The effect of orbital degrees of freedom on the exchange interactions in the spin-1 quasi-one-dimensional antiferromagnet CaV2O4 is systematically studied. For this purpose a realistic low-energy model with the parameters derived from the first-princ
iples calculations is constructed. The exchange interactions are calculated using both the theory of infinitesimal spin rotations near the mean-field ground state and the superexchange model, which provide a consistent description. The obtained behaviour of exchange interactions substantially differs from the previously proposed phenomenological picture based on the magnetic measurements and structural considerations, namely: (i) Despite quasi-one-dimensional character of the crystal structure, consisting of the zigzag chains of edge-sharing VO6 octahedra, the electronic structure is essentially three-dimensional, that leads to finite interactions between the chains; (ii) The exchange interactions along the legs of the chains appear to dominate; and (iii) There is a substantial difference of exchange interactions in two crystallographically inequivalent chains. The combination of these three factors successfully reproduces the behaviour of experimental magnetic susceptibility.
By combining first-principles electronic-structure calculations with the model Hamiltonian approach, we systematically study the magnetic properties of sodium superoxide (NaO2), originating from interacting superoxide molecules. We show that NaO2 exh
ibits a rich variety of magnetic properties, which are controlled by relative alignment of the superoxide molecules as well as the state of partially filled antibonding molecular pi_g-orbitals. The orbital degeneracy and disorder in the high-temperature pyrite phase gives rise to weak isotropic antiferromagnetic (AFM) interactions between the molecules. The transition to the low-temperature marcasite phase lifts the degeneracy, leading to the orbital order and formation of the quasi-one-dimensional AFM spin chains. Both tendencies are consistent with the behavior of experimental magnetic susceptibility data. Furthermore, we evaluate the magnetic transition temperature and type of the long-range magnetic order in the marcasite phase. We argue that this magnetic order depends on the behavior of weak isotropic as well as anisotropic and Dzyaloshinskii-Moriya exchange interactions between the molecules. Finally, we predict the existence of a multiferroic phase, where the inversion symmetry is broken by the long-range magnetic order, giving rise to substantial ferroelectric polarization.
Using realistic low-energy model with parameters derived from the first-principles electronic structure calculation, we address the origin of the quasi-one-dimensional behavior in orthorhombic NaV$_2$O$_4$, consisting of the double chains of edge-sha
ring VO$_6$ octahedra. We argue that the geometrical aspect alone does not explain the experimentally observed anisotropy of electronic and magnetic properties of NaV$_2$O$_4$. Instead, we attribute the unique behavior of NaV$_2$O$_4$ to one particular type of the orbital ordering, which respects the orthorhombic $Pnma$ symmetry. This orbital ordering acts to divide all $t_{2g}$ states into two types: the `localized ones, which are antisymmetric with respect to the mirror reflection $y rightarrow -$$y$, and the symmetric `delocalized ones. Thus, NaV$_2$O$_4$ can be classified as the double exchange system. The directional orientation of symmetric orbitals, which form the metallic band, appears to be sufficient to explain both quasi-one-dimensional character of interatomic magnetic interactions and the anisotropy of electrical resistivity.
We present the microscopic theory of improper multiferroicity in BiMnO3, which can be summarized as follows: (1) the ferroelectric polarization is driven by the hidden antiferromagnetic order in the otherwise centrosymmetric C2/c structure; (2) the r
elativistic spin-orbit interaction is responsible for the canted spin ferromagnetism. Our analysis is supported by numerical calculations of electronic polarization using Berrys phase formalism, which was applied to the low-energy model of BiMnO3 derived from the first-principles calculations. We explicitly show how the electric polarization can be controlled by the magnetic field and argue that BiMnO3 is a rare and potentially interesting material where ferroelectricity can indeed coexist and interplay with the ferromagnetism.
We argue that the centrosymmetric $C2/c$ symmetry in BiMnO$_3$ is spontaneously broken by antiferromagnetic (AFM) interactions existing in the system. The true symmetry is expected to be $Cc$, which is compatible with the noncollinear magnetic ground
state, where the ferromagnetic order along one crystallographic axis coexists with the the hidden AFM order and related to it ferroelectric polarization along two other axes. The $C2/c$ symmetry can be restored by the magnetic field $B sim 35$ Tesla, which switches off the ferroelectric polarization. Our analysis is based on the solution of the low-energy model constructed for the 3d-bands of BiMnO$_3$, where all the parameters have been derived from the first-principles calculations. Test calculations for isostructural BiCrO$_3$ reveal an excellent agreement with experimental data.
