Solution of the problem of catastrophic relaxation of homogeneous spin precession in superfluid $^3$He-B

TL;DR

This paper analyzes the catastrophic relaxation phenomenon in superfluid $^3$He-B, explaining it through decay instability of spin precession into spin waves, and distinguishes the dominant interactions in various experimental regimes.

Contribution

It extends previous models by including spin-orbital interactions for non-parallel orientations of ${f L}$, providing a more comprehensive understanding of the relaxation process.

Findings

Decay instability explains the abrupt signal decay.

Spin-orbital interactions dominate in non-parallel ${f L}$ configurations.

Analysis of experimental data identifies the main contributing interactions.

Abstract

The quantitative analysis of the "catastrophic relaxation" of the coherent spin precession in $^3$He-B is presented. This phenomenon has been observed below the temperature about 0.5 T$_c$ as an abrupt shortening of the induction signal decay. It is explained in terms of the decay instability of homogeneous transverse NMR mode into spin waves of the longitudinal NMR. Recently the cross interaction amplitude between the two modes has been calculated by Sourovtsev and Fomin \cite{SF} for the so-called Brinkman-Smith configuration, i.e. for the orientation of the orbital momentum of Cooper pairs along the magnetic field, ${\bf L}\parallel {\bf H}$. In their treatment, the interaction is caused by the anisotropy of the speed of the spin waves. We found that in the more general case of the non-parallel orientation of ${\bf L}$ corresponding to the typical conditions of experiment, the spin-orbital interaction provides the additional interaction between the modes. By analyzing experimental data we are able to distinguish which contribution is dominating in different regimes.