Supercurrent Diode Effect, Spin Torques, and Robust Zero-Energy Peak in Planar Half-Metallic Trilayers

TL;DR

This paper investigates a Josephson junction with ferromagnetic trilayers, revealing how magnetization configurations and strengths induce supercurrent flow, higher harmonics, phase control, diode effects, and zero-energy peaks, especially in the half-metallic phase.

Contribution

It introduces a comprehensive analysis of supercurrent behavior in ferromagnetic trilayers with arbitrary magnetizations, highlighting the emergence of supercurrent at zero phase difference and controllable phase states.

Findings

Supercurrent can flow at zero phase difference with orthogonal magnetizations.

Critical supercurrent is maximized in the half-metallic limit.

Zero-energy peaks are observed in the density of states for orthogonal magnetizations.

Abstract

We consider a Josephson junction with ${\rm F_1 F_2 F_3}$ ferromagnetic trilayers in the ballistic regime, where the magnetization in each ferromagnet ${\rm F}_i (i=1,2,3)$, can have arbitrary orientations and magnetization strengths. The trilayers are sandwiched between two $s$-wave superconductors with a macroscopic phase difference $\Delta \varphi$. A broad range of magnetization strengths of the central $\rm F_2$ layer are considered, from an unpolarized normal metal (N) to a half-metallic phase, supporting only one spin species. Our results reveal that when the magnetization configuration in ${\rm F_1 F_2 F_3}$ has three orthogonal components, a supercurrent can flow at $\Delta \varphi=0$, and a strong second harmonic in the current-phase relation appears. Upon increasing the magnetization strength in the central ferromagnet layer up to the half-metallic limit, the self-biased current and second harmonic component become dramatically enhanced, and the critical supercurrent reaches its maximum value. The higher harmonics in the current-phase relations can be controlled by the relative magnetization orientations, with negligible current damping compared to the corresponding ${\rm F_1 N F_3}$ counterparts. For a broad range of exchange field strengths in the central ferromagnet ${\rm F}_2$, the ground state of the system can be tuned to an arbitrary phase difference $\varphi_0$ by rotating the magnetization in the outer ferromagnet $\rm F_3$. For intermediate exchange field strengths in ${\rm F}_2$, a $\varphi_0$ state can arise that creates a superconducting diode effect, whereby $\Delta\varphi$ can be tuned to create a one-way dissipationless current flow. The density of states demonstrates the emergence of zero energy peaks for the mutually orthogonal magnetization configurations, which is strongest in the half-metallic phase.