Scaling up electrically synchronized spin torque oscillator networks

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

The emergence of exceptional points (EPs) in the parameter space of a non-hermitian (2D) eigenvalue problem has long been interest in mathematical physics, however, only in the last decade entered the scope of experiments. In coupled systems, EPs give rise to unique physical phenomena, and enable the development of highly sensitive sensors. Here, we demonstrate at room temperature the emergence of EPs in coupled spintronic nanoscale oscillators and exploit the system's non-hermiticity. We observe amplitude death of self-oscillations and other complex dynamics, and develop a linearized non-hermitian model of the coupled spintronic system, which describes the main experimental features. The room temperature operation, and CMOS compatibility of our spintronic nanoscale oscillators means that they are ready to be employed in a variety of applications, such as field, current or rotation sensors, radiofrequeny and wireless devices, and in dedicated neuromorphic computing hardware. Furthermore, 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 expanding to strongly nonlinear systems.

Robust Mutual Synchronization in Long Spin Hall Nano-oscillator Chains

Mutual synchronization of N serially connected spintronic nano-oscillators boosts their coherence by N and peak power by N². Increasing the number of synchronized nano-oscillators in chains holds significance for improved signal quality and emerging applications such as oscillator based unconventional computing. We successfully fabricate spin Hall nano-oscillator chains with up to 50 serially connected nanoconstrictions using W/NiFe, W/CoFeB/MgO, and NiFe/Pt stacks. Our experiments demonstrate robust and complete mutual synchronization of 21 nanoconstrictions at an operating frequency of 10 GHz, achieving line widths <134 kHz and quality factors >79,000. As the number of mutually synchronized oscillators increases, we observe a quadratic increase in peak power, resulting in 400-fold higher peak power in long chains compared to individual nanoconstrictions. While chains longer than 21 nanoconstrictions also achieve complete mutual synchronization, it is less robust, and their signal quality does not improve significantly, as they tend to break into partially synchronized states.

Mutual synchronization of spin-torque oscillators within a ring array

An array of spin torque nano-oscillators (STNOs), coupled by dipolar interaction and arranged on a ring, has been studied numerically and analytically. The phase patterns and locking ranges are extracted as a function of the number N, their separation, and the current density mismatch between selected subgroups of STNOs. If \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N\ge 6$$\end{document}N≥6 for identical current densities through all STNOs, two degenerated modes are identified an in-phase mode (all STNOs have the same phase) and a splay mode (the phase makes a 2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi$$\end{document}π turn along the ring). When inducing a current density mismatch between two subgroups, additional phase shifts occur. The locking range (maximum current density mismatch) of the in-phase mode is larger than the one for the splay mode and depends on the number N of STNOs on the ring as well as on the separation. These results can be used for the development of magnetic devices that are based on STNO arrays.

Electrically connected spin-torque oscillators array for 2.4 GHz WiFi band transmission and energy harvesting

The mutual synchronization of spin-torque oscillators (STOs) is critical for communication, energy harvesting and neuromorphic applications. Short range magnetic coupling-based synchronization has spatial restrictions (few µm), whereas the long-range electrical synchronization using vortex STOs has limited frequency responses in hundreds MHz (<500 MHz), restricting them for on-chip GHz-range applications. Here, we demonstrate electrical synchronization of four non-vortex uniformly-magnetized STOs using a single common current source in both parallel and series configurations at 2.4 GHz band, resolving the frequency-area quandary for designing STO based on-chip communication systems. Under injection locking, synchronized STOs demonstrate an excellent time-domain stability and substantially improved phase noise performance. By integrating the electrically connected eight STOs, we demonstrate the battery-free energy-harvesting system by utilizing the wireless radio-frequency energy to power electronic devices such as LEDs. Our results highlight the significance of electrical topology (series vs. parallel) while designing an on-chip STOs system.

Influence of flicker noise and nonlinearity on the frequency spectrum of spin torque nano-oscillators

The correlation of phase fluctuations in any type of oscillator fundamentally defines its spectral shape. However, in nonlinear oscillators, such as spin torque nano-oscillators, the frequency spectrum can become particularly complex. This is specifically true when not only considering thermal but also colored 1/f flicker noise processes, which are crucial in the context of the oscillator’s long term stability. In this study, we address the frequency spectrum of spin torque oscillators in the regime of large-amplitude steady oscillations experimentally and as well theoretically. We particularly take both thermal and flicker noise into account. We perform a series of measurements of the phase noise and the spectrum on spin torque vortex oscillators, notably varying the measurement time duration. Furthermore, we develop the modelling of thermal and flicker noise in Thiele equation based simulations. We also derive the complete phase variance in the framework of the nonlinear auto-oscillator theory and deduce the actual frequency spectrum. We investigate its dependence on the measurement time duration and compare with the experimental results. Long term stability is important in several of the recent applicative developments of spin torque oscillators. This study brings some insights on how to better address this issue.

