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Magnetic polarons are ferromagnetic spin clusters created by the exchange interaction of a carrier spin (electron or hole) with localized spins imbedded in a semiconductor lattice. They were first studied in magnetic semiconductors ; more recently, there have been extensive investigations  of polaron behavior in diluted magnetic semiconductors (DMS), such as Cd1−xMnxTe. DMS are favorable media for magnetic polaron studies because they have simple s-p bands and excellent optical properties. Two types of magnetic polarons have been identified in DMS - the bound magnetic polaron (BMP), whose carrier is localized by an impurity , and the free polaron (FP) consisting of a carrier trapped by its own, self-consistently-maintained, exchange potential .
We review recent applications of wavefunction engineering to the design of antimonide quantum heterostructures with favorable properties for infrared devices. Examples include electro-optical and all-optical modulators based on Г-L intervalley transfer, type-II quantum well lasers with enhanced gain per injected carrier, and type-II interband cascade lasers predicted to combine low thresholds and high output powers.
A Lagrangian formulation for the valence bands of bulk zinc blende and wurtzite compound semiconductors provides a direct approach to determining derivative operator ordering at layer interfaces in the multiband k·P description of electronic states, in the envelope function approximation. The current continuity condition is obtained through a gauge-variation on the Lagrangian. The principle of least action together with the discretization of the action integral naturally leads into a finite element approach for the modeling and simulation of the multiband Schrödinger equations. Being a variational method, the wavefunctions and energy eigenvalues can be systematically improved with quadratic convergence. By including the Poisson Lagrangian, a self-consistent treatment of the Schrödinger-Poisson band-bending in arbitrarily doped structures is obtained. Numerical examples are presented for the valence band electronic states for quantum wells and superlattices. We have also coupled the finite element method with layer parameter optimizations to design heterostructures for lasers emitting at given wavelengths. It is in this sense that wavefunction engineering goes beyond the notion of bandgap engineering in providing the means for optimizing wavefunction localization in layers, selecting layer thicknesses, enhancing optical matrix elements, and laser gain.
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