United States

Introduction: Transcranial magnetic stimulation (TMS) is an emerging method for depression and neuropathic pain therapy with a painless and noninvasive neuromodulation function [1]. The winding path of the TMS coil can be realized in several ways [2]. For instance, the H1 coil is designed for deep brain stimulation [3], the “hat-like” coil is designed to suppress temperature rise during stimulation [4], and the fdTMS coil comprehensively considers energy, depth, and focality [5]. However, a practical TMS coil satisfying both high energy efficiency and robustness against individual variabilities in head shape has not yet been realized. Purpose: To optimize an energy-efficient TMS coil that is robust against individual differences in head shape. Methods: The optimization scheme is shown in Fig. 1. Multiple MRI anatomical images are used to optimize the shape to facilitate fitting of the scalp at the target stimulation position. Subsequently, the winding path of this shape is optimized through the following steps. First, the forward model Ε=AΨ for the scalar stream function Ψ and target-induced electric field Ε is established. Second, the Tikhonov regularization is used to solve the stream function Ψ numerically, given Ε. Finally, the coil winding path is extracted from the contour lines of Ψ [4]. This coil was compared with two commercial TMS coils by simulating the eddy current distribution in the digital brain model. Result: The results are shown in Fig. 2. Under the same energy consumption condition, compared with planar fig-8 and butterfly coils, this “head-fit” coil has stimulus area increases of 87% and 67%, respectively, with the corresponding efficiency drops of only 2% and 3%. The expansion of the stimulation area indicates that stimulation to the target area can be ensured even with a slight movement of the head during ~30min treatment. Furthermore, considering the shape of the scalp of different subjects facilitates close fitting of the head. Conclusion: Our method allows the design of TMS coils suitable for practical TMS therapy.References: [1] J. P. Lefaucheur et al., “Evidence-based guidelines on the therapeutic use of repetitive transcranial magnetic stimulation (rTMS),” Clin. Neurophysiol., vol. 125, no. 11. Elsevier Ireland Ltd, pp. 2150–2206, 2014. [2] Z. De Deng, S. H. Lisanby, and A. V. Peterchev, “Electric field depth-focality tradeoff in transcranial magnetic stimulation: Simulation comparison of 50 coil designs,” Brain Stimul., vol. 6, no. 1, pp. 1–13, Jan. 2013. [3] H. M. Gellersen and K. K. Kedzior, “Antidepressant outcomes of high-frequency repetitive transcranial magnetic stimulation (rTMS) with F8-coil and deep transcranial magnetic stimulation (DTMS) with H1-coil in major depression: a systematic review and meta-analysis,” BMC Psychiatry, vol. 19, no. 1, pp. 139, 2019. [4] L. M. Koponen, J. O. Nieminen, and R. J. Ilmoniemi, “Coil optimisation for transcranial magnetic stimulation in realistic head geometry,” Brain Stimul., vol. 10, no. 4, pp. 795–805, 2017. [5] L. J. Gomez, S. M. Goetz, and A. V. Peterchev, “Design of transcranial magnetic stimulation coils with optimal trade-off between depth, focality, and energy,” J. Neural Eng., vol. 15, no. 4, pp. 1–31, 2018. [6] G. N. Peeren, “Stream function approach for determining optimal surface currents,” J. Comput. Phys., vol. 191, no. 1, pp. 305–321, 2003.

MMM 2020

Optimization of transcranial magnetic stimulator coil using stream function for reducing the influence of individual variabilities of head geometry

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The 65th Annual Conference on Magnetism and Magnetic Materials (MMM 2020) was held in a virtual form. The COVID-19 pandemic, with its associated uncertainty about international travel and the ability to gather in large groups, meant that the Steering Committee decided to cancel the face-to-face meeting that had been planned in Palm Beach, Florida November 2-6, 2020.

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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

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).

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

The efficient detection of a magnetic state at nanoscale dimensions is important for the development of spin logic devices. Magnetoresistance effects can be used to detect magnetic states, but they cannot produce sufficiently large signals when the dimensions of the devices are reduced to the nanoscale, nor do they generate an electromotive force that can be used to drive a circuit element for logic device applications.1 In this work2, we report a favorable scaling law for the detection of an in-plane magnetic state of a magnet by using the inverse spin Hall effect in cobalt–iron/platinum (Co50Fe50/Pt) nanostructure devices. By reducing the dimensions of the device, we obtain a large spin Hall signal of 0.4 Ω (0.3 Ω) at 10 K (room temperature) (see figure 1a), and quantify an effective spin-to-charge conversion rate for the ferromagnetic/heavy metal nanostructure system (see figure 1b). Finally, we predict that this spin-orbit detection of magnetic states could be used to drive spin logic circuitsReferences: [1] S. Manipatruni, D.E. Nikonov, C.C. Lin, et al., Nature 565, 35–42 (2019). [2] V.T. Pham*, I. Groen*, S. Manipatruni et al., Nat.Electron. 3, 309-315 (2020)

Spin-Orbit Magnetic State Readout in Scaled Ferromagnetic/Heavy Metal Nanostructures

