Taking into account the core anisotropy analytically to describe corrections to Eq. (2.14) due to the screening of the spin noncollinearities in the general case is difficult. However, one can consider this effects perturbatively, at least to clarify the validity limits of expression (2.14). In Ref. [97], the use of the general method outlined above (see section 2.3.1) led to a Helmholtz equation. In this case, there is no exact Green's function and as such the perturbation theory was used to write the Green's function in the presence of core anisotropy as the sum of the exact Green's function , obtained in the absence of core anisotropy, and a correction . The perturbation parameter:
(36) |
The contribution (2.20), called here the core-surface mixing (CSM) contribution, should satisfy which requires:
Rocio Yanes