Fingerprints of Spin-Orbital Physics in Crystalline O2_2

The alkali hyperoxide KO$_2$ is a molecular analog of strongly-correlated systems, comprising of orbitally degenerate magnetic O$_2^-$ ions. Using first-principles electronic structure calculations, we set up an effective spin-orbital model for the low-energy \textit{molecular} orbitals and argue that many anomalous properties of KO$_2$ replicate the status of its orbital system in various temperature regimes.Comment: 4 pages, 2 figures, 1 tabl

First-Principles Computation of YVO3; Combining Path-Integral Renormalization Group with Density-Functional Approach

We investigate the electronic structure of the transition-metal oxide YVO3 by a hybrid first-principles scheme. The density-functional theory with the local-density-approximation by using the local muffin-tin orbital basis is applied to derive the whole band structure. The electron degrees of freedom far from the Fermi level are eliminated by a downfolding procedure leaving only the V 3d t2g Wannier band as the low-energy degrees of freedom, for which a low-energy effective model is constructed. This low-energy effective Hamiltonian is solved exactly by the path-integral renormalization group method. It is shown that the ground state has the G-type spin and the C-type orbital ordering in agreement with experimental indications. The indirect charge gap is estimated to be around 0.7 eV, which prominently improves the previous estimates by other conventional methods

Ferromagnetic zigzag chains and properties of the charge ordered perovskite manganites

The low-temperature properties of the so-called ''charge ordered'' state in 50% doped perovskite manganites are described from the viewpoint of the magnetic spin ordering. In these systems, the zigzag antiferromagnetic ordering, combined with the double-exchange physics, effectively divides the whole sample into the one-dimensional ferromagnetic zigzag chains and results in the anisotropy of electronic properties. The electronic structure of one such chain is described by an effective 3$\times$3 Hamiltonian in the basis of Mn($3de_g$) orbitals. We treat this problem analytically and consider the following properties: (i) the nearest-neighbor magnetic interactions; (ii) the distribution of the Mn($3de_g$) and Mn($4p$) states near the Fermi level, and their contribution to the optical conductivity and the resonant x-ray scattering near the Mn $K$-absorption edge. We argue that the anisotropy of magnetic interactions in the double-exchange limit, combined with the isotropic superexchange interactions, readily explains both the local and the global stability of the zigzag antiferromagnetic state. The two-fold degeneracy of $e_g$ levels plays a very important role in the problem and explains the insulating behavior of the zigzag chain, as well as the appearance of the orbital ordering in the double-exchange model. Importantly, however, the charge ordering itself is expected to play only a minor role and is incompatible with the ferromagnetic coupling within the chain. We also discuss possible effects of the Jahn-Teller distortion and compare the tight-binding picture with results of band structure calculations in the local-spin-density approximation.Comment: 35 pages, 8 figure

Superexchange Interactions in Orthorhombically Distorted Titanates RTiO3 (R= Y, Gd, Sm, and La)

Starting from the multiorbital Hubbard model for the t2g-bands of RTiO3 (R= Y, Gd, Sm, and La), where all parameters have been derived from the first-principles calculations, we construct an effective superexchange (SE) spin model, by treating transfer integrals as a perturbation. We consider four approximations for the SE interactions: (i) the canonical crystal-field (CF) theory, where the form of the the occupied t2g-orbitals is dictated by the CF splitting, and three extensions, namely (ii) the relativistic one, where occupied orbitals are confined within the lowest Kramers doublet obtained from the diagonalization of the crystal field and relativistic spin-orbit (SO) interactions; (iii) the finite-temperature extension, which consider the effect of thermal orbital fluctuations near the CF configuration; (iv) the many-electron extension, which is based on the diagonalization of the full Hamiltonian constructed in the basis of two-electron states separately for each bond of the system. The main results are summarized as follows. (i) Thermal fluctuations of the orbital degrees of freedom can substantially reduce the value of the magnetic transition temperature. (ii) The anisotropic and antisymmetric Dzyaloshinsky-Moriya interactions are rigorously derived and their implications to the magnetic properties are discussed. (iii) The CF theory, although applicable for YTiO3 and high-temperature structures of GdTiO3 and SmTiO3, breaks down in LaTiO3. Instead, the combination of the many-electron effects and SO interaction can be responsible for the AFM character of interatomic correlations in LaTiO3. (iv) The SE interactions in YTiO3 strongly depend on the details of the crystal structure. Distortions in the low-temperature structure tend to weaken the ferromagnetic interactions.Comment: 23 pages, 9 tables, 4 figure

Ground State Properties and Optical Conductivity of the Transition Metal Oxide Sr2VO4{\rm Sr_{2}VO_{4}}

