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

Abstract

We consider a Josephson junction with F 1 F 2 F 3 ferromagnetic trilayers in the ballistic regime, where the magnetization in each ferromagnet 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 ∆ϕ. With our generalised theoretical and numerical techniques, we are able to study the planar spatial profiles and ∆ϕdependencies of the charge supercurrents, spin supercurrents, spin torques, and density of states for complex systems that are finite in two dimensions. A broad range of magnetization strengths of the central 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 F 1 F 2 F 3 has three orthogonal components, a supercurrent can flow at ∆ϕ = 0, and a strong second harmonic in the current-phase relation appears. Remarkably, 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 F 1 N F 3 counterparts. Additionally, for a broad range of exchange field strengths in the central ferromagnet F 2 , the ground state of the system can be tuned to an arbitrary phase difference ϕ 0 , e.g., by rotating the magnetization in the outer ferromagnet F 3 . For intermediate exchange field strengths in F 2 , a ϕ 0 state can arise that creates a superconducting diode effect, whereby ∆ϕ can be tuned to create a one-way dissipationless current flow. The spatial maps of the spin currents and effective magnetic moments reveal a long-ranged spin torque in the halfmetallic phase. Moreover, the density of states studies demonstrate the emergence of zero energy peaks for the mutually orthogonal magnetization configurations, which is strongest in the half-metallic phase. Our results suggest that this simple trilayer Josephson junction can be an excellent candidate for producing experimentally accessible signatures for long-ranged self-biased supercurrents, and supercurrent diode-effects.

Effect of Rashba and Dresselhaus spin–orbit coupling on supercurrent rectification and magnetochiral anisotropy of ballistic Josephson junctions

“…Very recent reports [30,31] have demonstrated the supercurrent diode effect in systems with valley-Zeeman SOI (where the rectification is driven by the out-of-plane field, as expected from theory [32]), in type II Dirac semimetal [33], or in magicangle twisted bilayer [34] or trilayer [35,36] graphene. In turn, such intriguing experimental evidences have stimulated a number of theoretical studies on non-reciprocal supercurrent in exotic systems [36][37][38][39][40][41][42]. As discussed in our previous work [27], in JJs with Rashba SOI, the supercurrent diode effect is strictly related to the ϕ 0 shift discussed above.…”

Theory of zero-field superconducting diode effect in twisted trilayer graphene

“…This feature has elicited fundamental theoretical and experimental studies to uncover the underlying mechanisms. To this end, recent reports of the superconducting diode effect-induced by magnetic field [2][3][4][5][6][7][8], magnetic proximity [8,9], or magnetic Josephson or tunnel junctions [10][11][12][13][14][15][16][17][18][19]-have emerged and attracted considerable attention. Excitingly, having nonreciprocity in common with the semiconductor, yet boasting zero resistance, superconducting diodes have potential as building blocks for future quantum electronics.…”