Spin-one Heisenberg ferromagnet with three-atom exchange

Abstract

We study the statistical mechanics of a spin-one ferromagnet with the nearest-neighbour bilinear Heisenberg exchange constant J and the three-atom coupling constant L using the equation-of-motion method for the two-time temperature-dependent Green function. It is seen that, as the three-atom coupling parameter alpha =L/J is increased positively, the Curie temperature TC first increases steeply and then increases very slowly and ultimately approaches the limiting value kBTC/Jz=4/3 as alpha tends to infinity. The situation is much more complicated for negative alpha but, as alpha to infinity , TC approaches the limiting value 4/3. The temperature variation in spontaneous magnetization m and the quadrupolar ordering parameter lambda for various values of alpha are studied. It is seen that there exists a critical value of alpha (which we shall call alpha c) beyond which the phase transition is first order for SC, BCC and FCC lattices. alpha c decreases as the number z of nearest neighbour increases. The discontinuity in m has been found to be extremely sensitive near alpha c. The results are discussed with reference to those obtained by earlier workers.