Fig. 4: Signatures of skyrmion creep in the elastic properties.

a–d Field dependence of the resonance frequency F₁₆₅₄ at various current densities j, measured at temperatures T = 28.4 K, 28.2 K, 27.7 K and 27.1 K, respectively. The curves are vertically offset for clarity. The double arrow on the right side of each panel denotes the scale of the frequency shift. The accuracy of determining relative frequency shifts with our RUS setup is better than 0.01%²⁴ as denoted by the black bar in the upper left corner of the panels a–d. e F₁₆₅₄ − F_bkg as a function of H at 27.7 K, where F_bkg is the smooth background of F₁₆₅₄. ΔF is defined as the maximum of F₁₆₅₄ − F_bkg. f ΔF vs. j for 27.1, 27.7, 28.2, and 28.4 K. The solid lines are fits to Anderson–Kim model, \(\Delta F(j)-\Delta F(j=0)\propto \exp [\beta (j-{j}_{{\mathrm{c}}}^{* })/{k}_{{\mathrm{B}}}T]\), where β is material dependent a prefactor. In the Anderson–Kim model the local pinning potential vanishes linearly with current ΔU = \(\beta (j-{j}_{{\mathrm{c}}}^{* })\). The arrows marks the critical current density value \({j}_{c}^{* }\) = 62 kA/m² for 27.7 K to illustrate how critical current densities where determined. g ΔF as a function of T in the absence of current. h Temperature dependent \({j}_{{\mathrm{c}}}^{* }\) (blue line and symbols). The full symbols are measured with an ultrasonic excitation two times larger than that for the open symbols. The orange line and symbols are reproduced from ref. ¹³ and denote the onset of coherent linear skyrmion lattice motion as determined by the reeduction of the topological Hall effect (THE) under current.