Effect of thermodynamic fluctuations of magnetization on the bound magnetic polaron state in ferromagnetic semiconductors

Abstract

We extend the theory of the bound magnetic polaron (BMP) in diluted paramagnetic semiconductors to the situation with a ferromagnetic phase transition. This is achieved by including the classical Gaussian fluctuations of magnetization from the quartic (non-Gaussian) term in the effective Ginzburg.Landau Hamiltonian for the spins. Within this approach, we find a ferromagnetically ordered state within the BMP in the temperature range well above the Curie temperature for the host magnetic semiconductor. Numerical results are compared directly with the recently available experimental data for the ferromagnetic semiconductor GdN. The agreement is excellent, given the simplicity of our model, and is because the polaron size (1.4 nm) encompasses a relatively large but finite number (N ≈ 400) of quasiclassical spins S = 7 2 coming from Gd3+ ions. The presence of BMP invalidates the notion of critical temperature and thus makes the incorporation of classical Gaussian fluctuations sufficient to realistically describe the situation.