We study the current tunable microwave signal properties of nano-constriction based spin Hall nano-oscillators (SHNOs) in oblique magnetic fields as a function of the nano-constriction width, $w=$~50--140 nm. The threshold current is found to scale linearly with $w$, defining a constant threshold current density of $J_{th}=$ 1.7 $\times$ 10$^{8}$ A/cm$^2$. While the current dependence of the microwave frequency shows the same generic non-monotonic behavior for all $w\geqslant$ 80 nm, the quality of the generated microwave signal improves strongly with $w$, showing a linear $w$ dependence for both the total power and the linewidth. As a consequence, the peak power for a 140 nm nano-constriction is about an order of magnitude higher than that of a 80 nm nano-constriction. The smallest nano-constriction, $w=$ 50 nm, exhibits a different behavior with a higher power and a worse linewidth indicating a crossover into a qualitatively different narrow-constriction regime.
Artificial Neural Network (ANN) -- Oscillatory Neural Network (ONN) Hybrid System Using Domain-Wall Synapse Devices and Nano-Constriction Spin Hall Nano Oscillators
Indian Institute of Technology Bombay（印度理工学院孟买分校）；Centre for Semiconductor Technologies (SemiX), Indian Institute of Technology Bombay（印度理工学院半导体技术中心 (SemiX)）
We study mutual synchronization in double nanoconstriction-based spin Hall nano-oscillators (SHNOs) under weak in-plane fields ($μ_0H_\mathrm{IP}$ = 30-40 mT) and also investigate its angular dependence. We compare SHNOs with different nano-constriction spacings of 300 and 900 nm. In all devices, mutual synchronization occurs below a certain critical angle, which is higher for the 300 nm spacing than for the 900 nm spacing, reflecting the stronger coupling at shorter distances. Alongside the synchronization, we observe a strong second harmonic consistent with predictions that the synchronizati…
Under the application of electrical currents, metal nanocrystals inside carbon nanotubes can be bodily transported. We examine experimentally and theoretically how an iron nanocrystal can pass through a constriction in the carbon nanotube with a smaller cross-sectional area than the nanocrystal itself. Remarkably, through in situ transmission electron imaging and diffraction, we find that, while passing through a constriction, the nanocrystal remains largely solid and crystalline and the carbon nanotube is unaffected. We account for this behavior by a pattern of iron atom motion and rearrangem…
An indirect exciton is a bound state of an electron and a hole in spatially separated layers. Two-dimensional indirect excitons can be created optically in heterostructures containing double quantum wells or atomically thin semiconductors. We study theoretically transmission of such bosonic quasiparticles through nano-constrictions. We show that quantum transport phenomena, e.g., conductance quantization, single-slit diffraction, two-slit interference, and the Talbot effect, are experimentally realizable in systems of indirect excitons. We discuss similarities and differences between these phe…
Spin Hall nano-oscillators (SHNOs) utilize pure spin currents to 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 sometimes mutually synchronize, in pairs or in short linear chains. Here we demonstrate robust mutual synchronization of two-dimensional SHNO arrays ranging from 2 x 2 to 8 x 8 nano-constrictions, observed both electrically and using micro-Brillouin Light Scattering microscopy. The signal quality factor, $Q=f/Δf$, increases linearly with number of mutually syn…
We demonstrate a combined frequency and time domain investigation of injection-locked, constriction-based spin Hall nano-oscillators by Brillouin light scattering (BLS) and time-resolved magneto-optical Kerr effect (TR-MOKE). This was achieved by applying an alternating current in the GHz regime in addition to the direct current which drives auto-oscillations in the constriction. In the frequency domain, we analyze the width of the locking range, the increase in intensity and reduction in linewidth as a function of the applied direct current. Then we show that the injection locking of the auto…
We use micromagnetic simulations to map out and compare, the linear and auto-oscillating modes in constriction-based spin Hall nano-oscillators as a function of applied magnetic field with varying magnitude and out-of-plane angle. We demonstrate that for all possible applied field configurations the auto-oscillations emerge from the localized linear modes of the constriction. For field directions tending towards the plane, these modes are of the so-called "edge" type, i.e. localized at the opposite sides of the constriction. When the magnetization direction instead approaches the film normal, …
