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$_{2}$B$% _{2}$C 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 N\'{e}el 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.