United States

A magnetic wire is one of the attractive candidates for high capacity memories and logic devices with low power consumption [1]. We reported that the wire of rare-earth transition metal (RE-TM) amorphous alloy show a current induced domain wall motion (CIDWM) with a faster wall speed of more than 1000 m/sec and a current induced magnetization switching (CIMS) with a lower current density of 5.5 MA/cm2 [2, 3]. However, domain creation method in the wire is one of the key technologies for their applications [4, 5]. In this paper, we demonstrate a laser assisted current induced magnetization switching in TbCo/Pt hetero-structure wire.
Figure 1 shows measuring setup for laser assisted current induced magnetization switching. A wire of 3 µm width is irradiated by laser spot of 1 µm diameter under applying both pulse current and external field. The film was fabricated on a thermally oxidized silicon substrate using a sputtering system. TbCo 12 nm layer was co-sputtered by Tb and Co targets and Pt layer was sputtered by Pt target as 2 nm under layer and 4 nm heavy metal layer. The film was patterned by SEM lithography with a liftoff method. CIMS was observed using a MOKE microscope.
Figure 2 shows 100 nsec pulse current dependencies of magnetizing switched domain diameter with/without laser assist, where external in-plane field of 500 Oe. The inset shows microscope view of the wire. Blue line showed a CIMS threshold for without laser assist. CIMS domain diameter increased with increasing current pulse heights. Laser assisted CIMS could reduce the threshold current more than 40 % that of without a laser assisted.
We demonstrated the laser assisted current induced magnetization switching of the magnetic wire. The method can reduce the current and controlled CIMS by laser. The laser assist CIMS is one of the attractive methods to create the domains in the magnetic wire.
This research was supported by KAKENHI (No. 20H02185, 21K18735, 21K14202), Japan.&lt;br&gt;&lt;br&gt;
**References**&lt;br&gt; [1] S. S. P. Parkin et al., Science 320, 190 (2008).
[2] D. Ngo et al., APEX Vol. 4, No. 9, 093002(2011).
[3] K. Asari et al., AIP Advances 7, 055930 (2017).
[4] S. Bandira et al., Appl. Phys. Let. Vol 99, No. 20, 202507(2011).
[5] N. Roschewsky et al., Appl. Phys. Let. Vol 109, No. 11, 112403(2016).
&lt;br&gt;&lt;br&gt;
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MMM 2022

Laser assisted current induced magnetization switching in a TbCo/Pt hetero structure wire

A magnetic wire is one of the attractive candidates for high capacity memories and logic devices with low power consumption [1]. We reported that the wire of rare-earth transition metal (RE-TM) amorphous alloy show a current induced domain wall motion (CIDWM) with a faster wall speed of more than 1000 m/sec and a current induced magnetization switching (CIMS) with a lower current density of 5.5 MA/cm2 [2, 3]. However, domain creation method in the wire is one of the key technologies for their applications [4, 5]. In this paper, we demonstrate a laser assisted current induced magnetization switching in TbCo/Pt hetero-structure wire.
Figure 1 shows measuring setup for laser assisted current induced magnetization switching. A wire of 3 µm width is irradiated by laser spot of 1 µm diameter under applying both pulse current and external field. The film was fabricated on a thermally oxidized silicon substrate using a sputtering system. TbCo 12 nm layer was co-sputtered by Tb and Co targets and Pt layer was sputtered by Pt target as 2 nm under layer and 4 nm heavy metal layer. The film was patterned by SEM lithography with a liftoff method. CIMS was observed using a MOKE microscope.
Figure 2 shows 100 nsec pulse current dependencies of magnetizing switched domain diameter with/without laser assist, where external in-plane field of 500 Oe. The inset shows microscope view of the wire. Blue line showed a CIMS threshold for without laser assist. CIMS domain diameter increased with increasing current pulse heights. Laser assisted CIMS could reduce the threshold current more than 40 % that of without a laser assisted.
We demonstrated the laser assisted current induced magnetization switching of the magnetic wire. The method can reduce the current and controlled CIMS by laser. The laser assist CIMS is one of the attractive methods to create the domains in the magnetic wire.
This research was supported by KAKENHI (No. 20H02185, 21K18735, 21K14202), Japan. 
**References** [1] S. S. P. Parkin et al., Science 320, 190 (2008).
[2] D. Ngo et al., APEX Vol. 4, No. 9, 093002(2011).
[3] K. Asari et al., AIP Advances 7, 055930 (2017).
[4] S. Bandira et al., Appl. Phys. Let. Vol 99, No. 20, 202507(2011).
[5] N. Roschewsky et al., Appl. Phys. Let. Vol 109, No. 11, 112403(2016).
 
