Signatures of a long-range spin-triplet component in an Andreev interferometer

We analyze the Josephson $I_J$ and dissipative $I_{\text{dis}}$ currents in a magnetic Andreev interferometer in the presence of the long-range spin triplet component (LRSTC). The Andreev interferometer has a crosslike geometry and consists of a ${\mathrm{SF}}_l\text{−}\mathrm{F}\text{−}{\mathrm{F}}_r\mathrm{S}$ circuit and perpendicular to it a N-F-N circuit, where S, ${\mathrm{F}}_{l,r}$ are superconductors and weak ferromagnets with noncollinear magnetizations ${\mathbf{M}}_{l,r}$, and F is a ferromagnet with a high exchange energy. The ferromagnetic wire F can be replaced with a nonmagnetic wire n. In the limit of a weak proximity effect (PE), we obtain simple analytical expressions for the currents $I_J=I_c(\alpha ,\beta )sin\phi$ and $I_{\text{dis}}=I_V(\alpha ,\beta )cos\phi$. In particular, the critical Josephson current in a long Josephson junction (JJ) is $I_c(\alpha ,\beta )=I_{c0}\chi (\alpha ,\beta )$, where the function $\chi (\alpha ,\beta )$ is a function of angles ${(\alpha ,\beta )}_{l,r}$ that characterize the orientations of ${\mathbf{M}}_{l,r}$. The oscillating part of the dissipative current $I_{\text{osc}}\left(V\right)=\chi (\alpha ,\beta )cos\phi I_{V0}\left(V\right)$ in the N-F/n-N circuit depends on the angles ${(\alpha ,\beta )}_{l,r}$ in the same way as the critical Josephson current $I_c(\alpha ,\beta )$ but can be much greater than the $I_c(\alpha ,\beta )$. At some angles the current $I_c(\alpha ,\beta )$ changes sign. We briefly discuss a relation between the negative current $I_c(\alpha ,\beta )$ and paramagnetic response. We argue that the measurements of the conductance in the N-F/n-N circuit can be used as another complementary method to identify the LRSTC in S/F heterostructures.

Figure 1

Schematic structure of the system under consideration. The current $I$ is the dissipative current in the N-F/n-N circuit.

Figure 2

The normalized amplitude of the oscillating part of the current $J_{\text{an}}={\mathcal{I}}_{\text{an}}(P_x,P_y,v,\lambda )/{\mathcal{I}}_{c,n}\left(P_x\right)$ as a function of the parameter $\lambda$ for $P_x=1$(black), and $P_x=2$(blue) with different scaling factors: $1*J_{\text{an}}\left(1\right)$ and $0.02*J_{\text{an}}\left(2\right)$. Other parameters are: $P_y=5$, $v=1$, where $P_x=L_x\sqrt{2T/D_x}$.

Figure 3

The same quantity as in Fig. 2 as a function of the dimensionless voltage $v=eV/2T$ for $P_x=1$ (black), $P_x=2$ (blue), and $P_x=3$ (red). The scaling factors are: $30*J_{\text{an}}\left(1\right)$, $1*J_{\text{an}}\left(2\right)$, and $0.03*J_{\text{an}}\left(3\right)$.

Figure 4

The normalized differential conductance $G_{\text{an}}$ vs the dimensionless voltage $v=eV/2T$ for the same parameters as in Fig. 3.

Figure 5

Comparison of the amplitude of oscillatory part of the current $J_{\text{an}}=0.23*{\mathcal{I}}_{\text{an}}\left(P_x\right)/{\mathcal{I}}_{c,n}\left(2\right)$ and the Josephson critical current $J_{\text{Jos}}={\mathcal{I}}_{c,n}\left(P_x\right)/{\mathcal{I}}_{c,n}\left(2\right)$ in S-n-S junction as functions of the parameter $P_x$. One can see that the phase-coherent part of the current in the N-F(n)-N circuit is much larger than the Josephson critical current $I_c$ in the S-n-S junction.

Figure 6

The ratio of the critical Josephson current in the system under consideration and in a S-n-S Josephson junction, $J_{\text{Jos}}={\mathcal{I}}_{\text{Jos}}(P_x,\lambda )/{\mathcal{I}}_{c,n}\left(P_x\right)$, with equal S/n or S/${\mathrm{F}}_{l,r}$ interface transparency as a function of the parameter $\lambda$ for $P_x=1$ (black) and $P_x=2$ (blue).