Non-hermiticity in spintronics: oscillation death in coupled spintronic nano-oscillators through emerging exceptional points

Abstract

The emergence of exceptional points (EPs) in the parameter space of a non-hermitian (2D) eigenvalue problem is studied in a general sense in mathematical physics, and has in the last decade successively reached the scope of experiments. In coupled systems, it gives rise to unique physical phenomena, which enable novel approaches for the development of seminal types of highly sensitive sensors. Here, we demonstrate at room temperature the emergence of EPs in coupled spintronic nanoscale oscillators and hence exploit the system’s non-hermiticity. We describe the observation of amplitude death of self-oscillations and other complex dynamics, and develop a linearized non-hermitian model of the coupled spintronic system, which properly describes the main experimental features. Interestingly, these spintronic nanoscale oscillators are deployment-ready in different applicational technologies, such as field, current or rotation sensors, radiofrequeny and wireless devices and, more recently, novel neuromorphic hardware solutions. Their unique and versatile properties, notably their large nonlinear behavior, open up unprecedented perspectives in experiments as well as in theory on the physics of exceptional points. Furthermore, the exploitation of EPs in spintronics devises a new paradigm for ultrasensitive nanoscale sensors and the implementation of complex dynamics in the framework of non-conventional computing.

Spin wave-driven variable-phase mutual synchronization in spin Hall nano-oscillators

“…The W/CoFeB/MgO nano-constrictions start out in a non-synchronized state (Region I), synchronize from about 0.55 mA to 0.68 mA (Region II), show almost no signal from 0.68 mA to 0.76 mA (Region III), and appear to synchronize again above 0.76 mA (Region IV). In contrast, the [49][50][51]. However, a faint residue of a single microwave signal can still be observed in Region III, which rules out oscillation death and is instead consistent with an out-of-phase, but not strictly anti-phase, mutually synchronized state.…”

Parity‐Time Symmetry in Magnetic Materials and Devices

“…[113] The PT-symmetry in magnetic nanodevices has been demonstrated to control two coupled spin torque nano-oscillators (STNOs). [114] As potential nextgeneration microwave signal generators, [115,116] STNOs are very suitable for studying the EPs since they have both the loss related to magnetic damping and the gain provided by the spin torque effect during the spin-polarized current injection. [117,118] Wittrock et al studied the collective dynamic behavior of the two coupled STNO, whose magnetizations are in a dynamic vortex state and referred to as STVOs (spin-torque vortex oscillators).…”

“…STNOs are well-suited for studying coupled non-Hermitian magnetic systems since STNOs possess two crucial attributes of magnetic loss and gain generated by the spin-polarized current injection. [113,114] In recent years, there have been advances in realizing higher-order network systems using STNOs. [117] The STNOs exhibit a nonlinear perturbation response to the external magnetic environment, which holds significance in the development of arrayed high-order EP devices with nonlinear sensing capabilities.…”

Current driven instabilities and non-linearities in magnetic systems.

“…Finally, we hope that our work, together with that of Deng et al [152], inspires the operation of STOs near EPs. In fact, while resubmitting this work a recent preprint appeared [158] which has experimentally observed EPs in STOs, albeit in a set-up that is slightly different from ours. acknowledgements J.S.H.…”