Spin Temperature in Magnetism and in Magnetic Resonance

Abstract

In Chapter 5 we employed the concept of spin temperature to discuss relaxation. The idea of spin temperature was introduced by Casimir and du Pre [6.1] to give a thermodynamic treatment of the experiments of Gorter and his students on paramagnetic relaxation. It was Van Vleck [6.2] who first employed the concept for a detailed statistical mechanical calculation of the relaxation times of paramagnetic ions. Both in this case, and also in his general statistical mechanical treatment of static properties of paramagnetic atoms [6.3], he recognized and emphasized the fact that expansion of the partition function Z in powers of l/T enabled one to calculate Z without the necessity of solving for the energies and eigenfunctions of the Hamiltonian. Waller evidently was the first person to use this property [6.4]. From the partition function, one can compute all the static properties of the system, such as the specific heat, the entropy, the magnetization, and the energy. For example, the average energy of a system, Ē, at a temperature T is given by

$$ \overline E = k{T^2}\frac{\partial }{{\partial T}}\ln Z $$

(6.1)

.