Condensed Matter seminars

How to make spin and lattice dynamical together

by Jonas Fransson (Uppsala University)

112:028 (Nordita South) ()

112:028 (Nordita South)

A coupled spin and lattice dynamics approach is developed which merges on the same footing the dynamics of these two degrees of freedom into a single set of coupled equations of motion. Our discussion begins with a microscopic model of a material in which the magnetic and lattice degrees of freedom are included. This description comprises local exchange interactions between the electron spin and magnetic moment as well as local couplings between the electronic charge and lattice vibrations. We construct an effective action for the spin and lattice variables in which the interactions between the spin and lattice components is determined by the underlying electronic structure. In this way we obtain expressions for the electronic contribution to the inter-atomic force constant, the isotropic and anisotropic spin-spin exchanges, as well as the electronically mediated coupling spin-lattice exchange. The last of these exchanges is provides a novel description for coupled spin and lattice dynamics. It is important to notice that our theory is strictly bilinear in the spin and lattice variables and provides a minimal model for the coupled dynamics of these subsystems. Questions concerning time-reversal and inversion symmetry are rigorously addressed and it is shown how these aspects are absorbed in the tensorial structure of the interaction fields. Using our novel results regarding the spin-lattice coupling, we can provide simple explanations of ionic dimerization in double anti-ferromagnetic materials, as well as, charge density waves induced by a non-uniform spin structure. In the final parts, we construct a set of coupled equations of motion for the combined spin and lattice dynamics, reduced to a form which is analogous to the Landau-Lifshitz-Gilbert equations for spin dynamics and damped driven mechanical oscillator for the ionic motion, however, comprising contributions that couple these descriptions into one unified formulation. We provide Kubo-like expressions for the discussed exchanges in in terms of integrals over the electronic structure and, moreover, analogous expressions for the damping within and between the subsystems.