Realistic modelling of transport properties at finite tempeature in magnetic materials by local quantization of a Heisenberg model

The quantitative description of the electrical resistivity of a magnetic material remains challenging to this day. Qualitatively, it is well understood that the temperature-induced lattice and spin disorder determines the temperature dependence of the resistivity. While prior publications reached good agreement with experiment in the so-called supercell or direct approach for non-magnetic materials where the spin-disorder contribution to the resistivity is negligible, an accurate, purely theoretical description of magnetic materials remains elusive. This shortcoming can be attributed to the missing accuracy in the description of the temperature-dependent spin-disorder itself. In this work, we employ a joint approach from \textit{ab-initio} transport calculations and atomistic modeling of the temperature-dependent spin-disorder. Using the example of $α$-Fe, we demonstrate that the inclusion of quantum mechanical effects using a semiclassical local quantization of the Heisenberg model significantly improves the description of the spin-disorder component to the electrical resistivity. Compared to previous approaches, this model includes the description of magnetic short-range order effects, enabling us to study temperature effects around and above the Curie temperature, where prior mean-field theory-based approaches inevitably predicted a constant contribution.