United States

Understanding how spin currents flow across metal-semiconductor interfaces at femtosecond timescales has impacts on ultrafast spintronics, data processing and storage applications. However, the possibility to directly access the propagation of spin currents on these time scales has been hampered by the simultaneous lack of both ultrafast site selective magnetic sensitive probes and tailored metal-semiconductor interfaces. By means of FEL-based core-resonant Kerr spectroscopy, we report direct experimental evidence of spin currents across a Ni/Si interface in terms of different magnetodynamics at the Ni M&lt;sub&gt;2,3&lt;/sub&gt; and Si L&lt;sub&gt;2,3&lt;/sub&gt; absorption edges. This further allows us to extract the propagation velocity of the spin current in Si as 0.2 nm/fs.

![](https://assets.underline.io/uploads/markdown_image/1/image/ba4eb9360a1db64b8e33f4c491757403.jpg)

Fig. 1: a) The sample stack consists of a Si substrate (blue), a thin Si3N4 passivation layer (grey), 7 nm of Ni film (red) and 2 nm of Ag capping layer (yellow). The white arrow represents the in-plane magnetization of the Ni film. The FEL pulses at the Si L2,3 edge (blue arrow) and at the Ni M2,3 edge (red arrow) are also depicted. The IR laser pulses at 1.55 eV hit the sample at a time delay t-t0, before the FEL pulses arrival. The penetration depths of the pump and the probes are represented by the length of the arrows. The fraction of the IR laser energy absorbed by each layer is reported above the probe arrow. b) Scheme of the FEL RMOKE set-up at MagneDyn. RMOKE was probed in longitudinal configuration at an angle of incidence of 45°. The polarization ε of the incoming FEL pulses (blue arrow) is in the scattering plane, while the Kerr rotation of the polarization of the reflected pulse is indicated as θ.

![](https://assets.underline.io/uploads/markdown_image/1/image/388e11ba365f236752de3629d9784f15.jpg)

Fig. 2: RMOKE magnetic hysteresis in degrees of Kerr rotation at the Ni M2,3 edge (a) and at the Si L2,3 edge (b). Empty and filled circles curves represent the unpumped and pumped hysteresis after 0.5 ps (Ni) and 0.3 ps (Si) (colored star markers in c). c) relative change of the site resolved magnetization M (Ni - red and Si - blue dots) as a function of time delay measured in saturation at 550 mT. The solid lines represent the tting results, from which we extract the characteristic times for demagnetization and recovery. The difference (ΔM/M)js is also shown (gray pentagons).

2022 Joint MMM-INTERMAG

All-Optical Spin Injection in Silicon Revealed by Element Specific Time-Resolved Kerr Effect

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INTERMAG 2021

Understanding how spin currents flow across metal-semiconductor interfaces at femtosecond timescales has impacts on ultrafast spintronics, data processing and storage applications. However, the possibility to directly access the propagation of spin currents on these time scales has been hampered by the simultaneous lack of both ultrafast site selective magnetic sensitive probes and tailored metal-semiconductor interfaces. By means of FEL-based core-resonant Kerr spectroscopy, we report direct experimental evidence of spin currents across a Ni/Si interface in terms of different magnetodynamics at the Ni M2,3 and Si L2,3 absorption edges. This further allows us to extract the propagation velocity of the spin current in Si as 0.2 nm/fs.

![](https://assets.underline.io/uploads/markdown_image/1/image/ba4eb9360a1db64b8e33f4c491757403.jpg)

Fig. 1: a) The sample stack consists of a Si substrate (blue), a thin Si3N4 passivation layer (grey), 7 nm of Ni film (red) and 2 nm of Ag capping layer (yellow). The white arrow represents the in-plane magnetization of the Ni film. The FEL pulses at the Si L2,3 edge (blue arrow) and at the Ni M2,3 edge (red arrow) are also depicted. The IR laser pulses at 1.55 eV hit the sample at a time delay t-t0, before the FEL pulses arrival. The penetration depths of the pump and the probes are represented by the length of the arrows. The fraction of the IR laser energy absorbed by each layer is reported above the probe arrow. b) Scheme of the FEL RMOKE set-up at MagneDyn. RMOKE was probed in longitudinal configuration at an angle of incidence of 45°. The polarization ε of the incoming FEL pulses (blue arrow) is in the scattering plane, while the Kerr rotation of the polarization of the reflected pulse is indicated as θ.

