Ab initiodetermination of spin Hamiltonians with anisotropic exchange interactions: The case of the pyrochlore ferromagnetLu2V2O7

Abstract

We present a general framework for deriving effective spin Hamiltonians of correlated magnetic systems based on a combination of relativistic ab initio density functional theory calculations, exact diagonalization of a generalized Hubbard Hamiltonian on finite clusters, and spin projections onto the low-energy subspace. A key motivation is to determine anisotropic bilinear exchange couplings in materials of interest. As an example, we apply this method to the pyrochlore ${\mathrm{Lu}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{7}$ where the vanadium ions form a lattice of corner-sharing spin-1/2 tetrahedra. In this compound, anisotropic Dzyaloshinskii-Moriya interactions (DMIs) play an essential role in inducing a magnon Hall effect. We obtain quantitative estimates of the nearest-neighbor Heisenberg exchange, the DMI, and the symmetric part of the anisotropic exchange tensor. Finally, we compare our results with experimental ones on the ${\mathrm{Lu}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{7}$ compound.