Spin-Lattice Relaxation near the Critical Point: RbMnF3, MnF2, EuO

Abstract

Electronic spin-lattice relaxation in disordered ferro- and antiferromagnets is discussed with particular emphasis on the region near the critical point. A general expression for the relaxation time is derived. The time it takes for the spins to come to thermal equilibrium with the lattice is directly proportional to the magnetic specific heat, as anticipated from thermo-dynamic arguments. It is shown that systems whose ordering temperature is at least comparable to the peak in the density of states of the acoustic-phonon modes can have very short relaxation times. This happens because the spins can interact with essentially all the acoustic modes. Relaxation times are estimated for three systems: RbMn${\mathrm{F}}_3$, Mn${\mathrm{F}}_2$, and EuO. The implication of these results for the interpretation of ultrasonic attenuation measurements is discussed. It is found that the calculated values for the relaxation times agree qualitatively with the values inferred from ultrasonic data for RbMn${\mathrm{F}}_3$. The behavior of EuO is analyzed. We find that our values of $T_1$ are compatible with the dominance of the spin-lattice mechanism in the decay of the energy-density fluctuations with wavelengths comparable to the wavelengths of the ultrasonic phonons.