Comprehensive inelastic neutron scattering study of the multiferroic M n 1 - x C o x W O 4

Using high-resolution inelastic neutron scattering, we examine the spin dynamics of ${Mn}_{1-x}{Co}_x{WO}_4$ in the collinear AF1, the $ac-b$ spiral AF2, and the $ac$ cycloidal AF5 phases. The spin wave excitations are well described by a Heisenberg model with competing long-range exchange interactions ( $J_i$ up to 12th nearest neighbors) and the single-ion anisotropy $K$ induced by the spin-orbit interaction. While the exchange constants are relatively unchanged, the dominant effect of doping is to change the single-ion anisotropy from easy axis $(K>0)$ in the collinear AF1 phase to easy plane $(K<0)$ in the two multiferroic phases.