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poster

#### Welcome to the 67th Annual Conference on Magnetism and Magnetic Materials, MMM 2022!

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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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Interfacial magnetic skyrmions are topological spin textures which have been proposed for use as information carriers in spintronic devices [1]. Hence, it is vital that their creation, annihilation, and motion can be accurately controlled [1]. Still, their thermal stability and interactions with lattice defects are not fully understood. Recently, many groups studied the skyrmion creation/annihilation energy paths by reconstructing associated free energy landscapes (FELs) and calculating the minimum energy paths, by combining micromagnetic simulations with an enhanced sampling technique called the nudged elastic band method (NEBM) [2]. However, micromagnetics and NEBM do not fully account for thermal effects. In addition, most computational models assume defect-free material interfaces with idealized magnetic parameters; while lattice defects alter the skyrmion dynamics and show potential to be used as pinning, destruction/creation points in future devices.

To address these, we use atomic scale magnetic simulations combined with an enhanced sampling technique named metadynamics to reconstruct non-trivial FELs of certain skyrmion degrees of freedom called as collective variables (CVs) in metadynamics. Metadynamics systematically adds a potential bias on the CVs to sample states outside of the thermodynamic equilibrium and explore the whole configurational space [3,4]. Traditionally, this has been used to understand how molecules bind to surfaces. Recently, metadynamics has been used in magnetism to study simple situations such as the temperature dependence of anisotropy CVs [5]. We use it to explore how spin textures interact with defects. Thus, we demonstrate that metadynamics can be extensively used in computational magnetism to study the behaviour of spin textures by selecting appropriate CVs. Mainly, we use metadynamics to study the thermal stability of skyrmions, via studying the annihilation/creation energy barriers as a function of temperature. Additionally, we investigate how various defects modify these FELs and their associated energy barriers. Ultimately, we explore if certain defects alter the skyrmion stability, trap/repel skyrmions, disturb their motion and prevent/help their creation/annihilation. 
**References** [1] A. Fert, N. Reyren, V. Cros, Nat Rev Mater 2, 17031 (2017)
[2] D. Cortés-Ortuño, W. Wang, M. Beg, et al. Sci Rep 7, 4060 (2017)
[3] A. Laio, L. Parrinello, PNAS 99, 20 (2002)
[4] G. Bussi, A. Laio, Nat Rev Phys 2, 200–212 (2020).
[5] B. Nagyfalusi, L. Udvardi, L. Szunyogh, Phys. Rev. B 100, 174429 (2019)

Metadynamics Calculations of Skyrmion Free Energy Landscapes

Currently, the commercialization of SOT-MRAM is hampered by high switching current density due to relatively low switching efficiency. One of the key parameters determines the switching efficiency is the spin hall angle (SHA, θSH). The maximum θSH of commonly used materials in foundries are: Ta (~-0.12), Pt (~0.1), and β-W (~-0.3) [1-3]. Even though there are promising SOT channel materials, like topological insulators (TI), showing high θSH > 1, the resistivity is several orders higher than above mentioned normal heavy metals (HM). Meanwhile, TI is hard for manufacturing as it consists of materials not friendly to be used in silicon-based fabs. Then, it is important to pursue high θSH for HM for the SOT-MRAM. The purpose of our study is to re-visit at the θSH of modified tungsten-based SOT channels. We demonstrated relatively high θSH up to -0.44 and low resistivity ~130 μΩcm in the nitrogen-doped W buffer (WN) /W interlayer/ferromagnetic hybrid system measured by spin-torque ferromagnetic resonance (ST-FMR). The θSH of the sample with WN/W SOT channel was nearly twice as large as 5nm β-W and 5nm β-WN (Fig. 1). The magnetic tunnel junctions (MTJ) with three kinds of SOT channels were also fabricated in order to check the device performance. Fig. 2 shows the typical R-J curves of MTJ devices by DC measurements. The switching current density of MTJs with the 3WN/2W SOT channel is 16.6 MA/cm2, which is 36.4% and 26.2% smaller than 26.1 MA/cm2 and 22.5 MA/cm2 respectively in the devices with 3.5W and 3.5WN SOT channels. The Damping like torques ξDL = TintθSH estimated from the switching current density is 0.28 for the system with 3WN/2W SOT channel, which is close to 2 times of that for the sample with 3.5W. The results from MTJ devices are consistent with values obtained from ST-FMR. Our promising results give potential solutions to the low switching efficiency issue for the W-based SOT-MTJ devices. 
**References** [1] Luqiao Liu, R. A. Buhrman, et al. Spin-torque switching with the giant spin hall effect of tantalum, Science 336 (6081) (2012) 555–558
[2] Minh-Hai Nguyen, R. A. Buhrman, et al. Spin torque study of the spin hall conductivity and spin diffusion length in platinum thin films with varying resistivity, Phys. Rev. Lett. 116 (2016) 126601
[3] Chi-Feng Pai, R. A. Buhrman, et al. Spin transfer torque devices utilizing the giant spin Hall effect of tungsten, Appl. Phys. Lett. 101 (2012) 122404 
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Enhanced charge to

