Triplet supercurrent due to spin-active zones in a Josephson junction

Motivated by a recent experiment evidencing triplet superconductivity in a ferromagnetic Josephson junction with a ${\text{Cu}}_2\text{MnAl}$-Heusler barrier, we construct a theoretical model accounting for this observation. The key ingredients in our model which generate the triplet supercurrent are spin-active zones, characterized by an effective canted interface magnetic moment. Using a numerical solution of the quasiclassical equations of superconductivity with spin-active boundary conditions, we find qualitatively very good agreement with the experimentally observed supercurrent. Further experimental implications of the spin-active zones are discussed.

Figure 1

(Color online) The model employed for a Josephson junction with a ferromagnetic Heusler ${\text{Cu}}_2\text{MnAl}$ barrier. The junction width is $L$, and we take into account a canted magnetization texture near the interfaces with misalignment angles ${\alpha }_{L,R}$ relative the bulk magnetization. These spin-active zones generate a long-range supercurrent.

Figure 2

(Color online) Plot of the critical current density vs the junction width $L$. Triangles (black) represent results for the case $\alpha =0$, i.e., no canted interface moments. Squares (red) represent results for misalignment angle $\alpha$ given by Eq. (6). We have set ${\alpha }_L={\alpha }_R$ with ${\alpha }_0=\pi /4$ and ${\gamma }_{\varphi }^{l,r}=15$. Assuming a superconducting coherence length of $\xi \simeq 14\text{nm}$ in dirty Nb (Ref. 19), we use $L_c/\xi =0.76$ to obtain the sharp drop-off near $L=10.5\text{nm}$ as in Ref. 12. Inset: zoom-out version of the current density.

Figure 3

(Color online) Plot of the critical current density vs temperature. To make contact with the experiment in Ref. 12 where $T_c\simeq 8\text{K}$, we normalize the current to its value at $T/T_c=0.25$. The rest of the parameters are as in Fig. 2.

Figure 4

(Color online) Plot of the critical current density vs the misalignment angle $\alpha$ in the spin-active zones. In (a), we set ${\alpha }_L={\alpha }_R$ while in (b) ${\alpha }_L=-{\alpha }_R$. From top to bottom at $\alpha =\pi /2$, the curves correspond to thicknesses $d_F/\xi =\left\{0.60,0.62,0.64,0.66,0.68,0.70\right\}$.