Multiple Spin Density Wave State and Symmetry in fcc Antiferromagnets

Abstract

Relative stabilities among various multiple spin density wave (MSDW) states specified by equivalent wave vectors are discussed on the basis of symmetry considerations for the first-, the second- and the third-kind antiferromagnetic structures in the fcc lattice. The energy of the MSDW state is expressed as the expansion with respect to normalized amplitudes for constituent single-Q states. The degeneracy among MSDW states, which is not lifted in the Heisenberg model, is shown to be removed by more than or equal to the fourth-order perturbation with respect to transfer integrals between atoms. Within the lowest order expression to remove the degeneracy, possible stable structures are discussed. The effect of higher order perturbations and the prospect to determine the most stable MSDW state in transition metals with the first-kind ordering are also discussed.