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Spin Hall nano-oscillators (SHNOs) have the unique ability to convert a direct current input to microwave signals by means of spin Hall effect and spin orbit torque [1]. The generated microwave signals depend on several factors inherent to having a flow of direct current such as the current density, Oersted fields, Joule heating and naturally the magnetic state in a given device geometry. In addition, other factors such as frequency locking or synchronisation onto an external microwave source can contribute to the microwave output of a given SHNO [2-5]. The interplay of all these factors affects the agility of the magnetisation auto-oscillations of an SHNO. We report the study of SHNOs while subject to current pulses as well as RF pulses, measured using time resolved micro-focused Brillouin light scattering (micro-BLS). The SHNOs under test consist of a double-disk constriction of NiFe(5 nm)/Pt(7 nm). First, we discuss how few-nanosecond pulses can still efficiently induce magnetisation auto-oscillations, thereby demonstrating that both the onset and outset of the auto-oscillations occur within a sub-nanosecond timescale. Then, we proceed to showing how auto-oscillations can be affected by external microwave pulses. Various degrees of enhancement (injection-locking) or suppression of the auto-oscillation signal can be achieved by choice of the frequency and the amplitude of the external microwave signal. The knowledge of the agility or the response to either intended or unwanted parasitic external excitations is paramount for SHNOs to be able to operate on very short time-scale with well defined responses in, for example, the context neuromorphic computing [6].References: [1] Demidov, V. E. et al., Nature Materials, 11(12), 1028–1031 (2012). [2] Demidov, V. E. et al., Nature Communications, 5(1), 3179 (2014). [3] Sato, N. et al. Physical Review Letters, 123(5), 057204 (2019). [4] Hache, T. et al., Applied Physics Letters, 116(19), 192405 (2020). [5] Hache, T. et al., Applied Physics Letters, 114(10), 102403 (2019). [6] Zahedinejad, M. et al., Nature Nanotechnology, 15(1), 47–52 (2020).

MMM 2020

Agility of spin Hall nano-oscillators measured using time-resolved micro-BLS

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Recently we studied magnetic inhomogeneity effects in magnetocaloric properties of a 7.6 nm La0.7Sr0.3MnO3 (LSMO) thin film to understand the nature of magnetic phases transitions1. We proved this sample has two main magnetic phase transitions: superparamagnetic ferromagnetic and ferromagnetic-paramagnetic phases transitions, at T = 240 K (= TB) and T = 270 K (= TC), respectively. Here we want to understand the spin dynamics and relaxation in this sample. Analysis of the results from our investigations of the temperature dependence of ac susceptibilities (χ/ and χ//) and magnetic viscosity in a 7.6 nm thin film of La0.7Sr0.3MnO3 grown on SrTiO3 (001) substrate are presented. The Curie temperature (TC) of this film is magnetic field (H) dependent varying as: [TC(H)-TC(0)] ~ Hn, n ~ 0.15. Temperature dependence of χ/ and χ// measured at ac frequencies fm in the range of 0.1 to 10 kHz shows a broad peak near 230 K associated with the blocking temperature of spin clusters present in the 1.4 nm surface layer and a frequency dependent peak near 270 K associated with TC (Fig. 1). The mean relaxation time τ determined from the Cole-Cole analysis of and is shown to fit the Vogel-Fulcher law: τ = τ0 exp[ΔE / kB(T-T0)] , with TB = 245 K, ΔE / kB = 270 K = TC, and τ = 1.2 10-9 (s) (Fig. 2). Magnetic viscosity S (measured in H = 0 for a sample cooled in H = 50 Oe) determined from the fit to the magnetization: M (t) = M (0) – S Ln t, with time t up to 2 hours, shows a peak at 230 K above which the M (2 hrs) switches to negative values for temperatures up to TC(0). It is argued that this negative magnetization results from interaction between the superparamagnetic like spin clusters and the ferromagnetic phase.References: 1 N. Mottaghi, R.B. Trappen, S.Y. Sarraf, M.S. Seehra, and M.B. Holcomb, J. Alloys Compd. 154200 (2020).

Spin dynamics and relaxation in thin film La0.7Sr0.3MnO3/SrTiO3: ac magnetic susceptibility and magnetic viscosity investigations.