Since it is important to find materials with large spin Hall angles for utilizing spintronic devices, various materials have been reported, e. g. Ir–O, Pt-Cu, Ta50W50, and BiSb [1-4]. We investigated the composition effect on spin Seebeck coefficient in YIG/Pt-based alloy systematically, where Pt-based alloy is Pt1−XRuX, Pt1−XCuX, and Pt1−X(Cu0.5Ru0.5)X. The additive elements of Cu and Ru have equally small spin Hall angles in the single state, whereas they have the different atom sizes. In all systems the composition of around 50 at% showed the maximum spin Seebeck coefficient, from which we estimated spin Hall angles [5, 6]. As a result, the spin Hall angle was increased from 0.1 to 0.19, 0.25, 0.34 by changing Pt to Pt-Ru, Pt-RuCu, and Pt-Cu. It means that additive Cu is more effective on spin Hall angle improvement than additive Ru although their own original spin Hall angles are comparably small. X-ray diffraction analysis revealed that Cu and/or Ru doping in Pt host decreased the unit cell size, and there is an obvious relation between the lattice constant and the spin Hall angle as shown in Fig. 1(a). Since the resistivity dependence on lattice constant exhibit the similar tendency in Fig. 1(b), it suggests that the unit cell size modification in heavy metal Pt layer increases the electron scattering including spin-dependent scattering, leading the extrinsic spin Hall angle enhancement.References: [1] K. Fujiwara, Y. Fukuma, J. Matsuno, H. Idzuchi, Y. Niimi, Y. Otani, and H. Takagi, Nat. Commun. 4, 1 (2013). [2] R. Ramaswamy, Y. Wang, M. Elyasi, M. Motapothula, T. Venkatesan, X. Qiu, and H. Yang, Phys. Rev. Appl. 8, 024034 (2017). [3] H. Yuasa, F. Nakata, R.Nakamura and Y. Kurokawa, J. Phys. D: Appl. Phys. 51, 134002 (2018). [4] N. H. D. Khang, Y. Ueda and P. N. Hai, Nat. Mater. 17, 808 (2018). [5] K. Tian and A. Tiwari, Sci. Rep. 9, 1 (2019). [6] H. Li, Y. Kurokawa, T. Niimura, T. Yamauchi, and H. Yuasa, Jpn. J. Appl. Phys. 59, 073001 (2020).

Spin Hall Angle Control by Doping Element into Pt Host

Ferromagnetic metals and insulators are widely used for generation, control, and detection of magnon spin signals. Most magnonic structures are based primarily on either magnetic insulators or ferromagnetic metals, while heterostructures integrating both are less explored. Here, by introducing a Pt/yttrium iron garnet (YIG)/permalloy (Py) hybrid structure grown on Si substrate, we studied the magnetic coupling and magnon transmission across the interface of the two magnetic layers [1]. Interestingly, we found the YIG and the Py layers show antiferromagnetic coupling when external field is small, and the two layers align to the same direction only when the in-pane field is above 150 mT, as evidenced by both vibrating-sample magnetometry and polarized neutron reflectometry measurements. More importantly, the parallel and antiparallel magnetization configurations in this YIG/Py structure could be utilized to control magnon spin flow in spin-pumping and spin Seebeck experiments. In Figure 1(a) and 1(b), we schematically illustrate the effect of magnetization configuration (antiparallel vs parallel) on the magnon current transmission efficiency across the two magnetic layers’ interface. In the spin-pumping experiment, as plotted in Figure 1(c), we demonstrate that a magnon spin-valve device with an ON/OFF ratio of ~130% can be realized out of this multilayer structure at room temperature. Owing to the efficient control of magnon current and the compatibility with Si technology, the Pt/YIG/Py hybrid structure could potentially find applications in magnon-based logic and memory devices.References: [1] Yabin Fan, P. Quaterman et al., Phys. Rev. Appl. 13, 061002 (2020).

Manipulation of coupling and magnon transport in magnetic metal-insulator hybrid structures

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).

Domain wall based spin-Hall nano-oscillators INVITED

The focus of lab-on-a-chip technology centers on small, low power devices that can be integrated on a microscopic scale to perform laboratory functions within one unit or “chip”. In order to achieve this, one has to understand how to transfer fluid at this scale. Due to the low Reynolds number limit, such devices need to break time-reversible symmetry to produce a net flow. There has been a degree of interest and research into using magnetic materials to achieve this. In this work, we propose a new model employing ferromagnetic elements for construction of a practical microfluidic pump. The design is based on a repeated chain of magnetic discs connected together via links with hinges at the centers of the discs, which allow the discs to rotate (Fig 1a). While the model is based on that of ferromagnetic swimmers[1]. The device is surrounded by fluid and is activated by an external AC magnetic field. The magnetic and elastic forces in this device can work together against the fluidic forces to create a time-irreversible movement, which results in a net flow. While magnetisation of all the discs are oriented in the same direction, the relative rotational stiffness of the discs (or hinge stiffness) is varied to produce a lag in the response to the magnetic torque. This collective effect is similar to that of a metachronal wave, which is ultimately responsible for the flow. We found that if both discs had the same rotational stiffness, then no flow was produced. Depending on the chosen frequency, there is an optimal rotation stiffness of the two discs where a maximum flow rate is achieved. We observed as the frequency increases so does the flow, until the frequency is too large for the discs to turn to their maximum angle before the direction of the magnetic field reverses. To conclude, we demonstrated that an elasto-magnetic device can produce a net flow at low Reynolds number. The flow direction can be controlled by altering the frequency of the driving magnetic field or by using different rotational stiffness. These results could lead to new types of ferromagnetic pumping devices.References: [1] A. D. Gilbert, et al., Q. J. Mech. Appl. Math., 64, 239 (2011).

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