Approach to Boltzmann Equilibrium of the Nuclear Spins in a Quadrupolar Solid

Abstract

A single crystal of NaN${\mathrm{O}}_3$ is oriented in an external magnetic field at an angle (${\theta }_1$) for which the quadrupole splitting is large. With radio-frequency radiation, a pair of Zeeman levels of the sodium nuclear spin system ($I=\frac{3}{2}$) is saturated. Then the crystal is quickly rotated to an angle where the inequality of the level spacings is a minimum (approximately ½ the line width) and where spin mixing can take place. The crystal is then quickly returned to ${\theta }_1$ where, by nuclear resonance pulse techniques, the populations of the four sodium levels can be determined. This sequence of operations is completed in a time short compared to the spinlattice relaxation time. When the $m=\pm \frac{1}{2}$ levels are initially saturated, the spin system rapidly comes to the expected spin temperature $T_S=\left(\frac{10}{9}\right)\times \left(\mathrm{the}\mathrm{lattice}\mathrm{temperature}\right)$. When the outer satellites are saturated, however, the resulting equilibrium populations of the levels are not those of a Boltzmann distribution. Also measured was the rate of approach of the spin system to equilibrium for various larger splittings. For splittings of the order of the line width, an unexpected plateau appears in the spin mixing rate. The usual rate equations do not seem adequate to describe the observed dynamic behavior of this spin system.