Helium-ion beams (HIB) focused to sub-nanometer scales have emerged as powerful tools for high-resolution imaging as well as nano-scale lithography, ion milling or deposition. Quantifying irradiation effects is essential for reliable device fabrication but most of the depth profiling information is provided by computer simulations rather than experiment. Here, we use atomic force microscopy (AFM) combined with scanning near-field optical microscopy (SNOM) to provide three-dimensional (3D) dielectric characterization of high-temperature superconductor devices fabricated by HIB. By imaging the i…
We experimentally study the auto-oscillating spin-wave modes in NiFe/$β-$W constriction-based spin Hall nano-oscillators as a function of bias current, in-plane applied field strength, and azimuthal field angle, in the low-field range of 40-80 mT. We observe two different spin-wave modes: i) a linear-like mode confined to the minima of the internal field near the edges of the nanoconstriction, with weak frequency dependencies on the bias current and the applied field angle, and ii) a second, lower frequency mode that has significantly higher threshold current and stronger frequency dependencie…
We present electron transport measurements on lithographically defined and etched graphene nanoconstrictions with different aspect ratios including different lengths (L) and widths (W). A roughly length-independent disorder induced effective energy gap can be observed around the charge neutrality point. This energy gap scales inversely with the width even in regimes where the length of the constriction is smaller than its width (L<W). In very short constrictions, we observe both resonances due to localized states or charged islands and an elevated overall conductance level (0.1-1e2/h), which i…
Ising Machines (IMs) are physical systems designed to find solutions to combinatorial optimization (CO) problems mapped onto the IM via the coupling strengths of its binary spins. Using the intrinsic dynamics and different annealing schemes, the IM relaxes over time to its lowest energy state, which is the solution to the CO problem. IMs have been implemented in quantum, optical, and electronic hardware. One promising approach uses interacting nonlinear oscillators whose phases have been binarized through injection locking at twice their natural frequency. Here we demonstrate such Oscillator I…
We investigate the electrical switching of charge and spin transport in a topological insulator nanoconstriction in a four terminal device. The switch of the edge channels is caused by the coupling between edge states which overlap in the constriction and by the tunneling effects at the contacts and therefore can be manipulated by tuning the applied voltages on the split-gate or by geometrical etching. The switching mechanism can be conveniently studied by electron interferometry involving the measurements of the current in different configurations of the side gates, while the applied bias fro…
The resistance due to the convergence from bulk to a constriction, for example, a nanopore, is a mainstay of transport phenomena. In classical electrical conduction, Maxwell, and later Hall for ionic conduction, predicted this access or convergence resistance to be independent of the bulk dimensions and inversely dependent on the pore radius, $a$, for a perfectly circular pore. More generally, though, this resistance is contextual, it depends on the presence of functional groups/charges and fluctuations, as well as the (effective) constriction geometry/dimensions. Addressing the context generi…
The density of the transmission eigenvalues of Pb nano-contacts has been estimated recently in mechanically controllable break-junction experiments. Motivated by these experimental analyses, here we study the evolution of the density of the transmission eigenvalues with the disorder strength and the number of channels supported by the ballistic constriction of a quantum point contact in the framework of the Dorokhov-Mello-Pereyra-Kumar equation. We find that the transmission density evolves rapidly into the density in the diffusive metallic regime as the number of channels $N_c$ of the constri…
We investigate a W-Ta alloying route to reduce the auto-oscillation current densities and the power consumption of nano-constriction based spin Hall nano oscillators. Using spin-torque ferromagnetic resonance (ST-FMR) measurements on microbars of W$_{\text{100-x}}$Ta$_{\text{x}}$(5 nm)/CoFeB(t)/MgO stacks with t = 1.4, 1.8, and 2.0 nm, we measure a substantial improvement in both the spin-orbit torque efficiency and the spin Hall conductivity. We demonstrate a 34\% reduction in threshold auto-oscillation current density, which translates into a 64\% reduction in power consumption as compared t…
