Triangular Spin Ordering in Mn₃Sn and Mn₃Ge

Abstract

The Fourier-transformed exchange matrix for the crystalline structure of Mn 3 Sn and Mn 3 Ge is analyzed in the case of a propagation vector parallel to the hexagonal principal axis and two modes of spin ordering are predicted, a helix of ferromagnetic basal net planes and a helix of triangular basal net planes. The effect of anisotropy energies is studied for the triangular spin ordering with zero propagation vector to uniquely determine the spin configuration and to account for the observation. Triangular helix, observed in Mn 3 Sn at low temperatures, is also discussed.