizations. These results strongly suggest that, in going from the metallic to the insulating state, the orbital occupation changes in a manner that charge fluctuations and effective band widths are reduced, that the system becomes more 1-dimensional and more susceptible to a Peierls-like transition, and that the required massive orbital switching can only be made if the system is close to a Mott insulating regime.

In the framework of the LDA+U approximation we propose the direct way of calculation of crystal-field excitation energy and apply it to La and Y titanates. The method developed can be useful for comparison with the results of spectroscopic measurements because it takes into account fast relaxations of electronic system. For titanates these relaxation processes reduce the value of crystal-field splitting by $\sim30%$ as compared with the difference of LDA one electron energies. However, the crystal-field excitation energy in these systems is still large enough to make an orbital liquid formation rather unlikely and experimentally observed isotropic magnetism remains unexplained., Comment: 13 pages, 5 figures, 3 tables

Utilizing a sum-rule in a spin-resolved photoelectron spectroscopic experiment with circularly polarized light, we show that the orbital moment in LaTiO$_3$ is strongly reduced both below and above the N\'{e}el temperature. Using Ti $L_{2,3}$ x-ray absorption spectroscopy as a local probe, we found that the crystal field splitting in the $t_{2g}$ subshell is about 0.12-0.30 eV. This large splitting does not facilitate the formation of an orbital liquid.

Optical properties of the isoelectronic compounds LaCoO$_3$ and HoCoO$_3$ has been experimentally and theoretically investigated. We've measured the real $\epsilon_1(\omega)$ and imaginary $\epsilon_2(\omega)$ parts of the dielectric function, reflectance $R(\omega)$ and optical conductivity at room temperature. The shift of the most pronounced spectral features to the high energy region on 0.3 eV associated with larger distortions due to the smaller rare earth ionic radii in HoCoO$_3$ in comparison with LaCoO$_3$ was observed. Also there was found an enhancement of absorption intensity in the range 1.3-2.3 eV in all kinds of spectra in HoCoO$_3$, which can be attributed basing on the results of LDA+U calculations to the different spin-states of Co$^{3+}$ ion in these compounds. The shift of the onset of the absorption from less than 0.1 eV in LaCoO$_3$ to 0.7 eV in HoCoO$_3$ and an absorption intensity enhancement in a narrow spectral range 1.2-2.6 eV in HoCoO$_3$ are clearly seen from the calculated convolution of partial densities of states obtained in the LDA+U approach. Such changes are assumed to be induced by the different Co$^{3+}$ spin-state in these compounds at room temperature., Comment: 10 pages, 3 figures

We present first principles LDA+U calculations of electronic structure and magnetic state for LaCoO3 and HoCoO3. Low Spin to Intermediate Spin state transition was found in our calculations using experimental crystallographic data for both materials with a much higher transition temperature for HoCoO3, which agrees well with the experimental estimations. Low Spin state t6e0 (non-magnetic) to Intermediate Spin state t5e1 (magnetic) transition of Co(3+) ions happens due to the competition between crystal field t_2g-e_g splitting and effective exchange interaction between 3$d$ spin-orbitals. We show that the difference in crystal structure parameters for HoCoO3 and LaCoO3 due to the smaller ionic radius of Ho ion comparing with La ion results in stronger crystal field splitting for HoCoO3 (0.09 eV ~ 1000 K larger than for LaCoO3) and hence tip the balance between the Low Spin and Intermediate Spin states to the non-magnetic solution in HoCoO3., Comment: 13 pages, 6 figures