Combining first-principles calculations with a technique for many-body problems, we investigate properties of the transition metal oxide ${\rm Sr_{2}VO_{4}}$ from the microscopic point of view. By using the local density approximation (LDA), the high-energy band structure is obtained, while screened Coulomb interactions are derived from the constrained LDA and the GW method. The renormalization of the kinetic energy is determined from the GW method. By these downfolding procedures, an effective Hamiltonian at low energies is derived. Applying the path integral renormalization group method to this Hamiltonian, we obtain ground state properties such as the magnetic and orbital orders. Obtained results are consistent with experiments within available data. We find that ${\rm Sr_{2}VO_{4}}$ is close to the metal-insulator transition. Furthermore, because of the coexistence and competition of ferromagnetic and antiferromgnetic exchange interactions in this system, an antiferromagnetic and orbital-ordered state with a nontrivial and large unit cell structure is predicted in the ground state. The calculated optical conductivity shows characteristic shoulder structure in agreement with the experimental results. This suggests an orbital selective reduction of the Mott gap.Comment: 38pages, 22figure

Origin of the giant magnetic moments of Fe impurities on and in Cs films

To explore the origin of the observed giant magnetic moments ($\sim 7 \mu_B$) of Fe impurities on the surface and in the bulk of Cs films, we have performed the relativistic LSDA + U calculations using the linearized muffin-tin orbital (LMTO) band method. We have found that Fe impurities in Cs behave differently from those in noble metals or in Pd. Whereas the induced spin polarization of Cs atoms is negligible, the Fe ion itself is found to be the source of the giant magnetic moment. The 3d electrons of Fe in Cs are localized as the 4f electrons in rare-earth ions so that the orbital magnetic moment becomes as large as the spin magnetic moment. The calculated total magnetic moment of $M = 6.43 \mu_B$, which comes mainly from Fe ion, is close to the experimentally observed value.Comment: 4 pages including 3 figures and 1 table. Submitted to PR

Satisfiability Modulo Transcendental Functions via Incremental Linearization

In this paper we present an abstraction-refinement approach to Satisfiability Modulo the theory of transcendental functions, such as exponentiation and trigonometric functions. The transcendental functions are represented as uninterpreted in the abstract space, which is described in terms of the combined theory of linear arithmetic on the rationals with uninterpreted functions, and are incrementally axiomatized by means of upper- and lower-bounding piecewise-linear functions. Suitable numerical techniques are used to ensure that the abstractions of the transcendental functions are sound even in presence of irrationals. Our experimental evaluation on benchmarks from verification and mathematics demonstrates the potential of our approach, showing that it compares favorably with delta-satisfiability /interval propagation and methods based on theorem proving

Long-Range Magnetic Interactions Induced by the Lattice Distortions and the Origin of the E-type Antiferromagnetic Phase in the Undoped Orthorhombic Manganites

With the increase of the lattice distortion, the orthorhombic manganites $R$MnO$_3$ ($R$$=$ La, Pr, Nd, Tb, and Ho) are known to undergo the phase transition from the layered A-type antiferromagnetic (AFM) state to the zigzag E-type AFM state. We consider the microscopic origin of this transition. Our approach consists of the two parts. First, we construct an effective lattice fermion model for the manganese 3d-bands and derive parameters of this model from the first-principles electronic structure calculations. Then, we solve this model in the Hartree-Fock approximation (HFA) and analyze the behavior of interatomic magnetic interactions. We argue that the nearest-neighbor interactions decrease with the distortion and at certain stage start to compete with the longer range (particularly, second- and third-neighbor) AFM interactions in the orthorhombic ab-plane, which lead to the formation of the E-phase. The origin of these interactions is closely related to the orbital ordering, which takes place in the distorted orthorhombic structure. The model is able to capture the experimental trend and explain why LaMnO$_3$ develops the A-type AFM order and why it tends to transform to the E-type AFM order in the more distorted compounds. Nevertheless, the quantitative agreement with the experimental data crucially depends on other factors, such as the magnetic polarization of the oxygen sites and the correlation interactions beyond HFA.Comment: 26 pages, 15 figure

Optimized Effective Potential for Extended Hubbard Model

Antiferromagnetic and charge ordered Hartree-Fock solutions of the one-band Hubbard model with on-site and nearest-neighbor Coulomb repulsions are exactly mapped onto an auxiliary local Kohn-Sham (KS) problem within a density-functional theory. The mapping provides a new insight into the interpretation of the KS equations. (i) With an appropriate choice of the basic variable, there is a universal form of the KS potential, which is applicable both for the antiferromagnetic and the charge ordered solutions. (ii) The Kohn-Sham and Hartree-Fock eigenvalues are interconnected by a scaling transformation. (iii) The band-gap problem is attributed to the derivative discontinuity of the basic variable as the function of the electron number, rather than a finite discontinuity of the KS potential. (iv) It is argued that the conductivity gap and the energies of spin-wave excitations can be entirely defined by the parameters of the ground state and the KS eigenvalues.Comment: 21 page, 3 figure