The spin Hall effect (SHE) and the inverse spin Hall effect (ISHE) have been widely utilized to interconvert the charge and spin current. In them, the charge current, spin current and spin polarization are orthogonal to each other [1]. Based on the general tensor requirement of the spin-charge conversion, additional possibilities can be introduced when the order parameter, the magnetization of a ferromagnet, is involved [2]. We herein report the spin-charge conversion in perpendicular magnetized Ti(3 nm)/Co(0.6 nm)/Pd(2 nm)/[Co(0.4 nm)/Pd(2 nm)]4 multilayers, simplified as Co/Pd multilayers, with the spin pumping measurements. We unambiguously observed the anomalous inverse spin Hall effect (AISHE) in Co/Pd multilayers, where the charge current is collinear with the spin polarization. And both the sign and magnitude of AISHE can be linearly regulated by the out-of-plane magnetization of Co/Pd multilayers. Further, the observed amplitude ratio of AISHE/ISHE in spin pumping measurements is independent of the applied microwave frequency, indicating that it is a material specific parameter. 
**References** [1] J. E. Hirsch, Phys. Rev. Lett. 83, 1834 (1999).
[2] X. R. Wang, Commun. Phys. 4, 55 (2021). 
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Anomalous inverse spin Hall effect in perpendicular magnetized Co/Pd multilayers

Inverse Rashba-Edelstein effect (IREE) [1] refers to the spin-to-charge conversion at the interface/surface with strong spin-orbit coupling and broken symmetry. Ag/Bi related system is a prototype system for studying the IREE and has been hotly discussed but with a long-term controversy [2-5]. In a joint effort of both experiments and first-principles calculations, we reconcile almost all the published experimental data in literatures with controversial conclusions and provide a coherent picture on the pure spin transport between Ag/Bi and ferromagnets. We demonstrate a strong IREE at the interface between Ag/Bi with a ferromagnetic metal (FM) but not with a ferromagnetic insulator. This is in sharp contrast with the previously claimed IREE at Ag/Bi interface or inverse spin Hall effect dominated spin transport. In addition, a more than one order of magnitude modulation of IREE signal is realized for different Ag/Bi-FM interfaces, casting strong tunability and a new direction for searching efficient spintronics materials. 
**References** [1] V. M. Edelstein, Solid State Commun. Vol. 73, p. 233 (1990).
[2] J. C. R. Sánchez, L. Vila, and A. Fert, Nat. Commun. Vol. 4, p. 2944 (2013).
[3] M. Matsushima, Y. Ando, and M. Shiraishi, Appl. Phys. Lett. Vol. 110, p. 072404 (2017).
[4] D. Yue, W. W. Lin, and C. L. Chien, Phys. Rev. Lett. Vol. 121, p. 037201 (2018).
[5] J. H. Shen, Z. Feng, and X. F. Jin, Phys. Rev. Lett. Vol. 126, p. 197201 (2021). 

