Theory of magnetization of n-type Pb_(1-x)Gd_xS diluted magnetic semiconductor

摘要

The present work describes our theory of magnetization (M) for the diluted magnetic semiconductor n-Pb_(1-x)Gd_xS which is expressed as a combination of two different contributing mechanisms namely localized magnetic impurities of Gd~(+3) and band effect. Three spin cluster model which includes single (isolated), two (pair) and three (triade) spin clusters is employed to calculate the magnetic impurity contribution. Moreover, we consider two types of triple spin clusters such as open and closed triplets. Furthermore, the distribution of Gd~(+3) ions over the non-magnetic host of PbS is assumed to be random. Apart from Zeeman interaction we consider the antiferromagnetic exchange interaction between magnetic ions in the nearest neighbour approximation. The band effect are considered via the lattice diamagnetism (X_(dia)) and carrier electron spin polarization (M_C). X_(dia) is calculated using the frame work of two band k.π.model for the host system and the effect Gd~(+3) impurities has been considered through the modification of the energy gap. Here π is the relativistic momentum operator in the presence of spin-orbit interaction. M_C is calculated using a six level k.π.theory. The magnetization is calculated for three values of x=0.009, 0.025 and 0.05 and magnetic fields up to 10 Tesla at temperature T=2 K. We have compared our calculated values with experiment where available and found good agreement, which is the other notable feature of our work.