Intrinsic spin–orbit interaction in ferromagnet/superconductor hybrid nanostructures: Unveiling the role in triplet generation and critical temperature modulation

Abstract

Recent theoretical advancements propose an innovative approach to induce triplet generation beyond the conventional inhomogeneous magnetic field-driven singlet–triplet conversion. Here, we investigate a hybrid nanostructure comprising a conventional BCS superconductor proximitized with a homogeneous ferromagnet possessing intrinsic spin–orbit coupling arising from broken symmetries due to lattice mismatch at the interface. Through extensive simulations, we explore the impact of spin–orbit interaction on the critical temperature, revealing the pivotal role played by the in-plane component of the magnetic exchange field and the dimensional characteristics of the hybrid system in singlet–triplet conversion. Remarkably, our findings demonstrate that a single homogeneous ferromagnet with intrinsic spin–orbit coupling governs triplet generation and exhibits a spin valve effect. Notably, we quantify our observations through the superconducting critical temperature ($T_c$), showcasing a spin-valve like functionality dependent on the orientation of magnetization. Moreover, we observe a significant reduction in the critical temperature of the hybrid structure, even reaching zero under specific dimensions, attributed to the controlled generation and regulation of spin-1 triplets. Crucially, our investigation also validates the notion of the mechanism where a $\frac{\pi }{2}$ rotation of the in-plane magnetic exchange field toggles superconductivity, offering a promising avenue for actively controlling triplet generation—a pivotal step towards high-performance storage devices in emerging superconducting spintronics applications.