SPIN-ONE HEISENBERG-FERROMAGNET WITH 3-ATOM EXCHANGE

We study the statistical mechanics of a spin-one ferromagnet with the nearest-neighbour bilinear Heisenberg exchange constant J and the thre e-atom coupling constant L using the equation-of-motion method for the two-time temperature-dependent Green function. It is seen that, as th e three-atom coupling parameter alpha = L/J is increased positively, t he Curie temperature T(C) first increases steeply and then increases v ery slowly and ultimately approaches the limiting value k(B)T(C)/Jz = 4/3 as alpha tends to infinity. The situation is much more complicated for negative alpha but, as alpha --> infinity, T(C) approaches the li miting value 4/3. The temperature variation in spontaneous magnetizati on 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 transitio n is first order for SC, BCC and FCC lattices. alpha(c) decreases as t he number z of nearest neighbour increases. The discontinuity in m has been found to be extremely sensitive near alpha(c). The results are d iscussed with reference to those obtained by earlier workers.