![](https://assets.underline.io/uploads/markdown_image/1/image/388e11ba365f236752de3629d9784f15.jpg)

Fig. 2: RMOKE magnetic hysteresis in degrees of Kerr rotation at the Ni M2,3 edge (a) and at the Si L2,3 edge (b). Empty and filled circles curves represent the unpumped and pumped hysteresis after 0.5 ps (Ni) and 0.3 ps (Si) (colored star markers in c). c) relative change of the site resolved magnetization M (Ni - red and Si - blue dots) as a function of time delay measured in saturation at 550 mT. The solid lines represent the tting results, from which we extract the characteristic times for demagnetization and recovery. The difference (ΔM/M)js is also shown (gray pentagons).

technical paper

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The spin-1/2 of an electron makes it an archetypal two-level system and inspires the description of other two-level systems using an analogous pseudospin. The quantized spin excitations of an ordered antiferromagnet can be viewed as pairs of spin-up and -down magnons and can be characterized by a magnonic pseudospin. The similarity between electronic spin and magnonic pseudospin has triggered the prediction of exciting phenomena like emergent spin-orbit coupling and topological states in antiferromagnetic magnonics. In the last year, first experimental observations of the associated dynamics of antiferromagnetic pseudospin have been reported [1,2]. Based on these findings, we will expand the concept of magnon pseudospin and the description of magnon pseudospin dynamics [3,4] and discuss the influence of dimensionality on the magnon Hanle effect. Additionally, we show our recent experiments demonstrating control of magnon spin transport and pseudospin dynamics in thin films with varying thickness of the antiferromagnetic insulator hematite (α-Fe2O3) utilizing two Pt strips for all-electrical magnon injection and detection [2] . We observe an oscillation in polarity of the magnon spin signal at the detector as a function of the applied magnetic field, which we quantitatively explain in terms of diffusive magnon transport. In particular, we observe a coherent precession of the magnon pseudospin caused by the easy-plane anisotropy and the Dzyaloshinskii-Moriya interaction. Moreover, we find peculiar changes in the magnon spin signal for thicker hematite layers. Our results are paramount in unnlocking the high potential of antiferromagnetic magnonics towards the realization of electronics-inspired phenomena. Financial support from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy - EXC-2111 - 390814868 and project AL2110/2-1, and the Research Council of Norway through its Centers of Excellence funding scheme, project 262633, "QuSpin" is gratefully acknowledged.

Antiferromagnetic Magnon Pseudospin Dynamics and the Magnon Hanle Effect in Hematite Thin Films

Antiferromagnetic materials (AFMs) provide a pathway to overcome the limitations of ferromagnet-based spintronics, enabling fast and high density memory devices, as well as terahertz detectors and sources. This has fueled intensive research on the electrical manipulation of metallic AFMs using interfacial spin-orbit torque (SOT) from a heavy metal (HM) layer [1-4]. However, the threshold current density in HM/AFM bilayers is typically large, thus creating non-magnetic contributions to resistive switching signals, complicating their interpretation. Here, we present a new device structure and measurement protocol based on differential voltage measurements, allowing in situ reference measurements and to systematically separate the switching signals originating in the AFM and HM layers of a HM/AFM heterostructure [5]. The proposed device consists of a double-cross HM structure with six terminals, where the AFM, patterned in a micropillar shape, is placed on one of the two crosses. We successfully use this method in devices formed by Pt and the non-collinear AFM IrMn3. The results provide clear evidence of electrical switching of the AFM order parameter in the IrMn3 pillar by SOT in the range of writing current densities from 36 to 50 MA/cm2 with no appreciable switching signal from the Pt layer. We discuss the role of different switching configurations (180° and 90° writing currents), as well as the role of thermal activation on the switching characteristics. Control experiments in Pt-only double-cross samples without an AFM pillar reveal HM-dominated switching at higher current densities ~60 MA/cm2. We discuss active readout of the switching signals using a differential amplifier, with large peak-to-peak output voltage ~100 mV. The structure allows for reliable electrical measurement of resistive signatures of AFM switching induced by SOT, which will be important not only for the fundamental understanding of current-induced AFM domain dynamics, but also as an electrical readout method for practical applications in memory and computing devices.

