Spin Fluctuations in Magnetic Quantum Dots*

We present a theoretical description of magnetism in quantum dots (QDs) doped with magnetic ions. It has been recognized that the mean-field theory (MFT) is inadequate for small magnetic systems, such as bound magnetic polarons (BMPs), at finite temperatures [1]. Magnetic QDs are in many respects similar to BMPs, however the latter are one-electron systems while the former may contain many electrons. Our approach requires the minimization of the generalized ``free energy'' functional [2] for QDs, which leads to a set of self-consistent Kohn-Sham-type equations that coincide with MFT-equations [3] in the thermodynamic limit. We reveal that the well-known spurious MFT second order phase transition in magnetization is completely removed by thermodynamic spin fluctuations. \\[4pt] [1] T. Dietl and J. Spalek, Phys. Rev. Lett. {\bf 48}, 355 (1982).\\[0pt] [2] A. G. Petukhov, I. Zutic, and S. C. Erwin, Phys. Rev Lett. {\bf 99}, 257202 (2007)\\[0pt] [3] R. M. Abolfath, A. G. Petukhov, and I. Zutic, Phys. Rev. Lett. {\bf 101}, 207202 (2008); R. M. Abolfath, P. Hawrylak, and I. Zutic, Phys. Rev. Lett. {\bf 98}, 207203 (2007).