Iron oxide nanoparticles (NP) are under investigation for many biomedical applications [1], including magnetic hyperthermia. The heating efficiency of magnetic hyperthermia depends on how well the single excitation frequency matches the Néel and Brownian relaxation frequencies of the NPs. We directly measured the magnetostatic interaction induced frequency distribution with a custom-built AC susceptometer [2]. Our results show that both the peak and amplitude of this distribution can be tuned by addition of a small DC field, thus enabling a better match to the AC excitation field frequency. We measured the AC magnetic susceptibility (ACS) of 10.7±1.2 nm Fe3O4 NPs dispersed in eicosane (0.15 vol%). The ZFC-FC curve shows a blocking temperature (TB) of ~ 105 K, and the greatest response of the real (χ’) and imaginary (χ”) parts of the ACS was found between 110 and 150 K. Fig. 1 shows the imaginary component of the ACS as a function of frequency, for HDC = 0, at different temperatures. The imaginary part shows a very broad peak at 110K. At higher temperatures the dispersive peak sharpens and the peak shifts to higher frequencies. Both the breadth of the peak and its shift with temperature show that magnetostatic interactions affect high frequency response even for dilute samples. We extended our ACS measurement at 140 K with additional DC fields, ranging from 0 to 4mT. Fig.2 shows the non-monotonical trend of the imaginary part of the ACS at various DC magnetic fields. Below 1.25 mT the peak frequency decreases and the amplitude increases with increasing DC fields. At and above 1.25 mT these trends reverse. The dissipation at 100 kHz increases by a factor of 3.8 between 0 and 1.25 mT. The peak DC field is comparable to the average magnetostatic interaction field. Applying the DC field overcomes part of the spin freezing and enables a larger fraction of the spins to contribute to the dissipation. This methodology can be extended to polydisperse NPs at higher concentrations at body temperature.References: [1] Q.A. Pankhurst, et al., J. Phys. D Appl. Phys. 36, R167 (2003). [2] E. Riordan, et al., Review of Scientific Instruments 90, 073908 (2019).

Tuning the Dynamics in Fe3O4 Nanoparticles for Hyperthermia Optimization

Antiferromagnetic (AFM) spin Hall oscillators driven by a sub-threshold spin current produce ultra-short (~ 5 ps) spikes in response to a weak external stimulus and can be used as ultra-fast artificial neurons [1, 2]. One of specific features of AFM oscillators is the effective inertia that originates from exchange coupling between two AFM magnetic sublattices and manifests itself, for instance, in hysteretic behavior of the threshold generation current [3]. Here, we theoretically investigate influence of the exchange inertia on the dynamics of AFM-based artificial neural networks. The exchange inertia leads to delay of the spike generated by an AFM neuron relative to the input stimulus signal. The delay time depends on the coupling strength between AFM neurons and can vary from ~ 10 ps to several 100s ps. This effect can be used to create a tunable periodic spike generator by coupling several AFM neurons in a ring structure, in which output of one neuron serves as an input for the next neuron. The exchange inertia can also be used to create an “inhibitor” neuromorphic circuit, in which propagation of a spike is suppressed in the presence of another (“inhibiting”) signal. The inhibitor works by splitting the signal path in two branches and controlling the delay time in one branch by the inhibiting signal. In the presence of the inhibiting signal, the spikes in two branches arrive at the output neuron at different times and do not induce an output spike. It should be noted, that such “inhibitor” circuit is impossible to realize with inertia-less integrate-and-fire neurons. Combining the inhibitor circuit with a ring structure allows one to realize a controllable neuromorphic memory loop (see example simulations in Fig. 1). These and other examples demonstrate that exchange inertia effects can be utilised to achieve new functionalities of AFM-based artificial neural networks.References: [1] R. Khymyn, I. Lisenkov, J. Voorheis, et al., Sci. Rep. 8, 15727 (2018). [2] O. Sulymenko, O. Prokopenko, I. Lisenkov, et al., J. Appl. Phys. 124, 152115 (2018). [3] R. Khymyn, I. Lisenkov, V. Tiberkevich, et al., Sci. Rep. 7, 43705 (2017).