Digital and analogue modulation and demodulation scheme using vortex-based spin torque nano-oscillators

In conventional communications systems, information is transmitted by modulating the frequency, amplitude or phase of the carrier signal, which often occurs in a binary fashion over a very narrow bandwidth. Recently, ultra-wideband signal transmission has gained interest for local communications in technologies such as autonomous local sensor networks and on-chip communications, which presents a challenge for conventional electronics. Spin-torque nano-oscillators (STNOs) have been studied as a potentially low power highly tunable frequency source, and in this report we expand on this to show how a specific dynamic phase present in vortex-based STNOs makes them also well suited as Wideband Analogue Dynamic Sensors (WADS). This multi-functionality of the STNOs is the basis of a new modulation and demodulation scheme, where nominally identical devices can be used to transmit information in both a digital or analogue manner, with the potential to allow the highly efficient transmittance of data.

Two-dimensional mutually synchronized spin Hall nano-oscillator arrays for neuromorphic computing

In spin Hall nano-oscillators (SHNOs), pure spin currents drive local regions of magnetic films and nanostructures into auto-oscillating precession. If such regions are placed in close proximity to each other they can interact and may mutually synchronize. Here, we demonstrate robust mutual synchronization of two-dimensional SHNO arrays ranging from 2 × 2 to 8 × 8 nano-constrictions, observed both electrically and using micro-Brillouin light scattering microscopy. On short time scales, where the auto-oscillation linewidth [Formula: see text] is governed by white noise, the signal quality factor, [Formula: see text], increases linearly with the number of mutually synchronized nano-constrictions (N), reaching 170,000 in the largest arrays. We also show that SHNO arrays exposed to two independently tuned microwave frequencies exhibit the same synchronization maps as can be used for neuromorphic vowel recognition. Our demonstrations may hence enable the use of SHNO arrays in two-dimensional oscillator networks for high-quality microwave signal generation and ultra-fast neuromorphic computing.

Investigation of room temperature ferromagnetism in transition metal doped BiFeO3

Spintronic functionality in ferromagnetic materials is a next-generation technique, to be used in data storage, high-frequency communications, and logic devices with minimum energy consumption. Ultra-low energy consumption in high-speed logic devices can be envisioned by inducing ferromagnetic behavior into room temperature multiferroic materials. However, there is a scarcity of room temperature multiferroic materials which have a definite spin degree of freedom. To fully exploit these technological challenges, we introduce the induced ferromagnetism in bismuth ferrite (BiFeO₃, BFO) by doping transition metal (Cr, Ni, Co) elements. Our investigation initiates with the experimental study on chemically synthesized BiFe_(1-x)M _x O₃ samples where x  =  0.0625 (6.25%) and M  =  Cr, Ni and Co. Experimental findings are verified by theoretical simulation using density functional theory (DFT  +  U) and gauge including projector augmented wave (GIPAW) based calculation. All the experimental studies are done at room temperature while the theoretical verification using DFT is carried to understand the underlying mechanism behind the magnetic behavior of doped BiFeO₃. It is done by optimizing the structural parameters comparable to the room temperature values. Microstructural and magnetic properties are studied using x-ray diffraction (XRD), transmission electron microscopy (TEM) and Vibrating sample magnetometer (VSM). All these experimental studies confirm the structural changes and induced ferromagnetism with doping. X-ray photoelectron spectroscopy (XPS) verified the reason behind this ferromagnetic property on the basis of oxygen vacancy content. Electron paramagnetic resonance (EPR) spectroscopy shows the tuning of Δg values due to enhanced magnetization. The density of states (DOS) calculations were performed on BFO (band-gap 1.89 eV) after structural optimization using DFT  +  U method, confirm our experimental findings. Magnetic moment values change drastically with doping elements (M), i.e. almost negligible for BFO (antiferromagnetic) to maximum (2.85 μ _B/f.u.) for Ni-doped sample. We also compute the EPR g-tensor using GIPAW method to confirm the tuning of Δg values due to enhanced magnetization. These results can highlight the impact and importance of suitable transition element doping to induce the room temperature ferromagnetism in BiFeO₃.