Doping GaAs with a small concentration of Mn leads to a dramatic change in its physical properties. Mn acts as an acceptor in GaAs with spin-5/2, so each Mn contributes a hole and a spin to the system. However, there is usually large compensation and the hole concentration is much less than the Mn concentration. As the doping increases, the material becomes an insulating ferromagnet, and then a metallic ferromagnet, with a Curie temperature (T_c) that has been observed to be as high as 170 K. This material is a testing ground for integrating magnetic functionalities with existing electronic and optical semiconductor technologies and hence a clear theoretical understanding of its properties is important. Introducing dopants also introduces disorder into the system, and we investigated the effect of positional disorder of Mn spins on magnetic properties of DMS in the insulating phase. We found that disorder enhances T_c relative to an ordered system, leads to inhomogeneous ferromagnetism, and controls the shape of the magnetization versus temperature curve. In the inhomogeneous ferromagnetic state, regions of high local charge density and large local magnetization coincide due to the enhanced exchange energy in this region. The inhomogeneity creates a percolating backbone of strongly localized magnetic regions which leads to an enhanced $T_c$. This in turn affects the shape of the magnetization vs temperature curve, which becomes concave, rather than the convex shape seen in conventional ferromagnets such as iron. I carried out these investigations mainly using numerical techniques, in particular by developing and then implementing an efficient hybrid Monte Carlo scheme to solve the numerically intensive problem of a model with classical spins coupled to fermions.

"Disorder and frustration in diluted, magnetic semiconductors at low carrier densities",
R. N. Bhatt, C. Zhou, M. Kennett, M. Berciu and X. Wan, Int. J. Mod. Phys. B 19, 5 (2005).

"Exchange anisotropy effects on ferromagnetism in diluted, magnetic semiconductors",
C. Zhou, M. P. Kennett, X. Wan, M. Berciu and R. N. Bhatt, J. Magn. Magn. Mat. 272-276, 2014 (2004).  

"Disorder effects on ferromagnetism in diluted, magnetic semiconductors",
M. P. Kennett, M. Berciu and R. N. Bhatt, J. Magn. Magn. Mat. 272-276, 1993 (2004).  

"Exchange anisotropy, disorder and frustration in diluted (predominantly) ferromagnetic Heisenberg spin systems",
C. Zhou, M. P. Kennett, X. Wan, M. Berciu and R. N. Bhatt, Phys. Rev. B 69, 144419 (2004). cond-mat/0310322.  

"Monte Carlo simulations of an impurity band model for III-V diluted, magnetic semiconductors",
M. P. Kennett, M. Berciu and R. N. Bhatt, Phys. Rev. B 66, 045207 (2002).  cond-mat/0203173

"Numerical simulations of random spin (and fermionic) models with a wide distribution of energy scales",
R. N. Bhatt, X. Wan, M. P. Kennett, and M. Berciu, Comp. Phys. Comm. 147, 684 (2002).

"Two-component model for thermodynamic properties of diluted, magnetic semiconductors",
M. P. Kennett, M. Berciu and R. N. Bhatt, Phys. Rev. B 65, 115308 (2002).    cond-mat/0102315 .

"Diluted magnetic semiconductors in the low carrier density regime",
R. N. Bhatt, M. Berciu, M. P. Kennett, and X. Wan, J. Supercond. 15 , 71 (2002). cond-mat/0111184