Moderate Magnetic Field Transverse Acoustics in Superfluid $^3$He-B

We present the results of transverse acoustics studies in superfluid $^3$He-B at fields up to 0.1 T. Using acoustic cavity interferometry, we observe the acoustic Faraday effect\footnote{G.F. Moores and J.A. Sauls, J. Low Temp. Phys. {\bf 91}, 13 (1993).}$^,$\footnote{Y. Lee {\it et al.}, Nature {\bf 400}, 431 (1999).} for a transverse sound wave propagating along the magnetic field, and we measure Faraday rotations of the polarization of the sound up to 990$^\circ$, significantly more extensive than has been previously reported. We use these results to extend previous calculations of the Land\'e \textit{g} factor. We also find the field dependence of cavity interference oscillations resulting from coupling to the imaginary squashing mode (ISQ), a collective mode of the order parameter with total angular momentum $J=2$. Measurements in large magnetic fields were performed at frequencies up to the pair breaking threshold, where there has been a recent report\footnote{J.P. Davis {\it et al.}, Nature Physics {\bf 4}, 571 (2008).} of a new collective mode with $J=4$. The discovery of Faraday rotations coming from this new mode is reported, along with their intersection with rotations from the ISQ. Support for this work from the NSF, grant DMR-0703656, is gratefully acknowledged.