Nucleation of Vortex State in Ru-inclusion in Eutectic Ruthenium Oxide Sr2RuO4-Ru

Eutectic samples of Sr2RuO4-Ru possess many micrometer-sized Ru-metal inclusions. Based on a Ginzburg-Landau formulation we analyze the interplay of the chiral p-wave state of Sr2RuO4 (Tc = 1.5 K) and the s-wave state of Ru metal (Tc,Ru = 0.5 K) for an inclusion of cylindrical geometry. As a consequence of the mismatch of the order parameter phase, the occurrence of a spontaneous flux distribution appears for T < Tc,Ru which evolves into a "Josephson vortex" on the Sr2RuO4-Ru interface. At a sufficiently low temperature a depinning transition can occur whereby the vortex moves to the center of the cylinder.