![](https://assets.underline.io/uploads/markdown_image/1/image/9f7b7e5713bbb79e6a1b7f3436e814c5.jpg)

Fig. 1. Design of double-cross device for differential voltage measurements and the measured differential voltage for the 180° switching configuration with 20 mA write pulses.

Observation of current-induced switching in non-collinear antiferromagnetic IrMn3 by differential voltage measurements

Antiferromagnetic materials have recently attracted much interest due to a number of advantages including high resonance frequencies up to the terahertz. Further, the possibility to electrically modulate the magnetic properties such as the anisotropy makes them an excellent candidate for energy-efficient devices at ultra-high frequencies. In this study, we theoretically explored one such application in the dynamic manipulation of electromagnetic responses with a broad tunable spectral range. The materials considered were dielectric antiferromagnets with strong magneto-electric or –elastic coupling which can achieve robust control in the perpendicular magnetic anisotropy. The metallic counterparts were not suitable due to the anticipated large loss. A theoretical analysis based on the Landau-Lifshitz equation was used to derive the frequency-dependent permeability and the resonant frequency of the antiferromagnet for different biaxial anisotropy profiles and incident electromagnetic wave polarizations. Numerical calculations based on typical parameters available in the literature (such as NiO) strongly indicated that the resonance frequency modulation as much as 10’s of percent may be possible in the sub-mm wavelength range, along with the corresponding changes in the permeability. Application to specific devices such as a bandpass filter further illustrated the validity of the concept. Funding Acknowledgement This work was supported, in part, by the U.S. Army Research Office (No. W911NF-16-1-0472).

![](https://assets.underline.io/uploads/markdown_image/1/image/6ffd93f402fd8b4c21123e86d0bbb698.jpg)

Fig.1 Schematic of the magnetic-piezoelectric composite. Electric field along out-of-plane direction causes magneto-elastic effects and influences eigen-frequency by modifying in-plane magnetic anisotropy. EM wave is incident along x-axis.


![](https://assets.underline.io/uploads/markdown_image/1/image/e677976b7cbcf549791f319205ea030e.jpg)

Fig.2 Data showing a high electric field tunable AFMR frequency shift with external voltage at 0, -V, and +V=8kV/cm (Not the final results)

Voltage-Controlled Dynamic Modulation of Electromagnetic Response in Antiferromagnetic Materials at Terahertz Frequencies

Recently antiferromagnetic materials have been gathering increasing attention from the spintronics community, as detecting and manipulating antiferromagnetic (AFM) order electrically is an important milestone for realizing antiferromagnetic devices. Characterizing the type and amplitude of the spin-orbit torques (SOT) is crucial for understanding and predicting AFM dynamics. One important technique to identify and measure SOTs is to perform harmonic Hall measurements in an AFM/heavy metal (HM) layer. In this study, we report the full angular dependence of 1st and 2nd harmonic voltage measurements in epitaxial c-axis oriented α-Fe2O3/Pt bilayer heterostructures (Fig. 1a). By modeling the harmonic resistance signals together with known material parameters such as the exchange field, anisotropy and DMI constant (Fig. 1b), we extract the amplitudes of field-like and anti-damping-like spin-orbit torques from field-dependent measurements in XY, XZ and YZ plane scans (Fig. 1a). Our model suggests a small angle tilt of the easy-plane and indicates that the amplitude of the field-like torques are significantly larger than anti-damping-like torques. Additionally, we show that there is an anomalous Hall-effect contribution in out-of-plane scans and that the Oersted fields are negligible compared to field-like torques. Our work provides a straight-forward way of characterization of spin-orbit torques in AFM/HM heterostructures.

