Properties of 2DH3eon Very ThinH4eFilms

We report measurements of the ${}^3\mathrm{He}$ spin diffusion, magnetization, and NMR relaxation times for submonolayer, $n_3=0.0064{Å}^{-2\mathrm{}}$ ( $\sim 0.10$ layer), ${}^3\mathrm{He}$ impurities on thin ${}^4\mathrm{He}$ films on Nuclepore. We find a mobility edge, a strong ${}^4\mathrm{He}$ coverage dependence for the ${}^3\mathrm{He}$ ground state energy, and the absence of an excited state for the ${}^3\mathrm{He}$ for very low ${}^4\mathrm{He}$ coverages. A $\sim {10}^3–{10}^4$ increase in the value of the diffusion coefficient occurs over a narrow ${}^4\mathrm{He}$ coverage range, $0.15\le n_4\le 0.23{Å}^{-2\mathrm{}}$, and a large Curie-like component is present in the magnetization for $n_4\le 0.20{Å}^{-2\mathrm{}}$.