3He Mobility and Localization in Thin4He Films

We report measurements of spin-diffusion coefficients for 0.1 monolayero${\mathrm{f}}^3$He adsorbed on thi${\mathrm{n}}^4$He filmsas a function of temperature an${\mathrm{d}}^4$He coverage. Fo${\mathrm{r}}^4$He coverages below a critical coverage $D_c$ the ${}^3$He are immobile. The ${}^3$He quasiparticles in the film experience a mobility edge as the ${}^4$He coverage is increased beyond $D_c$. This is accompanied by a vanishing of local moments as evidenced by the disappearance of a Curie-like component of the magnetization for coverages $D>\mathrm{}{D}_c$. A peak in the transverse relaxation $T_2$ occurs near $D_c$.