The Behavior of a Triplet Superconductor in a Spin Only Magnetic Field

We investigate the order parameter of Sr${}_2$RuO${}_4$ in an exchange-only magnetic field. A Ginzburg-Landau symmetry analysis implies three possibilities: a pure ${}^3$He A phase, a ${}^3$He A${}_1$ or a ${}^3$He A${}_2$ phase. We explore the exchange field dependence of the order parameter and energy gap in a one-band model of Sr${}_2$RuO${}_4$. The numerical solutions show no A${}_1$ phase and that the A${}_2$ phase is lower in free energy than the A phase. We explore heat capacity as a function of temperature and field strength and find quantitatively different behaviors for the A and A${}_2$ phases.