Molecular field approximation in theory of ferromagnetic phase transition in diluted magnetic semiconductors

TL;DR

This paper compares two theoretical approaches to ferromagnetic phase transitions in diluted magnetic semiconductors, highlighting their similarities and differences in predicting Curie temperature and spin interactions.

Contribution

It provides a detailed analysis of Weiss field and RKKY interaction models, clarifying their applicability and limitations in describing DMS ferromagnetism.

Findings

Both approaches predict the same Curie temperature under ideal conditions.

Second order effects introduce oscillatory RKKY interactions at finite carrier concentrations.

The models coincide for homogeneous, non-correlated spin distributions.

Abstract

In this pedagogical paper, the comparative analysis of two common approaches describing the ferromagnetic phase transition in diluted magnetic semiconductors (DMS) is expounded in terms of Weiss field approximation. Assuming a finite spin polarization of the magnetic ions, the treatment of carrier-ion exchange interaction in first order evokes the homogeneous Weiss molecular field that polarizes the spins of free carriers. In turn, this spin polarization of the free carriers exerts the effective field that may stabilize DMS spin polarization below a critical temperature Tc. The treatment of such self-consistent spontaneous DMS magnetization can be done in terms of spin-spin interaction independent on inter-ion distance and infinitesimal in thermodynamic limit. On the other hand, the taking additionally into account the second order effects of carrier-ion exchange interaction treat a Weiss field in term of the RKKY indirect spin-spin interaction, which oscillates and not disappears at finite inter-ion distance in case of finite carriers concentration. These both approaches result in same Curie temperature Tc provided non-correlated homogeneous random distribution of the localized spin moments over sample volume. We discuss the origin of such coincidence and show when this is not a case in other more realistic models of the conducting DMSs.