Effect of ${}^3\mathrm{He}$ Impurities on the Nonclassical Response to Oscillation of Solid ${}^4\mathrm{He}$

We have investigated the influence of impurities on the possible supersolid transition in ${}^4\mathrm{He}$ by systematically enriching isotopically pure samples with ${}^3\mathrm{He}$. The addition of ${}^3\mathrm{He}$ broadens the onset of nonclassical rotational inertia and shifts it to higher temperature, suggesting that the phenomenon is correlated with the condensation of ${}^3\mathrm{He}$ atoms onto the dislocation network in solid ${}^4\mathrm{He}$.

Figure 1

(a) Comparison of 1 ppb samples from TOF and Ref. [5]. To qualitatively compare the temperature dependencies, NCRIF and $\Delta Q^{-1}$ (dissipation) data for the CP sample [5] are divided by 12 and 5, respectively. No additional $T$ dependence is found below $T_S$. (b) Ultralow temperature scan of a 38 ppb sample from TOF.

Figure 2

$x_3$ dependence of NCRIF for BC samples obtained in this study and in other TO’s from our laboratory. There appears to be an optimal concentration of $\sim 1\mathrm{ppm}$, where NCRIF reaches a maximum value.

Figure 3

$T$ dependence of NCRIF (normalized by the value at $\sim 20\mathrm{mK}$) for different $x_3$ grown in (a) TOF and (b) TOP. (c) $T$ dependence for $x_3\ge 300\mathrm{ppb}$. Two traces obtained with an annular cell [22] are also shown. (d),(e),(f) The right three panels show the $x_3$ dependencies of the characteristic temperatures extracted from the adjacent plots.

Figure 4

$T_{50}$ versus $x_3$. Relative to $T_{50}$, values of $T_{10}$ and $T_{90}$ (excluded for clarity) are shifted vertically upward by $\sim 60\%$ and downward by $\sim 25\%$, respectively. From top to bottom, the three solid lines represent the condition, $T_{\mathrm{IP}}=T_x$, for $x=10$, 50, and 90. To apply Eq. (1) we assume that all samples have the same $L_N$ (and $\Lambda$). The fitting parameters are listed in Table . The theoretical phase separation boundary [11] (dotted line), anchored by pressure [9] and ultrasound [10] measurements, is inconsistent with the TO data.