Dynamic effects of exchange inertia in artificial neural networks based on antiferromagnetic oscillators

Memristors – two-terminal circuit elements whose resistance is ideally proportional to the integral of input over time – enable the implementation of synapses in artificial neural networks. However, “ideal” memristive functionality has not been yet achieved. We experimentally demonstrate the possibility to implement almost ideal memristors using thin-film ferromagnet/antiferromagnet (F/AF) bilayers, where frustrated exchange interaction at the F/AF interface results in the correlated spin liquid state of the AF characterized by viscous magnetization dynamics [1]. We utilize a bilayer formed by a 10 nm-thick F Permalloy (Py) and an 8 nm-thick AF NiO film. External magnetic field H serves as the driving input in our demonstration. The angle of magnetization rotation is proportional to the integral of the field over time, which is converted into resistance variations by anisotropic magnetoresistance (AMR). The resulting magnetoelectronic hysteresis loop is consistent with that expected for an ideal memristor. Analysis of the time-domain response shows deviations from ideal behaviors, which are associated with the inhomogeneity of viscous dynamical properties. We also discuss how the demonstrated memristive functionality can be achieved with current-driven nanostructures by utilizing spin torque [2]. The demonstrated memristors are amenable to downscaling and should exhibit high endurance, making them particularly attractive for neuromorphic applications.References: 1. S. Urazhdin, W. Li and L. Novozhilova, JMMM, Vol. 476, pp.75-85 (2019) 2. G.X. Chen, S. Ivanov, and S. Urazhdin, arXiv:2006.07996 (2020)

Memristive Functionality of a Thin-film Ferromagnet/Antiferromagnet Bilayer

Memristors are circuit elements whose resistance is ideally proportional to the total charge that passes through them, which can provide synaptic functionality in artificial neural networks. Many implementations of generalized memristors – devices whose resistance depends on their electronic history – have been explored, but ideal memristor functionality has not yet been achieved. We utilize analytical arguments and numerical simulations to show that ideal memristors can be realized using spin transfer torque (STT)-driven viscous magnetization dynamics. The latter can be achieved in the spin liquid state of thin-film F/AF heterostructures resulting from frustrated exchange interaction [1]. We show that the magnetization dynamics can be efficiently driven by STT, despite large damping associated with viscous dynamics. For a magnetic system with negligible in-plane anisotropy and large damping, magnetization response to current pulses with varied duration Δt and amplitude I0 depends only on the total pulse charge Q [Fig.1], consistent with ideal memristive behaviors. Additionally, we show that current-induced Joule heating can serve as an extra state control variable, resulting in the dependence of current-driven resistance variation on the relative timing of the current pulses [Fig.2]. This additional second-order memristive functionality [2] provides natural implementation for the spike-timing dependent plasticity in spintronic neuromorphic network with non-overlapping spikes. Our work thus opens a new route for the development of advanced spintronic neuromorphic hardware.References: [1] Urazhdin, Sergei, Weijie Li, and Lydia Novozhilova. "Magnetic freezing transition in a CoO/Permalloy bilayer revealed by transverse ac susceptibility." Journal of Magnetism and Magnetic Materials 476 (2019): 75-85. [2] Kim, Sungho, et al. "Experimental demonstration of a second-order memristor and its ability to biorealistically implement synaptic plasticity." Nano letters 15.3 (2015): 2203-2211.

Ideal memristor based on viscous magnetization dynamics driven by spin torque

Spin Torque Nano-Oscillators are magnetic devices that use tunnel magnetoresistance to emit microwaves. They hold great promise for neuromorphic computing [1], as we can use their non-linear dynamic to emulate neurons and they can be integrated by millions in CMOS chips. In previous works, it has been shown that their transient or coupled dynamics can be used to perform pattern recognition [2], [3]. In order to build deep neural networks [4] it is now crucial to find a way to interconnect different layers of neurons with artificial tunable synapses. Here we present an architecture using spintronic resonators to weight the microwave encoded signals of artificial RF spintronic nano-neurons. These synaptic resonators leverage the spin-diode effect [5,6]. The resistance of the devices oscillates at the same frequency as the signal they receive. The rectified voltages are proportional to the power of the microwaves and depend strongly on the frequency mismatch between the signal and the resonance frequency of the device. Hence to tune these resonance frequencies is analog to tune the synaptic weights. And because of the frequency selectivity of our resonators, each of them rectifies only the signal of its corresponding neuron. We use an analytical model and dynamical simulations to show that a chain of spintronic resonators wired in series, rectifying different microwave signals, is equivalent to the key operation of neural networks, called Multiply-And-Accumulate (MAC), despite the nonlinearity of these components. We also demonstrate experimentally with Magnetic Tunnel Junctions as resonators and several RF generators, the validity of this MAC operation. Finally, we simulate a full network with spintronic oscillators and resonators to test our architecture. We manage to achieve state-of-the-art recognition on a handwritten digit dataset. These are encouraging results for high density hardware neural network, as it is the first demonstration of a fully-spintronic radio-frequency neural network.References: [1] J. Grollier, D. Querlioz and M. D. Stiles, Proceedings of the IEEE, Vol. 104, p. 2024-2039 (2016) [2] J. Torrejon, M. Riou et al, Nature, Vol. 547, p. 428 (2017) [3] M. Romera, P. Talatchian, S. Tsunegi et al, Nature, Vol. 563 (7730), p. 230-234 (2018) [4] Yann LeCun et al, Nature, Vol. 521, p. 436-44 (2015) [5] C. Wang, Y.-T. Cui et al, Phys. Rev. B Vol. 79, p. 224416 (2009) [6] D. Marković, N. Leroux, A. Mizrahi, et al, Phys. Rev. Appl, Vol. 13 (4), p. 044050 (2020)

