Thermal and Magnetic Properties of Nd³⁺in Doped Garnets

Abstract

The Schottky specific heats and magnetic susceptibilities of the Nd3+ in five doped garnets, GGG, LuAG, LuGG, YAG and YGG, have been calculated using effective spin Hamiltonian formalism in connection with the crystal field theory in a temperature interval of 30 to 500 K. Both heat capacities and susceptibilities are determined by two different methods. The first method is dealing with the diagonalization of the effective spin Hamiltonian and then obtaining the quantities in a very general way of quantum statistical mechanics. The second method is based on the cumulant expansion of partition function and utilizing the invariance properties of the trace of the Hamiltonian matrices. It is thought that the specific heat and the susceptibility calculations may help to refine the crystal field parameters of such crystals.