Bound Magnetic Polarons in Diluted Magnetic Semiconductors
These notes develop the semi-classical theory of bound magnetic polarons (BMP) and use it to calculate their thermodynamic properties, such as energy, susceptibility, etc. The theory demonstrates that the polaron evolves continuously from a high temperature, fluctuation-dominated regime to a low temperature, collective state with large net moment (20–50μ B ). In the simplest cases (donor — BMP in materials such as Cd 1− x Mn x Se with small x), the theory is in good agreement with optical experiments that determine microscopic properties of the polaron. To date, there is no theory of the acceptor — BMP that fully incorporates valence band degeneracy. However, hydrogenic models are in fair agreement with experiment, and demonstrate saturation of the acceptor — BMP below 20K.
The semiclassical theory correctly predicts thermodynamic averages, but is inadequate for describing polaron kinetics or the detailed energy level structure. For that purpose, a fully quantum mechanical theory is required. Simplified, soluble, quantum mechanical models of the polaron have been developed by several authors. We discuss them using Feynman’s variational principle for the free energy. Optimized models will be compared with experiment and the semi-classical theory.
Finally, the behavior of polarons in materials with large Mn 2+ concentration will be discussed. Experimentally, in Cd 1− x Mn x Te the polaron binding energy peaks at x=0.2 and decreases thereafter. This effect is ascribed to competition between the ferromagnetic, polaron-forming interaction (mediated by the carrier) and the direct, antiferromagnetic Mn 2+−Mn 2+ interaction. A phenomenological polaron theory, that incorporates Jun Mn 2+−Mn 2+ interactions via the measured susceptibility, accounts for the observed saturation. To avoid saturation, which reduces polaron energies by a factor of five compared to those that would otherwise be attainable, we propose ordered DMS compounds. Growth of such crystals provides an important challenge to materials scientists.
KeywordsPartition Function Schrodinger Equation Semiclassical Approximation Nonlinear Schrodinger Equation Semiclassical Theory
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