Exchange anisotropy, disorder and frustration in diluted, predominantly ferromagnetic, Heisenberg spin systems

TL;DR

This study investigates how anisotropic exchange interactions and disorder affect low-temperature magnetization in diluted Heisenberg spin systems, revealing that exchange sign disorder more effectively suppresses magnetization than anisotropy.

Contribution

It demonstrates through Monte Carlo simulations that exchange anisotropy and disorder influence magnetization, highlighting the dominant role of exchange sign disorder in suppressing low-temperature magnetization.

Findings

Exchange anisotropy gradually reduces magnetization in low-connectivity models.

High connectivity models show suppressed anisotropy effects unless exchange distribution is very broad.

Sign disorder in exchange interactions more effectively suppresses magnetization than anisotropy.

Abstract

Motivated by the recent suggestion of anisotropic effective exchange interactions between Mn spins in Ga$_{1-x}$Mn$_x$As (arising as a result of spin-orbit coupling), we study their effects in diluted Heisenberg spin systems. We perform Monte Carlo simulations on several phenomenological model spin Hamiltonians, and investigate the extent to which frustration induced by anisotropic exchanges can reduce the low temperature magnetization in these models and the interplay of this effect with disorder in the exchange. In a model with low coordination number and purely ferromagnetic (FM) exchanges, we find that the low temperature magnetization is gradually reduced as exchange anisotropy is turned on. However, as the connectivity of the model is increased, the effect of small-to-moderate anisotropy is suppressed, and the magnetization regains its maximum saturation value at low temperatures unless the distribution of exchanges is very wide. To obtain significant suppression of the low temperature magnetization in a model with high connectivity, as is found for long-range interactions, we find it necessary to have both ferromagnetic and antiferromagnetic (AFM) exchanges (e.g. as in the RKKY interaction). This implies that disorder in the sign of the exchange interaction is much more effective in suppressing magnetization at low temperatures than exchange anisotropy.