We present a self-contained study of the dynamics of oscillating nanomenisci anchored on nanometric topographical defects around a cylindrical nanofiber -- radius below 100 nm. Using frequency-modulation atomic force microscopy (FM-AFM), we show that the friction coefficient surges as the contact angle is decreased. We propose a theoretical model within the lubrification approximation that reproduces the experimental data and provides a comprehensive description of the dynamics of the nanomeniscus. The dissipation pattern in the vicinity of the contact line and the anchoring properties are dis…
With a view to optimising the design of carbon-nanotube (CNT) windmills and to maximising the internal magnetic field generated by chiral currents, we present analytical results for the group velocity components of an electron flux through chiral carbon nanotubes. Chiral currents are shown to exhibit a rich behaviour and can even change sign and oscillate as the energy of the electrons is increased. We find that the transverse velocity and associated angular momentum of electrons is a maximum for non-metallic CNTs with a chiral angle of 18$^o$. Such CNTs are therefore the optimal choice for CN…
Nano-constriction spin-Hall nano-oscillators (NC-SHNOs) are one of the most promising alternatives among the microwave spintronics devices. They can provide highly coherent and widely tuneable microwave signals and can be fabricated at low temperatures, which makes them compatible with back-end-of-the-line CMOS processing. For its applications, the frequency stability of each device is crucial, in particular for synchronization of oscillator arrays. In this work, we focus on the influence of a realistic grain structure on the SHNO frequency stability using both measurements as well as micromag…
We demonstrate that the synchronization of an array of electrically coupled spin torque nano-oscillators (STNO) modelled by Landau-Lifshitz-Gilbert-Slonczewski (LLGS) equation can be enhanced appreciably in the presence of a common external microwave magnetic field. The applied microwave magnetic field stabilizes and enhances the regions of synchronization in the parameter space of our analysis, where the oscillators are exhibiting synchronized oscillations thereby emitting improved microwave power. To characterize the synchronized oscillations we have calculated the locking range in the domai…
A method for the evaluation of the angular width of an electron beam generated by a nanoconstriction is proposed and demonstrated. The approach is based on analysis of a narrow-width electron flow, that quantizes into modes inside a confining constriction which is described in the adiabatic approximation, evolving into a freely propagating electronic state after exiting the constriction. The method that we developed allows us to find the parameters and the shape of the constriction that are optimal for generation of extremely narrow electron beams. In the case of a constriction characterized b…
We investigate the impact of localized laser heating on the auto-oscillation properties of a 170 nm wide nano-constriction spin Hall nano-oscillators (SHNO) fabricated from a NiFe/Pt bilayer on a sapphire substrate. A 532 nm continuous wave laser is focused down to a spot size of about 500 nm at a power ranging from 0 to 12 mW. Through a comparison with resistive heating, we estimate a local temperature rise of about 8 K/mW. We demonstrate reversible laser tuning of the threshold current, the frequency, and the peak power, and find that the SHNO frequency can be tuned by up to 350 MHz, which i…
We demonstrate an optimized fabrication process for electric field (voltage gate) controlled nano-constriction spin Hall nano-oscillators (SHNOs), achieving feature sizes of <30 nm with easy to handle ma-N 2401 e-beam lithography negative tone resist. For the nanoscopic voltage gates, we utilize a two-step tilted ion beam etching approach and through-hole encapsulation using 30 nm HfO<sub>x</sub>. The optimized tilted etching process reduces sidewalls by 75% compared to no tilting. Moreover, the HfO<sub>x</sub> encapsulation avoids any sidewall shunting and improves gate breakdown. Our experim…
We define superconducting constrictions by ploughing a deposited Aluminum film with a scanning probe microscope. The microscope tip is modified by electron beam deposition to form a nano-plough of diamond-like hardness, what allows the definition of highly transparent Josephson junctions. Additionally a dc-SQUID is fabricated to verify appropriate functioning of the junctions. The devices are easily integrated in mesoscopic devices as local radiation sources and can be used as tunable on-chip millimeter wave sources.