![](https://assets.underline.io/uploads/markdown_image/1/image/87a94b08c94b21f9137b16231524bc27.jpg)

a) Transverse measurement configuration showing the Pt Hall cross with 5 µm channel width on AFM α-Fe2O3 layer. An AC current and the transverse voltage is measured with a lock-in amplifier. The thicknesses of α-Fe2O layer and Pt layers are 30 nm and 5 nm respectively. Next to it, geometry of magnetic field scans in the 3 principal planes (XY, XZ and YZ) is shown. b) Model geometry: D represents both the DMI vector and the hard axis direction. n is the Néel vector which lies in the easy plane. B is the external magnetic field. Alternating current is in x-direction and the spin accumulation in the y-direction. The Néel vector is perpendicular to both D and B.

Quantifying Spin-Orbit Torques in AFM/HM Heterostructures

Antiferromagnetic materials with non-collinear spin structures (NC-AFMs) offer significant potential for spintronic applications[1]. They have vanishingly small magnetization and ultrafast spin dynamics. In addition, they allow for the presence of important counterparts to the effects considered to be exclusive to materials with net magnetization, such as the anomalous Hall effect (AHE)[2], magneto-optical Kerr effect[3] or anomalous Nernst effect (ANE)[4]. One of the promising candidates of the NC-AFM class are Mn antiperovskites, with a typical representative being Mn3NiN. In this contribution we present ANE measurements on epitaxial thin films of Mn3NiN prepared on SrTiO3 substrate with spin structure lying in the (111) plane. Previous theoretical predictions suggest that despite the modest spin-orbit coupling, the magnitude of the ANE in Mn3NiN ought to exceed that of Mn3Sn NC-AFM due to the Berry phase boost[5]. We implement two complementary methods to detect the ANE response of the Mn3NiN films. First, the global Nernst response is measured using a micro-patterned Hall bar device with platinum resistive heaters generating an in-plane thermal gradient. The measured anomalous Nernst data (Fig.1(a)) are in good agreement with the AHE measurements[5], indicating a similar physical origin of the two effects. Second, to add a spatial resolution, scanning thermal gradient microscopy[4] is used. A laser beam incident on a micro-patterned device induces thermal gradients. The method reveals the sample’s domain structure. We find a signature of an ANE component that we can control with the external field due to the unsaturated moment present lying in the (111) plane, different from the previously measured Mn3Sn. This small moment provides a means for manipulating magnetic order, and even writing magnetic domain-like structures (Fig.1(b)). These two methods provide fruitful insight into the magnetic behaviour of NC-AFMs.

![](https://assets.underline.io/uploads/markdown_image/1/image/e3391f086f9d4953ae3f5db220e7247b.jpg)

Fig.1. Anomalous Nernst effect in Mn3NiN. (a) Global ANE as a function of the out-of-plane magnetic field at different base temperatures. (b) Scanning thermal gradient microscopy at T = 100 K. The domain-like structure was written by high-intensity laser beam and 500 mT in-plane magnetic field.

