Shear Modulus of Solid Helium Confined in Aerogel

Torsional oscillator experiments on $^4$He show supersolid behavior which appears to be associated with disorder. However, confining helium in the pores of an aerogel does not enhance the supersolid decoupling, even though x-ray measurements confirm that the crystals are highly disordered. Solid helium's shear modulus also shows anomalous behavior below 150 mK, stiffening as mobile dislocations are pinned by $^3$He impurities at low temperatures. A highly porous material such as aerogel should also provide effective pinning sites for dislocations. We have made shear modulus measurements on solid $^4$He grown in a 95\% porosity aerogel. We see large modulus decreases as the samples are warmed but these occur at much higher temperatures and over a broader range than in bulk $^4$He. The frequency dependence of the modulus and dissipation are consistent with a thermally activated process. The activation energies are roughly 10 to 15 K and may be associated with vacancy motion.