Linear spin-wave theory of incommensurably modulated magnets

Abstract

Calculations of linearized theories of spin dynamics encounter difficulties when applied to incommensurable magnetic phases: Lack of translational invariance leads to an infinite coupled system of equations. We resolve this for the case of a ‘‘single-Q’’ structure by mapping onto the problem of diagonalizing a quasiperiodic Hamiltonian of tight-binding type in one dimension. This allows for calculation of the correlation functions relevant to neutron scattering or magnetic resonance experiments. With the application to the case of a longitudinally modulated magnet a number of new predictions are made: at higher frequency there appear bands of response sharply defined in frequency, but broad in momentum transfer; at low frequencies there is a response maximum at the q vector corresponding to the modulation vector. We discuss generalizations necessary for application to rare-earth magnets.