Monte Carlo study of ferromagnetism in (III,Mn)V semiconductors

We report on Monte Carlo studies of the kinetic exchange model for (III,Mn)V ferromagnetic semiconductors in which $S=5/2\mathrm{}$ local moments, representing ${\mathrm{Mn}}^{2+}$ ions, are exchange coupled to band electrons. We treat the ${\mathrm{Mn}}^{2+}$ spin orientations as classical degrees of freedom and use the hybrid Monte Carlo algorithm to explore thermodynamically important $\mathrm{Mn}$ spin configurations. The critical temperature $T_c$ of the model is unambiguously signalled in our finite-size simulations by pronounced peaks in fluctuations of both $\mathrm{Mn}$ and band carrier total spins. The $T_c\mathrm{’}\mathrm{s}$ we obtain are, over much of the model’s parameter space, substantially smaller than those estimated using mean-field theory. When mean-field theory fails, short-range magnetic order and finite local carrier spin polarization are present for temperatures substantially larger than $T_c.$ For the simplest version of the model, which has a single parabolic band with effective mass $m^{*},$ the dependence of $T_c$ on $m^{*}$ is sublinear at large masses, in disagreement with the mean-field theory result $T_c\propto m^{*}.$