Effect of magnetic scattering on the superfluid transition of ${}^3\mathrm{He}$ in nematic aerogel

We present the results of high magnetic field experiments in pure ${}^3\mathrm{He}$ (in the absence of ${}^4\mathrm{He}$ coverage) in nematic aerogel. In this case the aerogel strands are covered with few atomic layers of solid paramagnetic ${}^3\mathrm{He}$, which enables the spin-exchange mechanism for ${}^3\mathrm{He}$ quasiparticles scattering. Our earlier NMR experiments showed that in low fields, instead of the polar phase, the $A$ phase is expected to emerge in nematic aerogel. We use a vibrating wire resonator with the sample of aerogel attached to it and measure temperature dependencies of resonance properties of the resonator at different magnetic fields. A superfluid transition temperature of ${}^3\mathrm{He}$ in aerogel, obtained from the experiments, increases nonlinearly in applied magnetic field. And this increase is suppressed compared with that for the bulk $A_1$ phase, which we attribute to an influence of the magnetic scattering channel, previously considered theoretically for the case of ${}^3\mathrm{He}$ confined in isotropic silica aerogel. However, we observe the essential quantitative mismatch with theoretical expectations.

Figure 1

Temperature dependencies of FWHM of the main resonance of the VW resonator measured in the presence of ${}^4\mathrm{He}$ coverage [20] (filled circles, $H=4.1$ kOe) and in pure ${}^3\mathrm{He}$ (open circles, $H=4.4$ kOe). Arrows indicate the features we associate with different superfluid transitions at temperatures $T_{P2}, T_{P1}, T_{A2}, T_{A1}$, and $T_{ca1}$ (see text for details). The $x$ axis represents the temperature normalized to the superfluid transition temperature in bulk ${}^3\mathrm{He}{T}_c=2.083$ mK. Inset: Signal measurement circuit of a VW immersed in liquid ${}^3\mathrm{He}$ in magnetic field $\mathbf{H}$. The strands of nematic aerogel are oriented along the oscillations.

Figure 2

The frequency of the main resonance of the VW resonator versus the FWHM measured on warming in a magnetic field of 19.4 kOe. Dashed arrows show the direction of the temperature change. Double-sided arrow indicates the FWHM range which is used to determine $T_{ca1}$ (see text for details).

Figure 3

Temperature dependencies of the FWHM of the main resonance of the VW resonator measured in magnetic fields of 2.2 kOe (squares), 8.2 kOe (circles), 12.6 kOe (triangles), and 19.4 kOe (diamonds) at corresponding excitation currents of 1.9, 0.5, 0.33, and 0.21 mA. Arrows indicate $T=T_{ca1}$ determined as described in the text.

Figure 4

The “upper” superfluid transition temperature of ${}^3\mathrm{He}$ in nematic aerogel in the absence of ${}^4\mathrm{He}$ coverage versus $H$ (circles, left and right axes). The solid line is the best fit of our data by Eq. (2) using ${\eta }_{A1}$ and $C_1$ as fitting parameters. Right axis: The best-fit lines for transition temperatures into the bulk $A_1$ phase [6] (dashed line) and into the $\beta$ phase in ${}^3\mathrm{He}$ in the present aerogel sample with ${}^4\mathrm{He}$ coverage [20] (dotted line).