Analysis of the Melting Process of Magnetized Solid 3He

We report on our analysis of the melting process of highly magnetized solid ³He. Akimoto et al. found that the solid-liquid interface becomes unstable during melting in a magnetic field of 9 T. The liquid then penetrates into the solid in the form of cellular dendrites. The instability, which was predicted by Puech et al., was attributed to a Mullins-Sekerka type of instability due to the magnetization gradient on the solid side. The measurements on which we base our analysis clearly show gradients on both sides of the interface. We present an extension of the linear stability analysis for this situation, as well as a numerical calculation of the dispersion relation of interface deformations. Our results are in good agreement with the experiment and explain the initial suppression of the instability, caused by the magnetization gradient in the liquid.