United States

Applying spintronics devices to neuromorphic computing have recently gained much attention. For example, a speech recognition task using a spin-torque oscillator (STO)
and based on the algorithm of physical reservoir computing was experimentally demonstrated [1]. In this experiment, the nonlinear magnetization dynamics in STO is used as a
computational resource, where the modulation of the dynamics due to the injection of human voice, converted to electric voltage, is used to recognize the input data. Therefore, it is
essential to investigate the relationship between the physical properties reflected in the magnetization dynamics and the computational capability of physical reservoir computing.
It has been widely believed that the computational capability of physical reservoir computing is enhanced at the edges of chaos because complex dynamics near the chaos is useful to
distinguish several kinds of input data. However, the physical reservoir computing in previous works has been performed in the dynamical state far away from chaos. Therefore, the
computational capability of STO near the edge of chaos is still unclear.
In this work, we investigated the relationship between the dynamical properties of STO and the computational capability in reservoir computing. We consider two kinds of STO, where the
one is a conventional STO consisting of a pinned (P) and free (F) layer, while the other, P/F/F, includes two free layers; see Fig. 1. This is because, in principle, the former cannot show
chaos while the latter has a possibility to show chaotic dynamics, and therefore, the comparison between them is useful to study the role of the chaos on the computational capability. We
evaluate the short-term memory capacity [2] as a figure of merit and the Lyapunov exponent [3] to distinguish the dynamical state. It was found that the short-term memory capacity in
P/F/F STO is greatly enhanced near the edge of chaos (see Fig. 2) and becomes much larger than the maximum value of the capacity in the conventional P/F STO.
References [1] J. Torrejon et al., Nature 547, 428 (2017).
[2] K. Fujii and K. Nakajima, Phys. Rev. Applied 8, 024030 (2017).
[3] S. H. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering (Westview Press, Boulder, CO, 2001).&lt;br&gt;

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/09c01428e1ce12b4a80fc7ddb5e1c030.png)&lt;br&gt;
Fig.1 Conceptual picture of (a) P/F and (b) P/F/F. &lt;br&gt;

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/03a7125ddd653ac21b4860e9c3be7f4c.png) &lt;br&gt;

Fig.2 (a) Short-term memory capacity and (b) Lyapunov exponent in P/F/F combination. &lt;br&gt;

MMM 2022

Computational Capability of Physical Reservoir Computing in Spin Torque Oscillator with Two Free Layers

Applying spintronics devices to neuromorphic computing have recently gained much attention. For example, a speech recognition task using a spin-torque oscillator (STO)
and based on the algorithm of physical reservoir computing was experimentally demonstrated [1]. In this experiment, the nonlinear magnetization dynamics in STO is used as a
computational resource, where the modulation of the dynamics due to the injection of human voice, converted to electric voltage, is used to recognize the input data. Therefore, it is
essential to investigate the relationship between the physical properties reflected in the magnetization dynamics and the computational capability of physical reservoir computing.
It has been widely believed that the computational capability of physical reservoir computing is enhanced at the edges of chaos because complex dynamics near the chaos is useful to
distinguish several kinds of input data. However, the physical reservoir computing in previous works has been performed in the dynamical state far away from chaos. Therefore, the
computational capability of STO near the edge of chaos is still unclear.
In this work, we investigated the relationship between the dynamical properties of STO and the computational capability in reservoir computing. We consider two kinds of STO, where the
one is a conventional STO consisting of a pinned (P) and free (F) layer, while the other, P/F/F, includes two free layers; see Fig. 1. This is because, in principle, the former cannot show
chaos while the latter has a possibility to show chaotic dynamics, and therefore, the comparison between them is useful to study the role of the chaos on the computational capability. We
evaluate the short-term memory capacity [2] as a figure of merit and the Lyapunov exponent [3] to distinguish the dynamical state. It was found that the short-term memory capacity in
P/F/F STO is greatly enhanced near the edge of chaos (see Fig. 2) and becomes much larger than the maximum value of the capacity in the conventional P/F STO.
References [1] J. Torrejon et al., Nature 547, 428 (2017).
[2] K. Fujii and K. Nakajima, Phys. Rev. Applied 8, 024030 (2017).
[3] S. H. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering (Westview Press, Boulder, CO, 2001). 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/09c01428e1ce12b4a80fc7ddb5e1c030.png) 
Fig.1 Conceptual picture of (a) P/F and (b) P/F/F. 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/03a7125ddd653ac21b4860e9c3be7f4c.png) 

Fig.2 (a) Short-term memory capacity and (b) Lyapunov exponent in P/F/F combination.

technical paper

#### Welcome to the 67th Annual Conference on Magnetism and Magnetic Materials, MMM 2022!

The Conference was held from October 31 to November 4 and offers both in-person and on-demand content.

