Sin(2$\phi )$ component in the current-phase relation of SFS Josephson junctions near the 0-$\pi $ transition

We directly determined the Josephson current-phase relation (CPR) of superconductor-ferromagnet-superconductor (SFS) junctions by rf-SQUID interferometry, and corroborated it with measurements of the critical current as a function of temperature and magnetic field and rf-induced Shapiro steps in the current-voltage characteristics. Our Nb-Cu$_{47}$Ni$_{53}$-Nb trilayer junctions, with 2x2$\mu $m$^{2}$ area and 7nm CuNi thickness, show a transition with temperature from the usual Josephson 0-junction state to a $\pi $-junction state, defined by a phase difference of $\pi $ in the ground state, at temperatures between 1.5K and 3.5K. Near the transition, we observe second harmonics in the CPR, deviations from the usual Fraunhofer diffraction pattern and half-integer Shapiro steps, all consistent with a sin(2$\phi )$ component in the CPR.