Theory of the spin EPR Shift in Diluted Magnetic Semiconductors - Misra, Prasanta K (Mesoscopic, Nanoscopic, and Macroscopic Materials (AIP Conference Proceedings Volume 1063), 2008)
The electron paramagnetic resonance (EPR) shift is a measure of the internal field created at the magnetic ion site in magnetic materials or materials with magnetic impurities by the partial polarization of electrons and/or carriers in an applied magnetic field. It constitutes an important study involving carriers and their interactions with the magnetic ions in an electronic system. In addition, it provides important information regarding the wave functions of the carriers as well as the Fermi surface characteristics of the system. We have derived a theory for the spin-contribution to the EPR shift (Ps) for an electronic system in the presence of a periodic potential, spin-orbit (SO) interaction, conduction electron-local moment interaction, and an applied magnetic field by using an effective equation of motion of the Green's function in a representation defined by the periodic part of the Bloch function. The spin-EPR shift is expressed as a function of the matrix elements of the momentum, Pauli spin-operators and conduction-electron-local moment interactions. Recently, the diluted magnetic semiconductors (DMS), particularly Pb1-xMnxTe and Pb1-x-yMnxSnyTe, have attracted considerable attention due to the possibilities of carrier-mediated ferromagnetism, which could be of use in the emerging subject of spintronics. Therefore, we have used our theory to calculate Ps at Mn2+ ion in Pb1-xMnxTe as a function of the carrier concentration. The electronic structure of the DMS is calculated using a modified six-level k.p(p is the momentum operator in the presence of SO interactions) model. The contributions from band-edge interactions as well as from far bands are included and Ps is found to be anisotropic arising mainly due to SO interactions. Calculation of Ps for two typical hole densities agree fairly well with the experimental results for p-Pb1-xMnxTe. The minor discrepancies between the theoretical and experimental results have been analyzed.