MMM 2022 is sponsored jointly by AIP Publishing and the IEEE Magnetics Society. Members of the international scientific and engineering communities interested in recent developments in fundamental and applied magnetism are invited to attend and contribute to the technical sessions. The technical program will include invited and contributed papers in oral and poster sessions, invited symposia, a tutorial, and several special sessions. This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

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A recent theoretical paper [1] predicted a significant Dzyaloshinskii-Moriya interaction (DMI) and perpendicular magnetic anisotropy induced at the interface of hexagonal boron nitride (h-BN) and ultrathin cobalt (Co) crystals. 

The interfacial DMI of the Au/Co/h-BN heterostructure was investigated through the Brillouin Light Scattering technique (BLS) [2]. The Brillouin spectra consist of two peaks, Stokes (S) and anti-Stokes (AS), associated with counter-propagating spin waves, which are affected by DMI in opposite ways, and so have different frequencies [2]. The high sensitivity of the BLS technique allows detection of the small frequency differences and thus measures the DMI strength.

Fig.1-a shows the BLS data obtained from Si/SiO2/Ta/Au/Co(1 nm)/h-BN/Au at different values of wave vector kSW under an external magnetic field of -962 mT. The sokes and anti-Stokes difference (fAS-fS) varies linearly with kSW (Fig.1-c ) following the expected relation: fAS − fS = vDMI/π .kSW

The magnon non-reciprocal velocity vDMI is proportional to the DMI strength (vDMI = 2/π γ Ds / Ms t ) where DS is the DMI parameter.

The vDMI of the Au/Co/h-BN stack is vDMI ≈ 49 m/s, as large as the one reported for the Graphene/Co/Pt interface (vDMI ≈ 50 m/s) [3]. The vDMI decreases with the Co thickness confirming its interfacial nature.

To check that the large DMI obtained for Au/Co/h-BN emerges from the Co/h-BN interface and not from the Au/Co interface, we have measured a reference sample composed of Au/Co (1nm)/Al and obtained
vDMI ≈ 14 m/s, which is three times smaller than the Au/Co/h-BN proving that hBN induces a large DMI. A similar analysis was performed for the interfacial anisotropy, and we found that a significant anisotropy is induced by the h-BN/Co interface, as predicted [1]. 

**References** [1] A. Hallal et al., Nano Letters 21,17, 7138-7144 (2021)
[2] M. Belmeguenai et al., Physical Review B 91, 180405 (2015)
[3] F. Ajejas et al., Nano Letters 9, 5364-5372 (2018)
![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/cfdb85cb0373d5d85b9212a6db706d45.png)

Large Dzyaloshinskii Moriya interaction at the h

Convolutional neural networks (CNN) are state of the art algorithms for image processing. Despite a small number of synaptic weights, the CNNs remain computationally costly to train in software due to the necessity to exchange huge data flows between memory and processing units. Unconventional hardware is suited to address this limitation. In neuromorphic spintronics, it has been previously demonstrated that the spin diode effect can be used to apply a synaptic weight on a radiofrequency signal [1][2]. Here we go a step beyond, to show an experimental implementation of a convolutional layer employing chains of spin-diodes. We design a compact architecture of 3 chains with 3 spin-diodes connected in series, that performs a padded convolution with a filter of 3 pixels on 5 input pixels multiplexed in frequency in one RF signal (See Figure 1). The synaptic weights corresponding to the filter are encoded by a small frequency detuning between the inputs and the spin-diodes resonance and are controlled in parallel using currents in 3 strip lines. This architecture exploits the intrinsic weight redundancy of convolutions (all filters share the same weights) to enhance the compacity of the hardware and greatly simplify the process of updating a weight, only requiring updating a the current in one strip line. We will also present processed experimental results highlighting the scalability of the proposed architecture. An error on the performed convolution as low as 0.28% was achieved (See Figure 2). The proposed architecture enables us to both reduce the size of this hardware implementation while, at the same time, performing the convolution in one timestep contrary to previous time-multiplexed implementations. According to a previous study [3] we can achieve to decrease by one order of magnitude the energy consumption compared to current GPUs and two orders of magnitude in operating latency. This proof of concept of spintronic CNN, opens the path to spintronic neural networks that can exploit the power of convolutional layers in a fully parallel, compact, and energy efficient way.