Anomalous Nernst effect in thin films of non-collinear antiferromagnet Mn3NiN

We combined XMLD, XMCD and MOKE measurements in order to follow the magnetic properties of epitaxial CoO(111)/Fe(110) [1] and NiO(111)/Fe(110) [2] bilayers. We find that in both studied cases FM sublayer plays a dominant role and determines the magnetic state of the neighboring AFM, however completely different interaction mechanisms are involved. In CoO/Fe bilayers the AFM spins are frozen and their orientation is imprinted by magnetization of Fe layer when the system passes the Neel temperature of CoO. Once the Fe layer grafts the particular magnetic anisotropy (MA) into the CoO overlayer, it later remains frozen and insensitive to external factors like external magnetic field or Fe magnetization direction [3]. Specifically, choice of particular magnetic state of Fe sublayer, when passing Néel temperature of CoO, determines both the axis and direction of interfacial antiferromagnetic spins after the sample is cooled and allows for imprinting their +/- 90° and 0/180° alignment within the sample plane. For example, particular direction of frozen AFM spins determines the corresponding sign of the shift field of exchange biased magnetic hysteresis loop (Fig.1). For NiO/Fe bilayers, due to the weak intrinsic MA of NiO, the AFM spins are rotatable and always follow the reorientation of Fe magnetization that can be controlled by external magnetic field or via the temperature and thickness driven SRT of Fe(110). Recently we showed that in a uniform thickness NiO(111)/Fe(110) system, two magnetic states with orthogonal spin orientations can be stabilized in antiferromagnetic NiO [2]. Field-free, reversible switching between these AFM states was demonstrated. Here we present results of systematic investigations of such field-free, temperature induced switching of AFM NiO spins. Fig. 2 shows temperature dependence of RL2 ratio for various thicknesses of Fe. Critical temperature of SRT in AFM NiO can be tuned in wide temperature window ~ (250 – 380 K) for field-free, reversible switching of AFM spins. XML(C)D-PEEM results obtained on individual self-organized NiO/Fe nanostripes will be also presented.

![](https://assets.underline.io/uploads/markdown_image/1/image/ea6cc84785bb0485bc069d8c09366d06.jpg)

Fig.1. Memory of frozen AFM spins in CoO(111)/Fe bilayer.

![](https://assets.underline.io/uploads/markdown_image/1/image/46723238dbaaa7708138289f718efd3d.jpg)

Fig.2. Temperature dependence of XMLD (RL2 ratio) for NiO/Fe [4].

Memory of frozen and rotatable antiferromagnetic spins in epitaxial CoO(111)/Fe and NiO(111)/Fe bilayers.

Synchronization of large spin Hall nano-oscillators (SHNO) arrays is an appealing approach toward ultra-fast non-conventional computing based on nanoscale coupled oscillator networks [1]. However, for large arrays, interfacing to the network, tuning its individual oscillators, their coupling, and providing built-in memory units for training purposes, remain substantial challenges. Here, we address all these challenges using memristive gating of W/CoFeB/MgO/AlOx based SHNOs. We use this type of stack as their substantial perpendicular magnetic anisotropy (PMA) can generate both localized and propagating spin waves [2]. In its high resistance state (HRS), the memristor modulates the perpendicular magnetic anisotropy (PMA) at the CoFeB/MgO interface purely by the applied electric field, which leads to both a voltage-controlled SHNO frequency and a voltage-controlled threshold current [3]. In its low resistance state (LRS), and depending on the voltage polarity, the memristor adds/subtracts a current Im to/from the SHNO drive. The operation in this LRS also affects the SHNO auto-oscillation mode and frequency, which can be tuned up to 28~MHz/V. This tuning allows us to reversibly turn on/off mutual synchronization in chains of four SHNOs and turn the chain into different partially synchronized states [4]. Memristor gating is, therefore, an efficient approach to input, tune, and store the state of the SHNO array for any non-conventional computing paradigm, all in one platform. Examples include SHNO based Ising Machines [5,6] and pattern recognition using memristive-controlled SHNO chains [4], which will both be discussed in detail in the presentation.

