Signatures of Long-Range Spin-Triplet Component in Andreev Interferometer

TL;DR

This paper investigates how long-range spin-triplet components influence Josephson and dissipative currents in a magnetic Andreev interferometer, revealing angle-dependent behaviors and proposing conductance measurements as a detection method.

Contribution

It provides analytical expressions for currents in a long Josephson junction considering the long-range spin-triplet component, highlighting the angle dependence and potential for experimental detection.

Findings

Critical Josephson current depends on magnetization angles.

Dissipative current oscillates with voltage and angle.

Negative critical current correlates with paramagnetic response.

Abstract

We analyze the Josephson,$I_{J}$, and dissipative,$I_{V}$, currents in a magnetic Andreev interferometer in the presence of the long-range spin triplet component (LRSTC). Andreev interferometer has a cross-like geometry and consists of a SF$_{l}$ - F - F$_{r}$S circuit and perpendicular to it a N - F - N circuit, where S, F$_{l,r}$ are superconductors and weak ferromagnets with non-collinear magnetisations $\mathbf{M}_{l,r}$, F is a strong ferromagnet with a high exchange energy. The ferromagnetic wire F can be replaced with a non-magnetic wire n. In the limit of a weak proximity effect (PE), we obtain simple analytical expressions for the currents $I_{J}$ and $I_{V}$. In particular, the critical Josephson current in a long Josephson junction (JJ) is $I_{c}(\alpha ,\beta )=I_{0c}\chi (\alpha ,\beta )$, 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 $I_{osc}(V)=\chi (\alpha ,\beta )\cos \varphi I_{0}(V)$ 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 $I_{c}$ and paramagnetic response. We argue that the measurements of the conductance in N - F(n) - N circuit can be used as another complementary method to identify the LRSTC in S/F heterostructures.