Microscopic theory for coupled atomistic magnetization and lattice dynamics

A coupled atomistic spin and lattice dynamics approach is developed which merges the dynamics of these two degrees of freedom into a single set of coupled equations of motion. The underlying microscopic model comprises local exchange interactions between the electron spin and magnetic moment and the local couplings between the electronic charge and lattice displacements. An effective action for the spin and lattice variables is constructed in which the interactions among the spin and lattice components are determined by the underlying electronic structure. In this way, expressions are obtained for the electronically mediated couplings between the spin and lattice degrees of freedom, besides the well known interatomic force constants and spin-spin interactions. These former susceptibilities provide an atomistic ab initio description for the coupled spin and lattice dynamics. It is important to notice that this theory is strictly bilinear in the spin and lattice variables and provides a minimal model for the coupled dynamics of these subsystems and that the two subsystems are treated on the same footing. Questions concerning time-reversal and inversion symmetry are rigorously addressed and it is shown how these aspects are absorbed in the tensor structure of the interaction fields. By means of these results regarding the spin-lattice coupling, simple explanations of ionic dimerization in double-antiferromagnetic materials, as well as charge density waves induced by a nonuniform spin structure, are given. In the final parts, coupled equations of motion for the combined spin and lattice dynamics are constructed, which subsequently can be reduced to a form which is analogous to the Landau-Lifshitz-Gilbert equations for spin dynamics and a damped driven mechanical oscillator for the ionic motion. It is important to notice, however, that these equations comprise contributions that couple these descriptions into one unified formulation. Finally, Kubo-like expressions for the discussed exchanges in terms of integrals over the electronic structure and, moreover, analogous expressions for the damping within and between the subsystems are provided. The proposed formalism and types of couplings enable a step forward in the microscopic first principles modeling of coupled spin and lattice quantities in a consistent format.This work was supported by the Vetenskapsrådet, the Wenner-Gren Foundation, the Icelandic Research Fund (Grant No. 163048- 052), a megagrant of the Ministry of Education and Science of the Russian Federation (Grant No. 14.Y26.31.0015), and Stiftelsen Olle Engqvist Byggmästare. J.F. gratefully acknowledges the generous hospitality shown by the T-Division at Los Alamos National Laboratory during his stay in 2012. J.H. is partly funded by the Swedish Research Council (VR) through a neutron project grant (BIFROST, Dnr. 2016-06955). The computations were performed on resources provided by the Swedish National Infrastructure for Computing (SNIC).Peer Reviewe