Spin Wave and Sound in High-Field Phase of Solid Helium-3

Abstract

The finite temperature correction to the spin wave velocity and magnon relaxation rate are calculated in the high-field phase (HFP) of solid ³He by employing the Holstein–Primakoff 1⁄S expansion. The properties of sound are also calculated according to the methods similar to those developed by Khalatnikov et al. The anisotropy of the crystal is taken into consideration in deriving the kinetic equation as was done in the U2D2 phase. Sound velocity is obtained as a function of magnetic field and temperature. Sound attenuation resulting from magnon–magnon scattering is evaluated by collision-time approximation with a collision integral I(n) that conserves energy and momentum. The results are compared with the experimental results of Sasaki et al.