Implementation of the magnetic force theorem for large-scale calculations of magnon bands: Application to yttrium iron garnet

We present an efficient implementation of the magnetic force theorem, which allows for direct evaluation of exchange parameters in $q$ space. The exchange parameters are calculated directly from Bloch states and the implementation does not rely on any mapping onto localized orbitals. This renders the approach well suited for high-throughput computations, where the construction of a localized basis set---for example, Wannier functions---often is impractical. We demonstrate the versatility of the method by applying it to yttrium iron garnet, where we obtain excellent agreement with the experimental magnon dispersion and Curie temperature without any prior assumptions of important exchange pathways. In particular, the calculations reveal the existence of several inequivalent exchange pathways associated with the same interatomic distances. Performing such calculations in $q$ space fully accounts for long-range exchange interactions and provides a convenient route for validating models obtained by fitting to inelastic neutron scattering data.