Evidence for magnetic crystallization waves at the surface of $^3$He crystal

Ultralow temperature crystals of the helium isotopes $^3$He and $^4$He are intriguing quantum systems. Deciphering the complex features of these unusual materials has been made possible in large part by Alexander Andreev's groundbreaking research. In 1978, Andreev and Alexander Parshin predicted the existence of melting/freezing waves at the surface of a solid $^4$He crystal, which was subsequently promptly detected. Successively, for the fermionic $^3$He superfluid/solid interface, even more intricate crystallization waves were anticipated, although they have not been observed experimentally so far. In this work, we provide preliminary results on $^3$He crystals at the temperature $T = 0.41$\;mK, supporting the existence of spin supercurrents in the melting/freezing waves on the crystal surface below the antiferromagnetic ordering temperature $T_N= 0.93$\;mK, as predicted by Andreev. The spin currents that accompany such a melting-freezing wave make it a unique object, in which the inertial mass is distinctly different from the gravitational mass.