Nonlinear Zeeman Shifts in the Collective-Mode Spectrum of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-$B$

Zeeman shifts in one of the $J=2\mathrm{}$ order-parameter collective-mode multiplets in ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-$B$ have been measured in magnetic fields up to 0.16 T. The observed shifts are extremely nonlinear at higher fields. The extent of nonlinearity decreases as $\frac{T}{T_c}\to 0$ and for a given $\frac{T}{T_c}$ is more predominant at lower pressures and/or frequencies. The observed effects can be attributed to the distortion of the $B$-phase energy gap in the presence of a magnetic field as suggested by Schopohl, Warnke, and Tcwordt.