Recently, we have observed the so-called devil’s staircase of high-order facets on the surface of hcp ${}^4$He crystals at 0.2 K. Such high roughening temperatures of high-order facets belonging to the $\left[10\overline{1}N\right]$ family suggest that there must be an anomaly in the stiffness of vicinal surfaces and of the step on the basal $c$ facet at the corresponding orientation. We were able to measure the stiffness of the step on the [0001] $c$ facet and the azimuthal stiffness of vicinal surfaces at small polar angles. We have found a strong anisotropy of the stiffnesses at low temperatures, as high as 5–10. The anisotropy rapidly decreases as temperature increases and saturates at low temperatures, in good agreement with the theory of renormalization by thermal fluctuations of the surface. The observed anomaly in the surface stiffness can explain the presence of high-order facets.

• Received 23 May 2011

DOI:https://doi.org/10.1103/PhysRevB.84.075132