Fully Parallel Convolution with Chains of Spin

Over the last decade, quantum systems offering new computational and sensing capabilities have emerged [1]. One of these promising hybrid systems involves the
interaction between photons and magnons. This interaction is quantitatively known by the strength coupling g and furthermore by its ratio with the cavity frequency g/ω. It exists three
different domains of this ratio: the Strong Coupling (SC) for g/ω < 0.1; the Ultra-Strong Coupling (USC) for 0.1 < g/ω < 1; and the Deep-Strong Coupling (DSC) for g/ω > 1. One of the
objectives of this last decade is to achieve the USC, and to approach the DSC [2]. A few experimental works already exist on the USC regime [3] and it is still complicated to understand
the different Hamiltonian approximations used to fit experimental data [2]. Here, we present a tuneable hybrid system which makes possible experimental observation of a coupling regime
from strong to ultra-strong at room temperature (RT).
The hybrid system presented here is made of a double re-entrant cavity and a commercial single crystal of YIG (see Fig. 1). It is possible to tune the ratio g/ω with decreasing the gap
between the top of pillars and cavity which will decrease ω without changing g. We optimized two different cavities considering two YIG shapes (sphere and slab). These two cavities work in the USC regime, from the SC/USC limit to g/ω = 0.6. One of these measures
is presented in Fig. 2 where is shown the S21 parameter according to a sweep on RF frequencies and the static H-field. With the use of Finite Element Modelling, we were able to follow the
coupling strength from the SC to the USC domains and were in a good agreement with measurements. We observed that the standard Hamiltonians (Dicke and Hopfield) do not describe
our system. With modifying the Dicke model with adding a frequency shift ωΔ on the FMR, we were able to fit measures and simulations. It should be noted that this added term is
proportional to g2/ω.
We demonstrated the capability of a 3D magnonic cavity to work in the USC regime and its tuneability
with playing with the gap. To reach the DSC, it will be interesting to work on other cavity shapes to have a bigger ratio g/ω.
**References** [1] D. Lachance-Quirion, Y. Tabuchi, A. Gloppe, Appl. Phys. Exp., vol. 12, p. 070101 (2019)
[2] I.A. Golovchanskiy, N.N. Abramov, V.S. Stolyarov, Phys. Rev. Applied., vol. 16, p. 034029 (2021)
[3] A.F. Kockum, A. Miranowicz, S. De Liberato, Nat. Rev. Phys., vol. 1, p. 19-40 (2019)

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/2bebaf6c860d0278cb8854b56f601370.png) 
Fig. 1: Machined cavity 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/8a647d4399590dfbaff83ff0e4148d48.png) 

