Linear field dependence of the Landau parameters and the $A_1$ transition in liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$

We present here the first calculation of the linear field dependence of the Landau parameters in liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$. From the Landau parameters we obtain the linear field splitting of the $A_1$ phase in superfluid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$. We conclude that the orientation of the magnetic moments of the paired spins in the $A_1$ phase are aligned along the field for all pressures.