Memristor-controlled mutual synchronization of spin Hall nano-oscillator arrays for neuromorphic computing and spintronic Ising machines

Band inversion of electrons due to strong spin-orbit coupling (SOC) is commonly seen in magnetic materials. It characteristically appears in topological insulators (TIs) with inverted bandgaps [1] and Weyl semimetals (WSMs) with pointlike band crossings [2], while metallic systems are also capable of having band inversion. In momentum space around the SOC-induced band inversion, the electron spin is often correlated to its momentum, known as spin-momentum locking (SML). Moreover, the electron system acquires nontrivial band topology characterized by the Berry curvature, which serves as an effective magnetic field in momentum space. It is well understood that the band topology gives a substantial contribution to anomalous transport phenomena, such as the anomalous Hall effect (AHE) and the spin Hall effect (SHE), due to the anomalous velocity of electrons triggered by the Berry curvature. Recent experimental attempts have been successful in synthesizing materials having both nontrivial band topology and magnetism (magnetic TIs, WSMs, etc.), and it is an important question if their magnetic functionalities are also governed by their band topology. In this talk, I show from theoretical aspect that the current-induced spin torques in such magnetic topological materials are influenced and occasionally enhanced due to their band topology. After reviewing the current status of theoretical and experimental studies on magnetic topological materials, I will introduce some of my recent works. From the general point of view, I first propose that the momentum-space topology gives rise to an "intrinsic" contribution to the spin torques, which is robust against disorder and thermal fluctuation similarly to the intrinsic AHE and SHE [3]. This intrinsic torque originates from electron spin polarization converted from the anomalous velocity by SML, and is distinct from the conventional spin-transfer torque (STT) and the spin-orbit torque (SOT) driven by electron spins in transport current. In particular, I point out the intrinsic torque exerting on magnetic textures, such as domain walls (DWs), which we call the "topological Hall torque (THT)". The THT is induced by the cooperation of the real-space magnetic texture and the momentum-space Berry curvature, and can emerge dominantly in bulk crystals without building any complex heterostructures. As a typical example, I show our microscopic calculation result of current-induced torques with the low-energy effective model of magnetic WSM [4]. The band crossing points, called "Weyl points", serve as source and sink of the Berry curvature in momentum space, accompanied with SML of electrons around them (see Fig. 1). The Weyl electrons are therefore capable of generating a strong intrinsic torque. From the microscopic calculation in response to an externally applied electric field, we have derived the SOT, the STT, and the THT exerted by the Weyl electrons. The THT gets enhanced at a sharp magnetic DW, due to the localized states of Weyl electrons formed at the DW [5,6]. For more realistic situations, I also show the phenomenological calculation of the THT in a metallic ferromagnet with band inversion [3]. In response to an external electric field applied to a DW (see Fig. 2), we have obtained a large THT. The THT acts on a DW in the same form as the conventional nonadiabatic STT, but with the unusual size of the nonadiabaticity parameter β≈2, which will enable an efficient control of DW motion by electric field. Experimental measurability of the THT in the metallic ferromagnet SrRuO3, in connection with the temperature dependence in its AHE [7], will also be mentioned.

![](https://assets.underline.io/uploads/markdown_image/1/image/d0716b6a26c3c8035d704ada28777bbc.jpg)

Schematic image of Weyl points emerging from band inversion. The Berry curvature (magenta curves) emerges in the vicinity of the Weyl points.

![](https://assets.underline.io/uploads/markdown_image/1/image/9d1d264c88091f5f7c8512236cd257bf.jpg)

Schematic image of the setup of magnetic DW in our calculations [3]. We consider an external electric field Eext applied across the DW, and calculate the torque in response to Eext.

