Yttrium iron garnet is a complex ferrimagnetic insulator with 20 magnon modes which is used extensively in fundamental experimental studies of magnetisation dynamics. As a transition metal oxide with moderate gap (2.8 eV), yttrium iron garnet requires a careful treatment of electronic correlation. We have applied quasiparticle self-consistent GW to provide a fully ab initio description of the electronic structure and resulting magnetic properties, including the parameterisation of a Heisenberg model for magnetic exchange interactions. Subsequent spin dynamical modelling with quantum statistics extends our description to the magnon spectrum and thermodynamic properties such as the Curie temperature, finding favourable agreement with experimental measurements. This work provides a snapshot of the state-of-the art in modelling of complex magnetic insulators.
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