Double-exchange theory of ferroelectric polarization in orthorhombic manganites with twofold periodic magnetic texture

We argue that many aspects of improper ferroelectric activity in orthorhombic manganites can be rationalized by considering the limit of infinite intra-atomic splitting between the majority- and minority-spin states (or the double exchange limit), which reduces the problem to the analysis of a spinless double exchange (DE) Hamiltonian. We apply this strategy to the low-energy model, derived from the first-principles calculations, and combine it with the Berry-phase theory of electric polarization. We start with the simplest two-orbital model, describing the behavior of the eg bands, and apply it to the E-type antiferromagnetic (AFM) phase, which in the DE limit effectively breaks up into one-dimensional zigzag chains. We derive an analytical expression for the electronic polarization (Pel) and explain how it depends on the orbital ordering and the energy splitting Delta between eg states. Then, we evaluate parameters of this model, starting from a more general five-orbital model for all Mn 3d bands and constructing a new downfolded model for the eg bands. From the analysis of these parameters, we conclude that the behavior of Pel in realistic manganites corresponds to the limit of large Delta. We further utilize this property in order to derive an analytical expression for Pel in a general two-fold periodic magnetic texture, based on the five-orbital model and the perturbation-theory expansion for the Wannier functions in the first order of 1/Delta. This expression explains the functional dependence of Pel on the relative directions of spins. Furthermore, it suggests that Pel is related to the asymmetry of the transfer integrals, which should simultaneously have symmetric and antisymmetric components. Finally, we explain how the polarization can be switched between orthorhombic directions a and c by inverting the zigzag AFM texture in every second ab plane.Comment: 41 page, 10 figure

Spin dependence of ferroelectric polarization in the double exchange model for manganites

The double exchange (DE) model is systematically applied for studying the coupling between ferroelectric (FE) and magnetic orders in several prototypical types of multiferroic manganites. The model was constructed for the magnetically active Mn $3d$ bands in the basis of Wannier functions and include the effect of screened on-site Coulomb interactions. The essence of our approach for the FE polarization is to use the Berry phase theory, formulated in terms of occupied Wannier functions, and to evaluate the asymmetric spin-dependent change of these functions in the framework of the DE model. This enables us to quantify the effect of the magnetic symmetry breaking and derive several useful expressions for the electronic polarization ${\bf P}$, depending on the relative directions of spins. The proposed theory is applied to the solution of three major problems: (i) The magnetic-state dependence of ${\bf P}$ in hexagonal manganites; (ii) The microscopic relationship between canted ferromagnetism and ${\bf P}$ in monoclinic BiMnO$_3$; (iii) The origin of FE activity in orthorhombic manganites. We show that for an arbitrary noncollinear magnetic structure, propagating along the orthorhombic $\boldsymbol{b}$ axis and antiferromagnetically coupled $\boldsymbol{c}$, ${\bf P}$ can be obtained by scaling the one of the E-phase with the prefactor depending only on the relative directions of spins and being the measure of the spin inhomogeneity. This picture works equally well for the twofold (HoMnO$_3$) and fourfold (TbMnO$_3$) periodic manganites. The basic difference is that the twofold periodic magnetic structure is strongly inhomogeneous, that leads to large ${\bf P}$. On the contrary, the fourfold periodic magnetic structure can be viewed as a moderately distorted homogeneous spin spiral, which corresponds to weaker ${\bf P}$.Comment: 32 pages, 7 figure

Lattice Distortion and Magnetism of 3d-t2gt_{2g} Perovskite Oxides

Several puzzling aspects of interplay of the experimental lattice distortion and the the magnetic properties of four narrow $t_{2g}$-band perovskite oxides (YTiO$_3$, LaTiO$_3$, YVO$_3$, and LaVO$_3$) are clarified using results of first-principles electronic structure calculations. First, we derive parameters of the effective Hubbard-type Hamiltonian for the isolated $t_{2g}$ bands using newly developed downfolding method for the kinetic-energy part and a hybrid approach, based on the combination of the random-phase approximation and the constraint local-density approximation, for the screened Coulomb interaction part. Then, we solve the obtained Hamiltonian using a number of techniques, including the mean-field Hartree-Fock (HF) approximation, the second-order perturbation theory for the correlation energy, and a variational superexchange theory. Even though the crystal-field splitting is not particularly large to quench the orbital degrees of freedom, the crystal distortion imposes a severe constraint on the form of the possible orbital states, which favor the formation of the experimentally observed magnetic structures in YTiO$_3$, YVO_, and LaVO$_3$ even at the HF level. Beyond the HF approximation, the correlations effects systematically improve the agreement with the experimental data. Using the same type of approximations we could not reproduce the correct magnetic ground state of LaTiO$_3$. However, we expect that the situation may change by systematically improving the level of approximations for dealing with the correlation effects.Comment: 30 pages, 17 figures, 8 tables, high-quality figures are available via e-mai

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

Realization of anisotropic compass model on the diamond lattice of Cu2+^{2+} in CuAl2_2O4_4

Spin-orbit (SO) Mott insulators are regarded as a new paradigm of magnetic materials, whose properties are largely influenced by SO coupling and featured by highly anisotropic bond-dependent exchange interactions between the spin-orbital entangled Kramers doublets, as typically manifested in $5d$ iridates. Here, we propose that a very similar situation can be realized in cuprates when the Cu$^{2+}$ ions reside in a tetrahedral environment, like in spinel compounds. Using first-principles electronic structure calculations, we construct a realistic model for the diamond lattice of the Cu$^{2+}$ ions in CuAl$_2$O$_4$ and show that the magnetic properties of this compound are largely controlled by anisotropic compass-type exchange interactions that dramatically modify the magnetic ground state by lifting the spiral spin-liquid degeneracy and stabilizing a commensurate single-$\boldsymbol{q}$ spiral

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

Hybridization and spin-orbit coupling effects in quasi-one-dimensional spin-1/2 magnet Ba3Cu3Sc4O12

We study electronic and magnetic properties of the quasi-one-dimensional spin-1/2 magnet Ba3Cu3Sc4O12 with a distinct orthogonal connectivity of CuO4 plaquettes. An effective low-energy model taking into account spin-orbit coupling was constructed by means of first-principles calculations. On this basis a complete microscopic magnetic model of Ba3Cu3Sc4O12, including symmetric and antisymmetric anisotropic exchange interactions, is derived. The anisotropic exchanges are obtained from a distinct first-principles numerical scheme combining, on one hand, the local density approximation taking into account spin-orbit coupling, and, on the other hand, projection procedure along with the microscopic theory by Toru Moriya. The resulting tensors of the symmetric anisotropy favor collinear magnetic order along the structural chains with the leading ferromagnetic coupling J1 = -9.88 meV. The interchain interactions J8 = 0.21 meV and J5 = 0.093 meV are antiferromagnetic. Quantum Monte Carlo simulations demonstrated that the proposed model reproduces the experimental Neel temperature, magnetization and magnetic susceptibility data. The modeling of neutron diffraction data reveals an important role of the covalent Cu-O bonding in Ba3Cu3Sc4O12.Comment: 11 pages, 12 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