Fig. 2: Spectral transmission S21

Spin Cavitronics System: from Strong to Ultra Strong Coupling

Amorphous magnetic systems provide a unique platform to study dynamics of exotic spin-textures which are fundamentally intriguing and potentially promising for
spintronics. A key question to address is how symmetric and anti-symmetric exchange coupling between atomic spins modulate the length scale of fluctuations near critical phase transition
points [1, 2]. Amorphous Fe-Ge thin films is a prototype system whereby controlling the Fe concentration one can tune the magnitude and randomness of the symmetric Heisenberg
exchange and anti-symmetric Dzyaloshinskii-Moriya interaction (DMI) respectively [3, 4]. In this work we performed soft x-ray photon correlation spectroscopy (XPCS) measurements to
probe the nanoscale magnetic fluctuations of stripe domains in amorphous FexGe1−x
thin films for x=0.51, 0.52 and 0.53 [5, 6]. At lower temperatures all the domains remain static but
with increase in temperature few domains of certain length scales start showing higher fluctuations indicative of intermittent behavior. As temperature reaches the phase transition, domains
of all length scales fluctuate collectively with increased magnitude showing the scale invariance nature at critical points. For similar reduced temperature, we observed dramatically
activated fluctuations for Fe = 0.51 concentration. Such enhanced fluctuations away from the critical temperature could be driven by the proximity from a critical point that is quantum in
origin [7]. The higher instability of the stripe domains with lowering in Fe concentration also corroborate the increased resistivity trend previously observed in those systems [3]. 
**References** 
1]. J. Wild, T. N. G. Meier, S. Pöllath, Science Advances., 3, e1701704 (2017)
2]. L. Shen, M. Seaberg, E. Blackburn, MRS Advances., 6, 221, (2021)
3]. D. S. Bouma, Z. Chen, B. Zhang, Phys. Rev. B., 101, 014402 (2020)
4]. R. Streubel, D. S. Bouma, F. Bruni, Advanced Materials., 33, 2004830 (2021)
5].S. K. Sinha, Z. Jiang, and L. B. Lurio, Advanced Materials., 26, 7764 (2014)
6]. M. Holt, M. Sutton, P. Zschack, Physical Review Letters., 98, 065501 (2007).
7]. Y. Feng, J. Wang, R. Jaramillo, Proceedings of the National Academy of Sciences., 109, 7224, (2012) 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/ade65df09f6f367e2c36a612872bc0e9.png) 

Figure 1. (a) Magnified images of the speckle pattern evolution at 210K for Fe = 0.52 from 1.9 sec to 1900 sec. Light blue and red color dotted circles showing a static and a dynamic
portion respectively of the speckle pattern. Mean intensity (gray colormap) and temporal heterogeneity (jet colormap) of (b, d, f & c, e, g) Fe0.51Ge0.49 and (h, j, l & i, k, m) Fe0.53Ge0.47 at
different temperatures. With increase in temperature more speckles fluctuate with higher amplitude. Red boxes in (b, h) maps the mean intensity with (c, i) fluctuation heterogeneity for
same Qr positions.

Domain Walls Dynamics in Randomized Dzyaloshinskii Moriya Interaction Mediated Amorphous Fe

Due to the strong spin fluctuation in two dimensions, the magnitude of the magnetization is highly dependent on both the exchange interaction and the magnetic anisotropy at any finite temperature and the existence of an energy gap is essential for the long-range order, which is known as the Wigner and Mermin theorem. As a result, the process of magnetic switching for the 2D magnets is completely different from the process we know for the 3D case. We show here several fundamentally different hysteresis properties between 2D and 3D magnets. The magnetization switching diagram known as the asteroid figure in the conventional Stoner-Wohlfarth model becomes highly temperature-dependent and asymmetric with respect to the transverse and longitudinal magnetic fields. Also, we show the difference in the magnetic switching dynamics between both cases. Our results provide new insights for 2D magnetic materials-based spintronics applications.

Magnetic Switching and Stoner Wohlfarth Model of 2D Single Domain Magnets

Under a longitudinal applied magnetic field, microwires increase/decrease length depending on the magnetostriction sign, where the magnetostrictive elongation is due to magnetization rotational processes as well known in classical magnetism. In amorphous alloys, magnetostriction is usually evaluated making use of inverse magnetoelastic effects (e.g., SAMR method) that sometimes is not fully reliable (e.g., for positive magnetostriction) [1]. 
This study in magnetostrictive and non-magnetostrictive amorphous microwires introduces two original aspects: i) Direct magnetostrictive elongation measurements as a function of applied field and tensile stress; and ii) Re-interpretation of the magnetization mechanism by comparing magnetostrictive elongation and magnetization curve. 
A home-made setup with suitable induction/pickup coils, a mechanical system to apply stress and a high-accuracy LVDT position sensor has been used to measure magnetization, M, and magnetostrictive elongation, δl/l,[2] in two amorphous microwire families: i) In-water-quenched (~145 μm diameter) highly magnetostrictive FeSiB, and vanishing positive/negative magnetostriction (CoFe)SiB microwires; and ii) Glass-coated FeSiBC microwire (20 μm diameter).
The figures show high-sensitivity (down to δl/l=10-8) representative data of δl/l vs. M/Mmax and H where the applied stress increases/reduces the elongation for negative/positive magnetostriction. Quantitative information on the rotational magnetization for low/high field regions is obtained: note in Fig. 1 the different elongation slopes for low (domain wall) and high (rotational) magnetization processes. It is also noticeable the magnetostrictive effect in Fig. 2 inset during domain wall motion in the tiny wire due to a helical magnetization component. This method to properly quantify the magnetostrictive elongation allows for a new magnetization/magnetostrictive analysis as required in mechanical sensor devices. 
**References:** [1] C. Gómez-Polo and M. Vazquez, J. Magn. Magn. Mater. 118, 86 (1993); K. Chichay et al., J. Appl. Phys. 116, 173904 (2014). 
[2] J. Moya et al., J. Magn. Magn. Mater. 476, 248 (2019). 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/1dc47202896b5978b613db88b267b339.png) 
Fig.1 Magnetostrictive elongation (δl/l) vs. Magnetization (M/Mmax) for a range of applied stresses (σ) in water quenched microwires. 
![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/2899920f693e4ffe650e3eedd4a9c203.png) 
Fig. 2 Magnetostrictive elongation (dl/l) vs. applied Field (H) in FeSiB glass-coated microwire. The inset shows the low-field magnetization and elongation loops.

