$^3$He impurities and mass transport through solid $^4$He: a universal temperature dependence and flux extinction

The flux, $F$, carried by solid $^4$He in the range $25.6 - 26.3$ bar rises with falling temperature and at a temperature $T_d$ the flux decreases toward zero. We study $F$ as a function of $^3$He impurity concentration, $\chi$. At temperatures above $T_d$ the flux has an unexpected universal temperature dependence and the flux terminates in a narrow window near a characteristic temperature $T_h \approx$ 610 mK, which is independent of $\chi$. We find that $T_d$ is an increasing function of increasing $\chi$. We document that the extinction of the flux at $T_d$ is prompt and precipitous, with the transition complete within a few mK. Comparison of our ($T_d, \chi$) results with a calculated phase separation line suggests that the extinction of the flux is related to phase separation.