Collective Modes of Spin Excitations and Phase Transitions in a Ferromagnet with Single-Ion Anisotropy

Abstract

Spin-1 Heisenberg ferromagnet with both axial anisotropy, D ∑ l ( S l z ) 2 , and rhombic anisotropy, E ∑ l {( S l x ) 2 -( S l y ) 2 }, are studied from a viewpoint of the collective mode. The parameter D is positive and much larger than exchange integral, and E is smaller than D . The double-time temperature dependent Green functions are used under the random phase approximation in order to calculate the collective mode and to determine the phase boundaries. The paramagnetic phase are divided into two regions from the character of the collective mode. The one is the region where the collective mode is similar to libron and the other that the collective mode is conventional spin-wave. It is shown that the rhombic anisotropy has a significant effect on the libron mode, whereas not on the spin-wave mode.