Magnetization process evaluation and tensile stress effect in direct magnetostriction measurement of amorphous microwires

The process parameters optimization in laser powder bed fusion (LPBF) technique have been studied extensively by using the volumetric energy input (E=P/(v.t.h)) equation, which includes the major build parameters; laser power (P), scan speed (v), layer thickness (t) and hatch spacing (h) [1-3]. Even though utilizing laser energy density to predict final properties of a specified materials is a good way to start, only considering this is not enough [4]. Researchers have generally focused on the effect of laser power and scan speed on the final properties [5-8]. This study indicates how major process parameters influence the physical and magnetic properties of LPBF-processed Fe-based amorphous/nanocrystalline composites ((Fe87.38Si6.85B2.54Cr2.46C0.77 (mass%)). The figure illustrates the magnetization (M)-magnetic field (H) loops corresponding sample microstructures fabricated by using same E (=60 J/mm3) and v (=1000 mm/s) and varying P, h and t (left corner). It is obvious that despite being printed with same energy density, changing h and t (Sample 1 and 2) or changing P and h (Sample 2, 3 and 4) led to the quite different results. It was found that bulk density improves as P increases, v, t and h decreases, i.e., high E is necessary, however, greater than 80 J/mm3 (due to the keyhole effect) and less than 45 J/mm3 (because of the insufficient energy input to the powder bed) causes either failing parts or large and high number of pores. Owing to the laser scanning nature, the microstructure evolves as molten pool (MP) and heat affected zones (HAZ) due to the high thermal gradient occurred between laser tracks [9]. MP form around the scans, having Fe2B nanograins mainly, whereas HAZ generally contains α-Fe(Si) and Fe3Si nanocrystalline clusters. The sizes and quantities of those nanocrystallites determine the magnetic properties. With same E (60 J/mm3), v (1000 mm/s) and t (50 µm), only changing P and h caused samples to have different saturation magnetization; 206 emu/gr (P: 90 W and h: 30 µm) and 150 emu/gr (P: 150 W and h: 50 µm) (Figure). 
**References:** [1] H. Gong, K. Rafi and H. Gu, Materials and Design, Vol. 86, p. 545-554 (2015). 
[2] S. Liu, H. Li and C. Qin, Materials and Design, Vol. 191, ID: 108642 (2020). 
[3] H. Gong, K. Rafi and H. Gu, Additive Manufacturing, Vol. 1, p. 87-98 (2014). 
[4] K. Prashanth, S. Scudino and T. Maity, Materials Research Letters, Vol. 5, p. 386-390 (2017). 
[5] S. Alleg, R. Drablia and N. Fenineche, Journal of Superconductivity and Novel Magnetism, Vol. 31, p. 3565-3577 (2018). 
[6] H. Jung, S. Choi and K. Prashanth, Materials and Design, Vol. 86, p. 703-708 (2015). 
[7] Y. Nam, B. Koo and M. Chang, Materials Letters, Vol. 261, ID: 127068 (2020). 
[8] D. Ouyang, W. Xing and N. Li, Additive Manufacturing, Vol. 23, p. 246-252 (2018). 
[9] C. Zhang, D. Ouyang and S. Pauly, Material Science and Engineering R, Vol. 145, ID: 100625 (2021). 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/8a303fbd2fb2b87b8ef323cee9b2c17f.png) 
Figure: M-H loops and micrographs of the samples LPBF-processed with same E (=60 J/mm3) and v (=1000 mm/s).

