Phase Diagram of the $\mathit{A}$ and $\mathit{B}$ Phases of Superfluid ${}^3\mathrm{He}$ in Aerogel

We report the first measurements of the $A-B$ phase transition of superfluid ${}^3\mathrm{He}$ confined within $98\%$ silica aerogel in high magnetic fields and low temperatures. A disk of aerogel is attached to a vibrating wire resonator. The resonant frequency yields a measure of the superfluid fraction ${\rho }_s/\rho$ of the ${}^3\mathrm{He}$ within the aerogel. The inferred ${\rho }_s/\rho$ value increases substantially at the $A$-to- $B$ transition of the confined superfluid, allowing us to map the $A-B$ phase diagram as a function of field and temperature. At 4.8 bars, the $B-T$ transition curve looks very similar to that in bulk with a simple reduction factor of order 0.45 for both transition field and temperature.