Critical fields and the spontaneous vortex state in the weakly ferromagnetic superconductor RuSr2GdCu2O8

A spontaneous vortex state (SVS) between 30 and 56 K was observed for the weak-ferromagnetic superconductor RuSr2GdCu2O8 with the ferromagnetic Curie temperature TC=131K and the superconducting transition temperature Tc=56K. The low-field (±20G) super-conducting hysteresis loop indicates a narrow Meissner state region within the average lower critical field Bc1(T)=Bc1(0)[1-(TT0)2], with average Bc1ave(0)=12G and T0=30K. Full Meissner shielding signal in very low applied field indicates an ab plane Bc1ab(0)∼4G with an estimated anisotropic parameter γ∼7 for this layered system. The existence of a spontaneous vortex state between 30 and 56 K is the result of weak-ferromagnetic order with a net spontaneous magnetic moment of ∼0.1μBRu, which generates a weak magnetic dipole field around 10 G in the CuO2 bilayers. The upper critical field Bc2 varies linearly as (1-TTc) up to 7-T field. The vortex melting line Bm varies as (1-TTm)3.5 with melting transition temperature Tm=39K and a very broad vortex liquid region due to the coexistence and the interplay between superconductivity and weak-ferromagnetic order.