A spin-torque nano-oscillator (STNO) driven by a ramped bias current can perform spectrum analysis quickly over a wide frequency bandwidth. The STNO spectrum analyzer operates by injection locking to external microwave signals and produces an output DC voltage $V_{\rm dc}$ that temporally encodes the input spectrum. We found, via numerical analysis with a macrospin approximation, that an STNO is able to scan a $10~\rm GHz$ bandwidth in less than $100~\rm ns$ (scanning rate $R$ exceeds $100~\rm MHz/ns$). In contrast to conventional quadratic microwave detectors, the output voltage of the STNO a…
Ballistic transport through nanoscale devices with time-dependent Rashba-type spin-orbit interaction (SOI) can lead to spin-polarized wave packets that appear even for completely unpolarized input. The SOI that oscillates in a finite domain generates density and spin polarization fluctuations that leave the region as propagating waves. Particularly, spin polarization has space and time dependence even in regions without SOI. Our results are based on an analytic solution of the time-dependent Schrödinger equation. The relevant Floquet quasi-energies that are obtained appear in the energy spectr…
We study the pump current and noise properties in an adiabatically modulated magnetic nanowire with double domain walls (DW). The modulation is brought about by applying a slowly oscillating magnetic and electric fields with a controllable phase difference. The pumping mechanism resembles the case of the quantum dot pump with two-oscillating gates. The pump current, shot noise, and heat flow show peaks when the Fermi energy matches with the spin-split resonant levels localized between the DWs. The peak height of the pump current is an indicator for the lifetime of the spin-split quasistationar…
Direct observation of propagating spin waves in a spin-Hall nano-oscillator
University of Cambridge（剑桥大学）；University of Gothenburg（哥德堡大学）；Max-Planck-Institut für Festkörperforschung（马克斯·普朗克固体研究所）；Indian Institute of Technology Bhubaneswar（布巴内斯瓦尔印度理工学院）；Tohoku University（东北大学）；Max-Planck-Institut für Intelligente Systeme（马克斯·普朗克智能系统研究所）；Helmholtz-Zentrum Berlin für Materialien und Energie（柏林亥姆霍兹材料与能源中心）
In the recent years, a spin-valve was developed with a current-confined-path structure consisting of a non-oxide-layer (NOL). We analyze magnetic structures of the current-confinedpath in the nano-oxide layer sandwiched between ferromagnetic electrodes and clarify the dependency of the magnetic structure on the shape and size of the current-confined-path. Our results of stiffness energy density and thermal stability shows that we should fabricate a CPP spin-valve with narrow current-confinedpaths with large aspect ratio and strong constriction in order to enhance the MR ratio.
