Short-Range Magnetic Order in an Anisotropic Ferromagnet in the Tyablikov Approximation

The nature of the spatial dependence of transverse spin correlators ( parameters of short-range order) has been investigated in both the paramagnetic and magnetically ordered regions in the model of a three-dimensional Heisenberg ferromagnet with a uniaxial anisotropy of the exchange interaction of nearest neighbors, which allows ferromagnetic ordering of both easy-axis and easy-plane type depending on the relationship between the parameters of exchange between the longitudinal and transverse spin components. It has been demonstrated in terms of the method of two-time Green's functions with the use of Tyablikov uncoupling that the anisotropy of the exchange between different spin projections leads to the anisotropy of correlation lengths in spin correlators and, correspondingly, to a difference in their temperature behavior upon transition from the paramagnetic into a magnetically ordered state. It is shown how in the model of exchange interactions between nearest neighbors the magnitudes of spin correlations between different sites can be expressed through the matrix elements of lattice Green's functions.