On various contributions to the magnetization of n-type Pb1–xGdxTe

Abstract

We present a calculation of the magnetization of n-type Pb1–xGdxTe. We consider three types of contributions. These are local moments from the randomly substituted Gd3+ ions, valence band diamagnetism and the spin-density of electrons. The statistical local moment contribution is considered by using three types of clusters: isolated spins or singles, pairs of spins and triads. The triads include both closed triplets and open triplets. The valence band diamagnetism is calculated using a two band model. Because of pronounced spin–orbit interaction in the system, the importance of a separate spin–orbit contribution to the diamagnetism is emphasized. Considerable anisotropy is noticed in the calculation. For the calculation of the contributions from degenerate electrons, we follow a six-band theory, where the band edge state Hamiltonians are diagonalized exactly and far bands are considered, using second order perturbation theory. The anisotropy in the carrier contribution comes from the effective g-factor and is due primarily to the spin–orbit interaction. Effects of carrier concentration, Gd3+ concentration and temperature are considered on the field-induced magnetization. Although the dominant contribution results from the local moment contributions, the diamagnetic contribution and the spin-density of carriers present interesting behaviour as functions of temperature and composition. Satisfactory agreement with experimental results is noticed, wherever such results exist.