Magnetostriction in Antiferromagnets

We consider magnetostriction in magnetic materials. Starting from a microscopic lattice model of the magneto-elastic coupling, we derive the continuum magnetostriction Hamiltonian in cubic ferromagnets and antiferromagnets. In ferromagnets, our results agree with established results. In antiferromagnets, we find a new central contribution which reflects the spin ordering. The additional term is essential in certain antiferromagnets where magnetic moments order in antiparallel ferromagnetic planes characterized by a normal axis. In such antiferromagnets, we predict that the magnetostrictive strain depends on the direction of the normal axis. Our findings are relevant for materials such as NiO and CoO, where there is a new spin-structure dependent strain, but not in RbMnF$_3$. We propose an experimental procedure to verify the importance of our findings in NiO that can be readily generalized to other materials. We also generalize the theory to include long-wavelength magnetoelastic coupling. We expect that the spin-structure dependent term critically affects the magnon-phonon coupling.