Effectiveness of the Self-Consistent Harmonic Approximation in ferromagnets with dipolar interactions

Abstract

Among the various methods for treating magnetic models, the Self-Consistent Harmonic Approximation (SCHA) has successfully described ferro and antiferromagnetism in many different scenarios. In particular, the SCHA is a valuable and easy formalism for determining transition temperatures as, for example, the Berezinskii-Kosterlitz-Thouless. The heart of the method includes thermal fluctuations through of a renormalization parameter depending on temperature. Nevertheless, most of the work has been done considering only short-range interactions, which results in an incomplete description of actual magnetic samples. Here, we generalize the SCHA to include the dipolar interaction in the thermodynamic analysis. The method is applied to analyze the well-known Europium Chalcogenides EuO and EuS. The SCHA results are in good agreement with the experimental measurements.

Theoretical analysis of FMR-driven spin pumping current and its properties via Self-Consistent Harmonic Approximation

“…To determine the renormalization parameter, we compare the value of Ṡz q Ṡz −q 0 obtained from the quadratic Hamiltonian 7 with the result obtained from H m without the series expansion (a more detailed demonstration is found in Appendix of Ref. [66]), which results in…”