Shear modulus of solid $^3$He in the bcc and hcp phases

The shear modulus of solid hcp $^4$He decreases significantly at temperatures above 100 mK [1, 2]. This is due to to dislocations which are localized when pinned by $^3$He impurities at low temperature but become mobile when $^3$He impurities ``evaporate'' at high temperature. The unpinned dislocations move freely in the basal plane of the hcp structure. This produces anisotropic and extraordinarily large softening of the shear elastic constant C$_{44}$, an effect referred to as ``giant plasticity'' [2]. Previous measurements [3] on solid $^3$He showed similar shear modulus changes in the hcp phase but not in the bcc phase. Here, we report new shear modulus measurements in both the bcc and hcp phases.$^3$He. These show a similar shear modulus anomaly in the bcc phase, indicating that dislocation softening is not unique to hcp phase of helium. We compare our results for bcc and hcp $^3$He to those hcp $^4$He, and discuss the roles that lattice structure and quantum statistics play in dislocation motion and impurity pinning. \\[4pt] [1] J. Day and J. R. Beamish, Nature 450, 853 (2007).\\[0pt] [2] A. Haziot et al., Phys. Rev. Lett. 110, 035301 (2013). [3] J. T. West et al., Nature Physics 5, 598 (2009).