Optimizing Laser Additive Manufacturing for Fe based Amorphous Magnetostrictive Materials

Hard-magnetic soft materials has a lot of application scenarios in the field of soft robots and flexible sensors. But, due to the coupling of magnetization process and
manufacturing process, the functions of these devices can not be changed. Therefore, the technique of repeatedly program magnetic anisotropy on magnetic elastomer is of great
significance for changing the functions of magnetic soft robot and sensor. This paper presented a reprogrammable mangetic elastomer based on
Liquid-metal/NdFeB/Silicone composites. The NdFeB particles wrapped in gallium can be re-orientated by thermal-ssisted magnetic programming(Figs.1a-1c). Thus, the magnetization
profile can be reconfigurated on the elastomer(Fig.1d).X-ray diffraction (XRD) analysis shows the phase composition of gallium, Silicone and Nd2Fe14B (Fig.2a). The elstomer's magnetic
properties are tested by the comprehensive physical property measurement system (PPMS). The moment-temperature (M-T) curve shows the material's moment jumps at 303 K（the melt
point of gallium)(Fig.2b). And the moment-magnetic field (M-H) curves indicate that the elastomer exhibit hard and soft magnetic properties respectively (Fig.2c), when the temperatureis
lower (293 K) or higher (313 K) than the phase-transition temperature of gallium. A hexagon-shape robot was manufactured and then programmed to two modals of grasping and walking
respectively(Figs.2d and 2e).The experimental results verify the reprogrammability of the proposed composite elastomer. The elastomer is expected to be used to manufacture multi-modal
magnetic soft robot. 

**References:** 

1. H. Chung, A. M. Parsons, L. Zheng.Magnetically Controlled Soft Robotics Utilizing Elastomers and Gels in Actuation: A Review. Advanced Intelligent Systems, 2020,
2000186. 
2. Y. Yan, Z. Hu, Z. Yang, etc. Soft magnetic skin for super-resolution tactile sensing with force self-decoupling. Science Robotics, 2021, 6, eabc8801. 
3. L. Cao, D. Yu, Z. Xia, etc. Ferromagnetic Liquid Metal Plasticine with Transformed Shape and Reconfigurable Polarity.Advanced Materials, 2020, 2000827. 
4. R. Zhao, H. Dai, H. Yao. Liquid-Metal Magnetic Soft Robot with Reprogrammable Magnetization and Stiffness.IEEE Robotics Automation and Letters, 2022, 7(2): 4535-4541. 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/53bc1b0331eab460b69cc42b5f1a161d.png)

Reprogrammable Liquid metal/NdFeB/Silicone Composite Magnetic Elastomer

Spin currents and spin-torques generated by spin-orbit coupling (SOC) are exploited in spintronics to meet the high data demand in information technology. Nowadays, the large SOC of 5d non-magnetic heavy metals (HMs) is required to generate a pure spin current by the spin Hall effect (SHE). In turn, the pure spin current generates a spin-orbit torque (SOT) on an attached magnetic layer [1]. 

It is generally accepted that in magnetic materials, the spin polarization of the generated spin current is aligned with the direction of the magnetization due to the exchange interaction. The generation of such spin current is referred to as the Spin Anomalous Hall Effect (SAHE) [2]. More recent theoretical works [3,4] have shown that the latter description is incomplete for magnetic materials with large spin-orbit coupling. In this case, the spin polarization can be preserved from alignment with the magnetization, as demonstrated in ferrimagnets [5]. The total spin current is therefore the sum of SAHE-like and SHE-like spin currents [2-4] as depicted in Fig 1. The SAHE-like spin current cannot induce a torque on the magnetization because the spin polarization is aligned with the magnetization. However, the SHE-like symmetry can generate a torque if the spin current is absorbed outside the layer. We refer this torque as self-torque because the material is the source of the torque on its magnetization. 

