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

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.

9 pages, 8 figures

References in corpus (17)

• Effects of Disorder on Ferromagnetism in Diluted Magnetic Semiconductors
• Effects of annealing time on defect-controlled ferromagnetism in Ga1-xMnxAs
• High Curie temperature GaMnAs obtained by resistance-monitored annealing
• Temperature-dependent magnetization in diluted magnetic semiconductors
• A disordered RKKY lattice mean field theory for ferromagnetism in diluted magnetic semiconductors
• Global versus Local Ferromagnetism in a Model for Diluted Magnetic Semiconductors Studied with Monte Carlo Techniques
• Noncollinear Ferromagnetism in (III,Mn)V Semiconductors
• Monte Carlo simulations of an impurity band model for III-V diluted magnetic semiconductors
• Anomalous Hall Effect in Ferromagnetic Semiconductors in the Hopping Transport Regime
• Magnetic properties of GaMnAS from an effective Heisenberg Hamiltonian
• Single-Band Model for Diluted Magnetic Semiconductors: Dynamical and Transport Properties and Relevance of Clustered States
• Metal-Insulator Transition and Ferromagnetism in Diluted Magnetic Semiconductors
• Impurity-Semiconductor Band Hybridization Effects on the Critical Temperature of Diluted Magnetic Semiconductors
• Influence of disorder on the ferromagnetism in diluted magnetic semiconductors
• Effective Hamiltonian for Ga_{1-x}Mn_xAs in the Dilute Limit
• Two-component approach for thermodynamic properties in diluted magnetic semiconductors
• Monte Carlo Simulations of Doped, Diluted Magnetic Semiconductors - a System with Two Length Scales

Cited by in corpus (14)

• Theory of ferromagnetic (III,Mn)V semiconductors
• Optical Properties of III-Mn-V Ferromagnetic Semiconductors
• Why RKKY exchange integrals are inappropriate to describe ferromagnetism in diluted magnetic semiconductors
• Magnetic Percolation and the Phase Diagram of the Disordered RKKY model
• Low-temperature magnetization of (Ga,Mn)As semiconductors
• Monte Carlo simulations of $\mathrm{NiF}{\mathrm{e}}_2{\mathrm{O}}_4$ Nanoparticles
• Positional Disorder, Spin-Orbit Coupling and Frustration in GaMnAs
• Carrier induced ferromagnetism in diluted local-moment systems
• Monte Carlo simulations of $\mathrm{R}{\mathrm{b}}_2\mathrm{Mn}{\mathrm{F}}_4$, a classical Heisenberg antiferromagnet in two-dimensions with dipolar interaction
• Hidden zero-temperature bicritical point in the two-dimensional anisotropic Heisenberg model: Monte Carlo simulations and proper finite-size scaling
• Disorder, spin-orbit, and interaction effects in dilute ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$
• The influence of structural short-range order on the phase diagrams of diluted FCC magnet with arbitrary spin and modified RKKY interaction
• Magnetic susceptibility of diluted magnetic semiconductors at low carrier densities
• Effects of dilution and disorder on magnetism in diluted spin systems