Renormalization of magnetic interactions due to thermal disorder from first principles

In magnetic materials, temperature dependent magnetic properties can be investigated using a Heisenberg Hamiltonian. In such a picture, raising T increases disorder in local magnetic moment orientations, the interaction of which are governed by a constant exchange parameter, J. In a more complete picture, however, such increase in moment disorder may affect the strength of the moment interactions, thereby renormalizing J as a function of T, J(T). Moreover, raising T also increases lattice disorder, which may also renormalize the interaction J(T) via spin-lattice coupling thus affecting physical quantities such as M(T) and phonon frequencies. In this study, we extend the Temperature Dependent Effective Potential (TDEP) framework to calculate such renormalized J(T) from first principles. Density Functional Theory (DFT) is employed using constrained noncollinear magnetic moments. We calculate J(T), M(T) and phonons for the test case of bcc Fe and find good agreement with experiment. We also find the lattice disorder to significantly renormalize J in the vicinity of the Curie Temperature.