In this talk, we present the study of a ferrimagnet with strong spin-orbit coupling: GdFeCo. The SAHE and SHE spin current contributions are studied by complementary Spin Torque Ferromagnetic Resonance (ST-FMR) techniques and self-torque characterization were performed by means of harmonic Hall voltage measurements. We show in GdFeCo/Cu/NiFe trilayer that the ST-FMR voltage at NiFe resonance that is sensitive to GdFeCo SHE-like symmetry does not change sign across the magnetic compensation temperature [6]. The addition of a dc current to ST-FMR experiments allows to quantify the total contribution [6,7]. Additionally, we show in GdFeCo/Cu that the effective fields associated to the self-torques are amplified in the vicinity of the magnetic compensation temperature of the ferrimagnet and reverse their sign across it [7] (see Fig 2). Finally, we present more experimental results with signatures that highlight the difference between external SOT and self-torque taking advantage of characteristics temperatures in ferrimagnets. This study paves the way for further research into the generation of spin currents in ferrimagnets and the exploitation of self-torque generated in single magnetic layer for spintronic devices. 

This work was supported partially from Agence Nationale de la Recherche (France) under contract N° ANR-18-CE24-0008 (MISSION), ANR-19-CE24-0016-01 (TOPTRONICS) and ANR-17-CE24-0025 (TOPSKY), from the French PIA project “Lorraine Universite d’Excellence”, reference ANR-15IDEX-04-LUE. This study is partially funded by MSCA-RISE 2020-Project N°101007825 - ULTIMATE-I. D. C.-B., A.Y.A.C and H. D, acknowledge SPIN IJL team for their internship fellow 2018, 2019 and 2020, respectively. DCB also thanks “LUE Graduated” program internship 2019 from “Lorraine Université d’Excellence”. 
**References** [1] A. Manchon et al., Reviews of Modern Physics, vol. 91, no 3, p. 035004, (2019). 
[2] T. Taniguchi et al., Physical Review Applied, vol. 3, no 4, p. 044001, (2015). 
[3] V. P. Amin, et al., Physical Review B, vol. 99, no 22, p. 220405, (2019). 
[4] K-W. Kim, et al., Physical Review Letters, vol. 125, no 20, p. 207205, (2020). 
[5] Y. Lim, et al., Physical Review B, vol. 103, no 2, p. 024443, (2021). 
[6] H. Damas, et al., p. 2200035, PSS RLL (2022). 
[7] D. Céspedes, H. Damas, et al., Advanced Materials, vol. 33, no 12, p. 2007047, (2021). 

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Spin currents generation and self Spin Orbit torque in GdFeCo ferrimagnet

Symmetry plays a central role in determining the form of electrically-generated spin torques in magnetic devices. Here, we show that an unconventional out-of-plane damping-like torque can be generated in ruthenium oxide (RuO2)/permalloy devices when the Néel vector of the collinear antiferromagnet RuO2 is canted relative to the sample plane [1]. By measuring characteristic changes in all three components of the electric-field-induced torque vector as a function of the angle of the electric field relative to the crystal axes, we find that the RuO2 generates a spin current with a well-defined tilted spin orientation that is approximately parallel to the Néel vector. This dependence is the signature of an antiferromagnetic spin-Hall effect predicted to arise from momentum-dependent spin splitting within the bandstructure of RuO2, rather than from spin-orbit coupling [2]. The unconventional components are absent in the isostructural but non-magnetic rutile oxide IrO2[3]. The out-of-plane antidamping component of the spin torque from RuO2 is among the strongest measured in any material even with the antiferromagnetic domain structure uncontrolled, suggesting that high efficiencies are useful for switching magnetic devices with perpendicular magnetic anisotropy might be achieved by controlling the domain structure. 

**References:** 

[1] A. Bose, N. J. Schreiber, R. Jain, et. al. Nature Electronics 5, 267 (2022). doi.org/10.1038/s41928-022-00744-8 
[2] R. González-Hernández, L. Šmejkal, K. Výborný et al., Phys. Rev. Lett. 126, 127701 (2021). 
[3] A. Bose, J. Nelson, X. S. Zhang. et al. Effects of anisotropic strain on spin-orbit torque produced by the Dirac nodal line semimetal IrO2. ACS Appl. Mater. Interfaces 12, 55411–55416 (2020). 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/6a48eb9c2f8c65dbb2616e8a12630299.png) 

(a) Schematic representation of the tilted spin-current generated from RuO2 from the spin-split bands. Angular dependence of the generated torques in Py/(101)RuO2 bilayers originating from the y-component of the spins (a), z-component spins (b), and x-component spins (c), exhibiting angular dependence of cos2Φ, cosΦ, and sin2Φ respectively.

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