We report the observation of positive magnetization on field cooling (PMFC) in low applied magnetic fields ($H⩽100$ Oe) in a single crystal of Ca${}_3$Rh${}_4$Sn${}_{13}$ near its superconducting transition temperature ($T_c\approx 8.35$ K). For 30 Oe $⩽H⩽100$ Oe, the PMFC response crosses over to a diamagnetic response as the temperature is lowered below 8 K. For 100 Oe $⩽H⩽300$ Oe, the diamagnetic response undergoes an unexpected reversal in its field dependence above a characteristic temperature (designated as $T_{\text{VL}}^{*}=7.9$ K), where the field-cooled cool-down magnetization curves intersect. The in-phase and out-of-phase ac susceptibility data confirm the change in the superconducting state across $T_{\text{VL}}^{*}$. We ascribe the PMFC response to a compression of magnetic flux caused by the nucleation of superconductivity at the surface of the sample. In very low fields ($H⩽20$ Oe), the PMFC response has an interesting oscillatory behavior, which persists up to about 7 K. The oscillatory nature underlines the interplay between competing responses contributing to the magnetization signal in the PMFC regime. We believe that the (i) counterintuitive field dependence of the diamagnetic response for $H⩾100$ Oe and above $T_{\text{VL}}^{*}$ (lasting up to $T_c$), (ii) the oscillatory character in the PMFC response at low fields, and (iii) the PMFC peaks near 8.2 K in 30 Oe $⩽H⩽100$ Oe provide support in favor of a theoretical scenario based on the Ginzburg-Landau equations. The scenario predicts the possibility of complex magnetic fluctuations associated with transformation between different metastable giant vortex states prior to transforming into the conventional vortex state as the sample is cooled below $T_{\text{VL}}^{*}$.

• Received 14 October 2010

DOI:https://doi.org/10.1103/PhysRevB.84.014501