Spin Waves in Complex Lattices

Consideration is given to a lattice which has an arbitrary number of magnetic atoms, or spins, in each magnetic unit cell. The Hamiltonian for this spin system is taken to include the usual isotropic exchange and magnetic field terms. This Hamiltonian is diagonalized in the spin-wave approximation for the case where the spin-deviation from the + or - $z$ direction is small for each spin. The thermal average values of the $z$ component of each spin are calculated and found in general to be different for spins on inequivalent sites in the unit cell. Insofar as the model Hamiltonian and the spin-wave approximations are valid, it is suggested that nuclear magnetic resonance measurements might be interpreted to give some information about the effective anisotropy fields.