Superharmonic Josephson relation at $0\text{−}∕\pi$-junction transition

Critical current was recently measured near the transition from 0 to $\pi$-contact in superconductor/ferromagnet/superconductor Josephson junctions. Contrary to expectations, it does not vanish at the transition point. It shows instead a tiny, though finite, minimum. The observation of fractional Shapiro steps reenforces the idea that the vanishing of the main sinusoidal term in the Josephson relation gives room to the next harmonics. Within the quasiclassical approach we calculate the Josephson relation while taking into account the magnetic scattering. We find that the observed minimum is compatible with the value of the second harmonics expected from the theory.

Figure 1

(Color online) Fit to experimental data for the critical current of Ref. 13 (boxes), for the three solutions reported in the table of the isotropic model. The three solutions give nearly indistinguishable curves. Inset: temperature dependence near $T^{*}$ of the calculated $I_c={\max }_{\varphi }\left[\mid I\left(\varphi \right)\mid \right]$, $I_1$ (dashed), and $I_2$ (dotted), for the first solution. The minimum of $I_c$ coincides with $I_2$.

Figure 2

(Color online) Length dependence at $T=4.2\mathrm{K}$ of $I_c$ (full line) and $I_2$ (dashed line) for the parameters obtained with the fit to the isotropic model. We show the solution 1 (upper panel) and 2 (lower panel). The zero at $L=17\mathrm{nm}$ is visible in both cases. Solution 2 displays a second zero for $L<17\mathrm{nm}$.