In this work, we develop a nanoscale magnetic field sensor based on a spin-Hall nano-oscillator (SHNO) device. We fabricate constriction-based SHNO devices using Ni$_{81}$Fe$_{19}$/Au$_{0.25}$Pt$_{0.75}$ bilayer and use them to demonstrate quasi-DC sensing up to kilohertz-scale frequencies under a bias field of 400 Oe in the sample plane. The magnetic field sensing is based on the linear dependence of SHNO oscillation frequency on external magnetic field. The detectivity of the sensor is as low as 0.21 $μ$T/$\sqrt{\mbox{Hz}}$ at 100 Hz, with an effective sensing area of 0.32 $μ$m$^2$, making S…
Spin dependent electron transport measurements on graphene are of high importance to explore possible spintronic applications. Up to date all spin transport experiments on graphene were done in a semi-classical regime, disregarding quantum transport properties such as phase coherence and interference. Here we show that in a quantum coherent graphene nanostructure the non-local voltage is strongly modulated. Using non-local measurements, we separate the signal in spin dependent and spin independent contributions. We show that the spin dependent contribution is about two orders of magnitude larg…
A novel method and nanodevice are introduced that allows to rotate the single electron spin confined in a gated electrostatic InSb nanowire quantum dot. Proposed method does not require application of any (oscillating or static) external magnetic fields. Our proposal instead employs spatial and time modulation of confining potential induced by electric gates, which, in turn leads to oscillating Rashba type spin-orbit coupling. Moving electron back and forth in such a variable Rashba field allows for realization of spin rotations around two different axes separately without using an external ma…
We propose to use oscillating spin currents with slowly varying frequency (chirp) to manipulate and control the magnetization dynamics in a nanomagnet. By recasting the Landau-Lifshitz-Slonczewski equation in a quantum-like two-level formalism, we show that a chirped spin current polarized in the direction normal to the anisotropy axis can induce a stable precession of the magnetic moment at any angle (up to $90^\circ$) with respect to the anisotropy axis. The drive current can be modest ($10^6\,\rm A/cm^2$ or lower) provided the chirp rate is sufficiently slow. The induced precession is stabl…
Electric weak links, the term used for those parts of an electrical circuit that provide most of the resistance against the flow of an electrical current, are important elements of many nanodevices. Quantum dots, nanowires and nano-constrictions that bridge two bulk conductors (or superconductors) are examples of such weak links. Here we consider nanostructures where the electronic spin-orbit interaction is strong in the weak link but is unimportant in the bulk conductors, and explore theoretically the role of the spin-orbit active weak link (which we call a "Rashba spin splitter") as a source…
A theoretical and experimental description of the threshold, amplitude, and stability of a self-oscillating nanowire in a field emission configuration is presented. Two thresholds for the onset of self-oscillation are identified, one induced by fluctuations of the electromagnetic environment and a second revealed by these fluctuations by measuring the probability density function of the current. The ac and dc components of the current and the phase stability are quantified. An ac to dc ratio above 100% and an Allan deviation of 1.3x10-5 at room temperature can be attained. Finally, it is shown…
We study the impact of spin wave damping ($α$) on the auto-oscillation properties of nano-constriction based spin Hall nano-oscillators (SHNOs). The SHNOs are based on a 5 nm Pt layer interfaced to a 5 nm Py$_{100-x-y}$Pt$_{x}$Ag$_{y}$ magnetic layer, where the Pt and Ag contents are co-varied to keep the saturation magnetization constant (within 10 %), while $α$ varies close to a factor of three. We systematically investigate the influence of the Gilbert damping on the magnetodynamics of these SHNOs by means of electrical microwave measurements. Under the condition of a constant field, the th…
We study scanning gate microscopy (SGM) conductance mapping of a $\mathrm{MoS}_2$ zigzag ribbon exploiting tight-binding and continuum models. We show that, even though the edge modes of a pristine nanoribbon are robust to backscattering on the potential induced by the tip, the conductance mapping reveals presence of both the edge modes and the quantized spin- and valley-current carrying modes. By inspecting the electron flow from a split gate quantum point contact (QPC) we find that the mapped current flow allows to determine the nature of the quantization in the QPC as spin-orbit coupling st…
We show how the charge input signal applied to the gate electrode in a double and triple quantum dot may be converted to a pulse in the Kondo cotunneling current being a spin response of a nano-device under a strong Coulomb blockade. The stochastic component of the input signal results in the infrared cutoff of Kondo transmission. The stochastization of the orbital component of the Kondo effect in triple quantum dots results in a noise-induced SU(4) - SU(2) quantum transition.
