Measurement of the current-phase relation of superconductor/ferromagnet/superconductor $\pi$ Josephson junctions

We present measurements of the current-phase relation (CPR) of superconductor-ferromagnet-superconductor (SFS) Josephson junctions as a function of temperature. The CPR is determined by incorporating the junction into a superconducting loop coupled to a dc SQUID, allowing measurement of the junction phase difference. We find that the critical current of $\mathrm{Nb}\text{−}{\mathrm{Cu}}_{0.47}{\mathrm{Ni}}_{0.53}\text{−}\mathrm{Nb}$ Josephson junctions with barrier thickness $\sim 22\mathrm{nm}$ changes sign at $T<T_{\pi }\sim 2–4\mathrm{K}$, indicating that the junction becomes a $\pi$ Josephson junction. We find no evidence for second-order Josephson tunneling near $T_{\pi }$ in the CPR predicted by several theories.

Figure 1

(a) Current vs voltage for a Nb-CuNi-Nb Josephson junction measured at $T=1.4\mathrm{K}$. (b) Variation of the critical current with temperature showing re-entrance at $T\approx 2.7\mathrm{K}$ characteristic of a transition into a $\pi$ junction state.

Figure 2

(a) Circuit for measuring the current-phase relations of a SFS junction. (b) Magnetic flux $\Phi$ in the rf SQUID loop vs applied current $I$ showing a transition from hysteretic to nonhysteretic curves as $\mid I_c\mid$ drops. Curves offset for clarity.

Figure 3

Modulation of the magnetic flux in the rf SQUID loop as a function of current applied across the SFS junction for a series of temperatures. As the temperature is lowered, the critical current vanishes at $T=3.59\mathrm{K}$, below which the modulation shifts phase by $\pi$. Curves offset for clarity.

Figure 4

Current-phase relation derived from the rf SQUID modulation curves of Fig. 3 showing the transition to a $\pi$ Josephson junction as the temperature is lowered.

Figure 5

Variation of $I_c$ and $I_{c2}$, the $\sin \varphi$ and $\sin \left(2\varphi \right)$ components of the Josephson critical current, with temperature, showing the sign change in $I_c$ and absence of a significant $I_{c2}$.