Radio-frequency synapses for neural networks made of spin-torque nano-oscillators

After the discovery of the giant spin Hall effect (SHE) in certain heavy metals [1], topological materials have drawn considerable attraction [2-3]. In this work, we report crystal orientation-dependent large spin Hall conductivity (SHC) in epitaxially grown IrO2 thin film [4]. IrO2 is predicted to host Dirac nodal lines (DNL) in the band structure [5], which could lead to a large SHC. Our ARPES studies show the presence of DNL in (001) IrO2 films [6] that exhibit exceptionally high damping like torque efficiency ranging from 0.45 at 293 K to 0.65 at 30 K which sets the lower bounds of SHC to be 1900 µΩ-cm and 3750 µΩ-cm respectively [4], ten times higher and opposite than the available theoretical prediction [5]. In contrast, anisotropic strain breaks the symmetry of (110) film and opens a gap in the band anti-crossing due to the strain effect which deteriorates the SHC substantially. We also report the SHC varying from dirty metal regime to clean metal regime as IrO2 conductivity increases from (001) to (110) films. This work establishes the correlation of the presence of DNL and strain on the SHC.References: [1] L. Liu et. al. Science 336, 555 (2012) [2] A. R. Mellnik et. al. Nature (London) 511, 449 (2014) [3] Y. Fan et. al. Nature Mater. 13, 699 (2014) [4] A. Bose et. al. arXiv:2006.04365 [5] Y. San et. al. Phys. Rev. B. 95, 235104 (2017) [6] J. N. Nelson et. al. Phys. Rev. Mater. 3, 064205 (2017)

Role of Dirac Nodal Lines and Strain on the Spin Hall Conductivity of Epitaxial IrO2 Thin Films

Realizing efficient spin-charge conversion is an important issue in spintronics, especially for the development of low-power-consumption magnetization switching. A spin-charge conversion is generally induced in a nonmagnetic (NM) layer by the inverse spin Hall effect. The spin-charge conversion efficiency, so-called the spin Hall angle θSHE, is limited by the spin-orbit interaction of the NM layer. Thus, artificially enhancing the θSHE to greater than its intrinsic value is difficult. Here, using spin pumping measurements on all-epitaxial single-crystalline heterostructures composed of ferromagnetic (FM) Co2FeAl0.5Si0.5 (CFAS) and an NM n-type Ge, we demonstrate that the θSHE can be strongly enhanced by annealing the sample and the resulting interdiffusion of the atoms within only ~3.7 nm around the CFAS/n-Ge interface. The magnitude of the electromotive force was significantly different between the as-grown and annealed samples as shown in Fig. 1. From these results, θSHE is estimated to be 0.0058–0.0079 for the as-grown sample and 0.015–0.019 for the annealed one at 70–300 K (Fig. 2), which is much larger than the intrinsic value of the θSHE reported for Ge (0.00096–0.002) [1-3] and is comparable to θSHE values reported for Pt. This enhancement is attributed to strong scattering of the spin current in the intermixed layer formed at the interface by annealing. Our results indicate that the θSHE is strongly influenced by the atomic structure of the FM/NM interface, which suggests a new and efficient method to control spin-charge conversion by precise control of the FM/NM interface [4]. This work was partly supported by Grants-in-Aid for Scientific Research (No.18H03860, 19H05616), CREST of JST (No. JPMJCR1777), and the Spintronics Research Network of Japan (Spin-RNJ).References: [1] M. Koike et al., Appl. Phys. Express 6, 023001 (2013). [2] A. Jain et al., Phys. Rev. Lett. 109, 106603 (2012). [3] J. C. Rojas-Sánchez et al., Phys. Rev. B 88, 064403 (2013). [4] S. Kaneta-Takada et al., submitted (2020).

