Dynamic magnetostriction for antiferromagnets

In this paper we propose a Hamiltonian framework for the dynamics of magnetic moments, in interaction with an elastic medium, that can take into account the dynamics in phase space of the variables that describe the magnetic moments in a consistent way. While such a description involves describing the magnetic moments as bilinears of anticommuting variables that are their own conjugates , we show how it is possible to avoid having to deal directly with the anticommuting variables themselves, only using them to deduce non-trivial constraints on the magnetoelastic couplings. We construct the appropriate Poisson bracket and a geometric integration scheme, that is symplectic in the extended phase space and that allows us to study the switching properties of the magnetization, that are relevant for applications, for the case of a toy model for antiferromagnetic NiO, under external stresses.