2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/18991We 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.15 pages, 4 figuresSuperconductivitytext