Observation of the spontaneous vortex phase in the weakly ferromagnetic superconductor ErNi${}_2$B${}_2$C: A penetration depth study

Abstract

The coexistence of weak ferromagnetism and superconductivity in ErNi${}_2$BC suggests the possibility of a spontaneous vortex phase (SVP) in which vortices appear in the absence of an external field. We report evidence for the long-sought SVP from the in-plane magnetic penetration depth $\Delta \lambda (T)$ of high-quality single crystals of ErNi${}_2$B${}_2$C. In addition to expected features at the Néel temperature $T_N$ = 6.0 K and weak ferromagnetic onset at $T_{WFM}=2.3$K, $\Delta \lambda (T)$ rises to a maximum at $T_m=0.45$ K before dropping sharply down to $\sim$0.1 K. We assign the 0.45 K-maximum to the proliferation and freezing of spontaneous vortices. A model proposed by Koshelev and Vinokur explains the increasing $\Delta \lambda (T)$ as a consequence of increasing vortex density, and its subsequent decrease below $T_m$ as defect pinning suppresses vortex hopping.

5 pages including figures; added inset to Figure 2; significant revisions to text