Simultaneous Measurement of Torsional Oscillator and NMR of Dilute $^3$He in Solid $^4$He

We have carried out simultaneous measurements of on $^3$He-concentrations in solid $^4$He using state-of-the-art NMR technique and a torsional oscillator (TO) method. Our NMR results from a sample with a relatively high concentration ($\sim$ hundred ppm of $^3$He), suggest existence of three different ``states'' of $^3$He which depend on temperature. The first one is characterized by almost invisibly long spin-lattice relaxation T$_{1}$. This would imply that each $^3$He atom behaves as gaseous in a solid $^4$He-matrix. Another characterized by a reasonably long component in T$_{1}$ is a cluster of $^3$He, which appears below the isotopic phase separation temperature. The third one is characterized by a relatively short spin-lattice relaxation time T$_{1}$, which also shows up below the isotropic phase separation temperature. This state may correspond to $^3$He clusters in the disordered part of the crystal, since it does not disappear right away even above the phase separation temperature. As found by other studies, broadening out of the $\Delta$Q$^{-1}$-peak as well as the NCRIf were found in TO. In addition we have also observed a TO response for 0.3 ppm sample. Further studies to clarify this issue are in progress.