Many-body Green's function theory for thin ferromagnetic films: exact treatment of the single-ion anisotropy

Abstract

A theory for the magnetization of ferromagnetic films is formulated within the framework of many-body Green's function theory which considers all components of the magnetization. The model Hamiltonian includes a Heisenberg term, an external magnetic field, a second-and fourth-order uniaxial single-ion anisotropy, and the magnetic dipole-dipole coupling. The single-ion anisotropy terms can be treated exactly by introducing higher-order Green's functions and subsequently taking advantage of relations between products of spin operators which leads to an automatic closure of the hierarchy of the equations of motion for the Green's functions with respect to the anisotropy terms. This is an improvement on the method of our previous work, which treated the corresponding terms only approximately by decoupling them at the level of the lowest-order Green's functions. RPA-like approximations are used to decouple the exchange interaction terms in both the low-order and higher-order Green's functions. As a first numerical example we apply the theory to a monolayer for spin S = 1 in order to demonstrate the superiority of the present treatment of the anisotropy terms over the previous approximate decouplings.

Anisotropic susceptibilities of thin ferromagnetic films within many-body Green function theory: single-ion anisotropy versus exchange anisotropy

“…Although we have shown in Ref. [4] how the single-ion anisotropy can be treated exactly (for any strength of the anisotropy) by introducing higher-order Green's functions, the application to multilayers and S > 1 is very cumbersome. This is not the case when using, as we did in Refs.…”

“…Contrary to Ref. [4], where we proceed to higherorder Green's functions, we stay here at the level of the lowest-order equations. For the exchange-interaction terms, we use a generalized Tyablikov-(or RPA-) decou-…”

Many-body Green’s function theory of ferromagnetic Heisenberg systems with single-ion anisotropies in more than one direction

“…12,22 . In previous work [12][13][14][15][16][17][18][19], the operators A and B were the spin operators:…”

“…One of the main advantages of the present formulation is that the matrix P turns out to be Hermitian, whereas in earlier work 12,13,15,17 , the corresponding matrix at this stage of the decoupling was real and non-Hermitian.…”

“…The Green's function formalism was also applied to uniaxial out-of-plane and uniaxial in-plane exchange anisotropies 18,19,20 . The papers above [12][13][14][15][16][17] dealt only with a uniaxial out-of-plane single-ion anisotropy. In the present paper, we generalize the model by introducing single-ion anisotropies in all directions of space, thus obtaining the in-plane and out-of-plane anisotropies as special cases, and also allowing for a reorientation of the magnetization from out-of-plane to in-plane and vice versa, depending on the chosen parameters.…”