We present a Landau-type semiphenomenological theory for the zero-sound dispersion relation in normal-liquid${\mathrm{-}}^3$He films in the presence of a magnetic field or for partially polarized films. We express our result in terms of the spin-dependent (${\mathit{F}}_0^{\mathit{a}}$) and spin-independent (${\mathit{F}}_0^{\mathit{s}}$) first Landau parameters. We give the zero-field result and the lowest-field correction. We find that the field effect should be readily observable for the presumably attainable experimental accuracy.

• Received 14 December 1993

DOI:https://doi.org/10.1103/PhysRevB.49.16042