Theory of Spin Torques Emerging from Band Topology

The motion of domain walls by the use of the magnetic fields as well as spin polarized currents has been a major part of spintronics in the last two decades. The two mechanisms of current induced domain wall motion are Spin transfer torque(STT) and Spin orbit torques(SOT). In the recent years, compensated ferrimagnets have been in focus due to their ability to reach the magnetic and the angular momentum compensation points. At the angular mometum compensation point the precessional motion of the local magnetic moment becomes negligible which has shown to have massively increase the domain wall velocity[1,2]. Here we will focus on a rare-earth free ferrimagentic nitride called Manganese Nitride (Mn4N). We have previously shown epitaxially grown Mn4N has a very low magnetization (71 kA/m) and a very high perpedicular magnetic anisotropy (PMA) with mm sized domains[3]. This low magnetization is due to the two different Mn sub-lattices in the anti-perovskite crystal structure. With such a small magnetization and a high spin polarization led us to obtain a very high domain wall velocity of more than 900m/s at J=1.3*1012 A/m2 using pure STT[4]. In this work, we have have shown an even larger domain wall velocity approaching 3000 m/s at J=1.26*1012 A/m2 using pure STT near the magnetic and the angular compensation points in epitaxially grown Ni doped Mn4N[5]. The magnetic and angular momentum compensation points are obtained by the adjustment of Ni doping in this system at room temperature. These high domain wall velocities are comparable to the best velocities obtained by SOT. Also, in this system there is no requirement for an external in-plane field as shown in some other systems by SOT. Moreover, we also demonstrate a reversal of the domian wall motion direction after crossing the compensation points where the domain walls move in the same direction as the flow of electrons. This phenomenon will be explained with the help of ab-initio calculations.

![](https://assets.underline.io/uploads/markdown_image/1/image/c0c2ec29f2ef977b88dd4a5f908583e9.jpg)

Current density vs Velocity curves for Mn4-xNixN thin films. Filled symbols show samples before and the open symbols after the compensation point.


![](https://assets.underline.io/uploads/markdown_image/1/image/b73b2f498d533d34f95601fada6e88b3.jpg)

MS vs Velocity plot, measured for J=1*1012 A/m2(blacksquares) is compared with the best fit obtained using the q−φmodel.

Current driven domain wall dynamics across the angular momentum compensation point in epitaxially grown ferrimagnetic Ni-doped Mn4N thin films

Spin-torque oscillator (STO) is a class of emerging spintronic devices that can find applications in wireless communication systems in the form of radio frequency (rf) generator1,2 and rf detector3. The STO offers a compatibility with CMOS technology and high frequency tunability2. However, the single STO output is not sufficient for the rf applications. In order to overcome this, the mutual synchronization of STOs is critical for communication, energy harvesting and neuromorphic applications. The 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 (&lt; 500 MHz), restricting them for on-chip GHz-range applications. Here, we demonstrate electrical synchronization of four non-vortex uniformly-magnetized STOs at 2.4 GHz WiFi band4, resolving the frequency-area quandary for designing STO based on-chip systems. We use a single dc source to synchronize canted free layer STOs, thereby simplifying the synchronization scheme. Due to mutual synchronization, STOs show a power enhancement and linewidth reduction [Fig. 1a,b]. When injection-locked with an external rf source, the synchronised STOs show a wide locking range around 2.4 GHz [Fig. 1c,d], which can be useful for neuromorphic computing. Under injection locking, synchronized STOs demonstrate an excellent time-domain stability and improved phase noise performance [Fig. 1e,f]. Our results highlight the significance of electrical topology (series vs. parallel) while designing an on-chip STOs system.

![](https://assets.underline.io/uploads/markdown_image/1/image/5c47ef17602057fa745ff11bcef50d6b.jpg)

Fig. 1. a,b Oscillation power (P) and linewidth (△f) versus numbers of oscillators (N) in parallel (a) and series (b), respectively. Solid lines are linear fit and N−1 scaling for the power and linewidth, respectively. c,d STO frequency (f0) versus radio frequency (frf) response for a single oscillator (red) and four oscillators (blue) at Prf = −20 dBm for the parallel (c) and series (d) connection. The locking range defines the region where f0 ~ frf. e,f Phase noise for 1 ms time-domain trace in parallel (e) and series (f). The solid black and blue lines in (f) shows the 1/f2 and 1/f3 phase noise, respectively.

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