Artificial enhancement of the spin Hall angle of Ge using the interdiffusion of atoms in Co2FeAl0.5Si0.5/n-Ge heterostructures

Mutually synchronized spin-torque nano-oscillators (STNOs) are one of the promising platforms for bioinspired computing and microwave signal generation [1]. Using STNOs one can achieve 90% recognition rate in spoken vowels [2]. However, in order to do more complex tasks, larger-scale synchronized oscillators are needed, something that is not easily done with the STNOs demonstrated so far. In my talk, I will describe a different type of spin current-driven device called spin Hall nano-oscillators (SHNOs), which can generate microwave frequencies over a very wide frequency range [3]. The SHNOs are based on 50 – 120 nm wide nano-constrictions in Pt(5)/Hf(0.5)/NiFe(3) trilayers (all numbers in nm). When multiple nano-constrictions are fabricated close to each other (300 – 1200 nm separation) they can mutually synchronize and chains of up to nine nano-constrictions have been demonstrated to exhibit complete synchronization [4]. For the first time, we can now also synchronize two-dimensional SHNO arrays with as many as 8 x 8 = 64 SHNOs [5]. The mutual synchronization is observed both electrically and using scanning micro-BLS microscopy. Both the output power and linewidth of the microwave signal improves substantially with increasing number of mutually synchronized SHNOs, such that quality factors of about 170,000 can be reached. Following the approach of Romera et al, we also demonstrate neuromorphic computing using a 4 x 4 SHNO array with two injected microwave signals as inputs. Given their high operating frequency (~10 GHz), easy fabrication, and highly robust synchronization properties, nano-constriction SHNO arrays are likely the most promising candidates for neuromorphic computing based on oscillator networks.References: [1] Torrejon J., et al. Neuromorphic computing with nanoscale spintronic oscillators. Nature 547, 428 (2017) [2] Torrejon J., et al. Vowel recognition with four coupled spin-torque nano-oscillators. Nature 563, 230 (2018) [3] Chen T., et al. Spin-torque and spin-Hall nano-oscillators. Proc. IEEE 104, 1919 (2016) [4] Awad A. A. et al. Long-range mutual synchronization of spin Hall nano-oscillators. Nature Physics 13, 292 (2017) [5] Zahedinejad M., et al. Two-dimensional mutually synchronized spin Hall nano-oscillator arrays for neuromorphic computing. Nature Nanotechnology 15, 47 (2020)

2D Mutually Synchronized Spin Hall Nano-Oscillator Networks for Neuromorphic Computing INVITED

In the last decade, two revolutionary concepts emerged in nano-magnetism from research for advanced information processing and storage technologies. The first suggests the use of magnetic domain walls (DWs) in ferromagnetic nanowires to permanently store information in DW racetrack memories. The second proposes a hardware realisation of neuromorphic computing in nanomagnets using nonlinear magnetic oscillations in the GHz range. Both ideas originate from the transfer of angular momentum from conduction electrons to localised spins in ferromagnets, either to push data encoded in DWs along nanowires or to sustain magnetic oscillations in artificial neurones. Even though both concepts share a common ground, they live on very different time scales which rendered them incompatible so far. Here, we bridge both ideas by demonstrating the excitation of magnetic auto-oscillations inside nano-scale DWs [1] using pure spin currents originating from the spin-Hall effect. While the auto-oscillations are in a domain wall are shown for a bilayer from a heavy metal (HM) and a ferromagnet (FM) we also demonstrated the realization of a bipolar spin-Hall Nano-oscillator using a FM/HM/FM trilayer system [2].References: [1] N. Sato, K. Schultheiss, L. Körber, N. Puwenberg, T. Mühl, A. A. Awad, S. S. P. K. Arekapudi, O. Hellwig, J. Fassbender, and H. Schultheiss, Phys. Rev. Lett. 123, 057204 (2019). [2] T. Hache, Y. Li, T. Weinhold, B. Scheumann, F. J. T. Gonçalves, O. Hellwig, J. Fassbender, and H. Schultheiss, Appl. Phys. Lett. 116, 192405 (2020).

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