On the Green’s function theory of the Heisenberg ferromagnet with crystal field anisotropy

Abstract

In a previous paper (1) the Green's function method was applied to the XY-model of ferromagnetism of a two-spin S ---89 system, using Tyabl ikov ' s decoupling (2) (shortly called RPA random-phase approximation). The conclusion reached is tha t RPA is adequate to t rea t isotropie systems in which solely transverse correlations are involved. This means tha t RPA is inadequate to t rea t the zero-field response of a magnetic system which is described by the X1T-model, which consists of an extreme case of anisotropy of the Heisenberg ferromagnet. In the Green's functions theory of the Heisenberg magnetic system with crystal field anisotropy one finds different kinds of higher-order Green's functions. One of them, the exchange Green's function, follows from the exchange term of the Hamil tonian of the system, and has spin operators a t tached to different lat t ice sites. The second, the anisotropic Green's flmction, follows from the crystal field term and has two spin operators a t tached to the same lat t ice site. Some difficulties appear when s tandard decoupling is used for the anisotropie Green's function, because in this case the transverse and longitudinal motions will be decorrelated (3). NARATH (4) has used RPA deeoupling and A~I)V.Rso~ and CALL]~N (5) have used symmetric decoupling (e) and they have found the same result as in the is0tropic system for ((S~)2~ in the paramagnet ie region. LIN~S (7) has proposed a modified scheme to decouple the anisotropic Green's function, but as in former cases the transi t ion temperature goes to infinity as the crystal field anisotropy also goes to infinity (s). Recently different methods have been proposed by several authors (3.9.~o). In these methods a closed set of equations of motion