Validity and limitations of the superexchange model for the magnetic properties of Sr2IrO4 and Ba2IrO4 mediated by the strong spin-orbit coupling

Abstract

Layered perovskites Sr2IrO4 and Ba2IrO4 are regarded as the key materials for understanding the properties of magnetic relativistic insulators, mediated by the strong spin-orbit (SO) coupling. One of the most fundamental issues is to which extent these properties can be described by the superexchange (SE) model, formulated in the limit of the large Coulomb repulsion for some appropriately selected pseudospin states, and whether these materials themselves can be classified as Mott insulators. In this work, we address these issues by deriving the relevant models and extracting parameters of these models from the electronic-structure calculations with the SO coupling, based on the density functional theory. First, we construct the effective Hubbard-type model for the magnetically active t2g bands, by recasting the problem in the language of localized Wannier orbitals. Then, we map the obtained electron model onto the pseudospin model by applying the theory of SE interactions, which is based on the second-order perturbation theory with respect to the transfer integrals. We discuss the microscopic origin of anisotropic SE interactions, inherent to the compass Heisenberg model, and the appearance of the antisymmetric Dzyaloshinskii-Moriya term, associated with the additional rotation of the IrO6 octahedra in Sr2IrO4. In order to solve the pseudospin Hamiltonian problem and evaluate the Néel temperature (TN), we employ the nonlinear sigma model. We have found that, while for Sr2IrO4 our value of TN agrees with the experimental data, for Ba2IrO4 it is overestimated by a factor of 2. We argue that this discrepancy is related to limitations of the SE model: while for more localized t2g states in Sr2IrO4 it works reasonably well, the higher-order terms in the perturbation theory expansion play a more important role in the more "itinerant" Ba2IrO4, giving rise to the new type of isotropic and anisotropic exchange interactions, which are not captured by the SE model. This conclusion is supported by unrestricted Hartree-Fock calculations for the same electron model, where in the case of Ba2IrO4, already on the mean-field level, we were able to reproduce the experimentally observed magnetic ground state, while for Sr2IrO4 the main results are essentially the same as in the SE model. © 2015 American Physical Society.