Phase Diagram of the Disordered RKKY Model in Dilute Magnetic Semiconductors

We consider ferromagnetism in spatially randomly located magnetic moments, as in a diluted magnetic semiconductor, coupled via the carrier-mediated indirect exchange RKKY interaction. We obtain, via Monte Carlo calculations, the magnetic phase diagram as a function of the impurity moment density $n_{i}$ and the relative carrier concentration $n_{c}/n_{i}$. As evidenced by the diverging ferromagnetic correlation length and magnetic susceptibility, the boundary between ferromagnetic and nonferromagnetic phases constitutes a line of zero temperature critical points which can be viewed as a magnetic percolation transition. In the dilute limit, we find that bulk ferromagnetism vanishes for $n_{c}/n_{i} > 0.1$. We also incorporate the local antiferromagnetic direct superexchange interaction between nearest neighbor impurities and examine the impact of a damping factor in the RKKY range function. This work has been done in collaboration with Sankar Das Sarma at the University of Maryland and supported by the US-ONR and NSF. \newline \newline [1] D.J. Priour, Jr. and S. Das Sarma, Phys. Rev. Lett., {\bf 97}, 127201 (2006). \newline [2] D.J. Priour, Jr. and S. Das Sarma, Phys. Rev. B, {\bf 73}, 165203 (2006). \newline [3] D.J. Priour, Jr., E.H. Hwang, and S. Das Sarma, Phys. Rev. Lett. {\bf 95}, 037201 (2005). \newline [4] S. Das Sarma, E.H. Hwang, and D.J. Priour, Jr., Phys. Rev. B {\bf 70}, 161203 (2004). \newline [5] D.J. Priour, Jr., E.H. Hwang, and S. Das Sarma, Phys. Rev. Lett. {\bf 92}, 117201 (2004).