$A_1$ and $A_2$ Transitions in Superfluid ${}^3\mathrm{H}\mathrm{e}$ in 98% Porosity Aerogel

Superfluid ${}^3\mathrm{H}\mathrm{e}$ in high porosity aerogel is the system in which the effects of static impurities on a p-wave superfluid can be investigated in a systematic manner. We performed shear acoustic impedance measurements on this system (98% porosity aerogel) in the presence of magnetic fields up to 15 T at the sample pressures of 28.4 and 33.5 bars. We observed the splitting of the superfluid transition into two transitions in high fields in both bulk and liquid in aerogel. The field dependence of the splitting in aerogel resembles that of the bulk superfluid ${}^3\mathrm{H}\mathrm{e}$ caused by the presence and growth of the $A_1$ phase. Our results provide the first evidence of the $A_1$ phase in superfluid ${}^3\mathrm{H}\mathrm{e}/\mathrm{\text{aerogel}}$.

Figure 1

Acoustic traces for 3, 5, and 15 T at 33.5 bars on warming. The bottom graph shows the acoustic trace at 15 T along with that of the vibrating wire. The sharp jumps in the VW trace are identified as $A_1$ and $A_2$ transitions in the bulk liquid. The acoustic trace also shows two sharp features at the exactly same time positions. $T_{aA1(2)}$ indicates the position of $A_{1(2)}$ transition in aerogel. The same scale is used in all three graphs for the acoustic signal. The straight lines in the top panel are shown to illustrate the change in slopes at the transition.

Figure 2

Transition temperatures vs magnetic field for 28.4 and 33.5 bars. Open (solid) circles are for the bulk (aerogel) transitions determined by the two point calibration scheme. Open squares for 28.4 bars are obtained by the single point calibration method. Crosses are based on the constant warming rate. See the text for the temperature calibration procedures. The solid (dashed) lines are the results of linear fit for aerogel (bulk) (see the text). The dash-dotted lines represent the paramagnetic to high field phase transition line and on the dotted line, $|dP/dT|=0.1\mathrm{k}\mathrm{P}\mathrm{a}/\mathrm{m}\mathrm{K}$.