Magnetic structure of the Jahn-Teller systemLaTiO3

Abstract

We investigate the effect of the experimentally observed Jahn-Teller distortion of the oxygen octahedra in LaTiO 3 on the magnetic exchange. We present a localized model for the effective hopping between nearestneighbor Ti ions and the intrasite Coulomb interactions, based on a nondegenerate orbital ground state due to the static crystal field. The latter corresponds to an orbital order which has recently been confirmed experimentally. Using perturbation theory we calculate, in addition to the Heisenberg coupling, antisymmetric (Dzyaloshinskii-Moriya) and symmetric anisotropy terms of the superexchange spin Hamiltonian, which are caused by the spin-orbit interaction. Employing this spin Hamiltonian, we deduce that at low temperatures the spins have predominantly a G-type antiferromagnetic ordering along the crystallographic a axis, accompanied by a weak ferromagnetic moment along the c axis and by a weak A-type antiferromagnetic moment along the b axis. The first two components are found to be in good agreement with experiment. Disciplines PhysicsThis journal article is available at ScholarlyCommons: http://repository.upenn.edu/physics_papers/333 We investigate the effect of the experimentally observed Jahn-Teller distortion of the oxygen octahedra in LaTiO 3 on the magnetic exchange. We present a localized model for the effective hopping between nearestneighbor Ti ions and the intrasite Coulomb interactions, based on a nondegenerate orbital ground state due to the static crystal field. The latter corresponds to an orbital order which has recently been confirmed experimentally. Using perturbation theory we calculate, in addition to the Heisenberg coupling, antisymmetric ͑Dzyaloshinskii-Moriya͒ and symmetric anisotropy terms of the superexchange spin Hamiltonian, which are caused by the spin-orbit interaction. Employing this spin Hamiltonian, we deduce that at low temperatures the spins have predominantly a G-type antiferromagnetic ordering along the crystallographic a axis, accompanied by a weak ferromagnetic moment along the c axis and by a weak A-type antiferromagnetic moment along the b axis. The first two components are found to be in good agreement with experiment.

Optical study of orbital excitations in transition-metal oxides

“…On the basis of our optical conductivity data, we did not find any clear evidence for strong orbital fluctuations. Also the isotropic spin-wave dispersion of LaTiO 3 observed in inelastic neutron scattering [31] can be explained within a crystal-field scenario [116,117]. The small ordered moment may result from the combination of quantum fluctuations within the spin channel, spin-orbit coupling and the small Hubbard gap.…”

Spin–orbital superexchange physics emerging from interacting oxygen molecules in KO2

“…Below we will certainly verify this picture by considering more rigorous arguments without any assumptions about the superiority of the relativistic spinorbit interaction over other interactions in the system. We would also like to note that a similar strategy has been applied to the analysis of SE interactions in the limit of large crystal-field splitting [29].…”

The cubic Kugel–Khomskii model for triply degenerate t2gelectrons

“…The presence of orbital order at low temperatures has also been concluded from measurements of the dielectric properties and the dynamical conductivity [31]. A model for the magnetism of LaTiO 3 , which is based on the crystal-field calculation given in [11] is presented in [32]. This calculation starts from a point-charge summation of the static crystal field for the Ti ions, employing a full Madelung sum over the crystal.…”

“…Schmitz et al [32] have used a Slater-Koster parametrization of the Ti-O hopping to obtain an effective hopping matrix between the d orbitals of nearest-neighbour Ti ions. Treating this Ti-Ti hopping and the on-site spin-orbit coupling as perturbations, they calculated the superexchange coupling between the non-degenerate crystal-field ground states of the Ti 3+ ions.…”

“…The latter is constructed by decomposing the entire Ti-lattice into four sublattices (each magnetic unit cell includes four Ti ions, just as the crystallographic unit cell). Assigning a fixed-magnitude magnetization (per site) to each sublattice, M i , the macroscopic magnetic Hamiltonian takes the form [32] …”