Angular and linear momentum of excited ferromagnets

The angular momentum vector of a Heisenberg ferromagnet with isotropic exchange interaction is conserved, while under uniaxial crystalline anisotropy the projection of the total spin along the easy axis is a constant of motion. Using Noether's theorem, we prove that these conservation laws persist in the presence of dipole-dipole interactions. However, spin and orbital angular momentum are no longer conserved separately. We also define the linear momentum of ferromagnetic textures. We illustrate the general principles with special reference to spin transfer torques and identify the emergence of a nonadiabatic effective field acting on domain walls in ferromagnetic insulators.