Theory of magnetization of p-type Sn1−xGdxTe: Contributions from local moments, lattice diamagnetism and carriers

Abstract

We derive a theory of magnetization for the diluted magnetic semiconductor, p-type Sn1−xGdxTe including the contributions from Gd3+ local moments, carrier-local moment hybridization and lattice diamagnetism as a function of temperature and magnetic field. The local moment contribution Mlocal is a sum of three contributions: Mlocal=Ms+Mp+Mt, where Ms is the dominant single-spin contribution, and Mp and Mt are the contributions from clusters of two- and three-spins, respectively. We have also calculated the contribution due to spin-polarized holes for carrier densities of order 1020cm−3, using a k⇀⋅π→ model, where π→ is the momentum operator in the presence of the spin–orbit interaction and k→ is the hole wave vector. This contribution includes the carrier-local moment hybridization. We have also included a diamagnetic lattice contribution, which comes from inter-band orbital and spin–orbit contributions. In this contribution, the symbol k→ is used for the electronic wave vector. The local moment contribution is dominant and primarily comes from the isolated spins. However, the two- and three-spin contributions increase with increase in the magnetic impurity concentration. The magnitude of the hole–spin polarization is about two orders less than the local moment contribution even at field strength of 25T. However, the magnetization due to carrier spin-density has intrinsic importance due to its role in possible spintronics applications. The lattice diamagnetism shows considerable anisotropy. The total magnetization is calculated from all the three contributions Mlocal, Mc (due to carriers, here holes) and Mdia. We have compared our results with experiment wherever available and the agreement is fairly good.