Order-parameter collective modes in 3He-A and their effect on nuclear magnetic resonance (NMR) and ultrasonic attenuation

Abstract

A generalization of our previous microscopic theory is used to derive the spin and density correlation functions for the Anderson-Brinkman-Morel (ABM) state. The coupling of the 18 fluctuation components of the order parameter due to the nuclear dipole interaction is taken into account rigorously. The results are valid for arbitrary temperature, frequency, wave number (with q parallel to the anisotropy axis), and magnetic field. Damping by pair-breaking processes is calculated explicitly; however, quasiparticle collisions are neglected. The frequencies of the clapping modes that couple to spin, and the frequencies of the flapping modes that couple to density, are found to split in a magnetic field. Near T c the linewidth of the clapping mode and, at low T, the linewidth of the normal-flapping mode become small while the linewidth of the super-flapping mode is broad at all temperatures. The linewidth of the transverse NMR and the ultrasound attenuation coefficient, considered as functions of temperature, exhibit pronounced peaks at low temperatures. These arise from a coupling, induced by the dipole interaction, between spin or density fluctuations and the normal-flapping mode. Our results for the linewidth and line shift of the longitudinal NMR at low temperatures due to orbital effects are in agreement with results of Combescot.