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A coherent picture on the pure spin transport between Ag/Bi and ferromagnets

Spin pumping is one of the most common ways to generate the desired spin current in experiment. With much shorter timescales than in ferromagnets (FM), antiferromagnetic (AFM) spin dynamics can offer much more attractive properties for potential applications in ultrafast spintronics devices. In recent years, although the AFM sub-terahertz spin pumping has been sucessfully observed, there is still some debate over the existence of cross-sublattice spin pumping in AFM. Here, we start from the most general form of AFM spin pumping and phenomenologically derive its Onsager reciprocal effect--current induced torque. By symmetry analysis we argue that the off-diagonal elements of spin-mixing conductance in net magnetization m and Neel vector n basis must vanish for a collinear AFM. The anti-damping like torques and cross-sublattice torques are shown to be proportional to the symmetric and asymmetric parts of the diagonal spin-mixing conductance respectively. For a conclusive evidence, we explicitly derive a more general form of spin-mixing conductance by scattering matrix method. For a insulating compensated AFM interface, the asymmetric parts of the diagonal spin-mixing conductance vanishes, manifesting the absence of cross-sublattice torques and spin pumping in collinear AFM. 
**References** [1] Ran Cheng, Jiang Xiao, Qian Niu, and Arne Brataas. Phys. Rev. Lett.113,057601 (2014).
[2] Akashdeep Kamra and Wolfgang Belzig.Phys. Rev. Lett.119,197201 (2017).
[3] Roberto E. Troncoso, Mike A. Lund, Arne Brataas, and Akashdeep Kamra. Phys. Rev.B 103, 144422 (2021).
[4] Kjetil M. D. Hals Yaroslav Tserkovnyak and Arne Brataas. Phys. Rev. Lett.106, 107206 (2011).

Absence of cross sublattice spin pumping and spin torques in collinear antiferromagnets: symmetry and microscopic theory

We numerically studied the spin transfer torque oscillation (STO) in a magnetic orthogonal configuration by introducing a strong biquadratic magnetic coupling [1]. The advantage of the orthogonal configuration is the high efficiency of spin transfer torque leading the high STO frequency, but it is difficult to maintain the STO in a wide range of electric current. By introducing a biquadratic magnetic coupling into the orthogonal structure, it became possible to expand the electric current region realizing the stable STO, resulting that a high STO frequency. In this report, we systematically compared STO properties between the orthogonal magnetization disks with and without the biquadratic magnetic coupling, that is, B12=0.0 and -0.6.
In our model, the orthogonal configuration is FePt 2 nm/spacer 2 nm/Co90Fe10, or Ni80Fe20, or Ni 2 nm. The time-domain magnetization precessions of the top layer Ni under current density J=0.5×107 A/cm2, 3.0×107 A/cm2, and 6.0×107 A/cm2 are shown in Fig.1 (a), (b) and (c). Only B12 was changed and A12 is set 0 for simplicity. In the case of the biquadratic magnetic coupling B12=0.0, the STO was observed only when J=0.5×107 A/cm2. Compared to this, in the case of B12=-0.6, the STO can be obtained in the wide range of J. This means that by introducing biquadratic magnetic coupling, we can expand the electric current region realizing the stable STO and increase the frequency. In Fig. 2, we show the STO frequency and the intensity as a function of the current density. First, even when the top layer is changed from Ni, to Ni80Fe20, or Co90Fe10, the current density region realizing the stable STO is widened by introducing the biquadratic magnetic coupling. In addition, we increased STO frequency and the intensity, meaning the stable STO. 
**References** [1] C. Liu, et al. IEEE Trans. Mag., 58 (2022) 172504.
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High Frequency Spin Torque Oscillation in Orthogonal Magnetization Disks with Strong Biquadratic Magnetic Coupling

Continued efforts toward both fundamental knowledge and application of spintronics rely on improved materials for converting spin to charge and vice-versa. We recently demonstrated that the longitudinal spin Seebeck effect (LSSE) [1] shows large spin-charge conversion and large spin Seebeck voltages of thermally-evaporated chromium thin films relative to sputtered platinum at room temperature. However, determining the exact nature and control of thermal gradients in LSSE experiments is imperative, especially at the interface [2,3]. In this work, we adopt the Hall bar geometry and current-driven heating [4,5] for LSSE experiments in a vacuum cryostat for better manipulation of thermal gradients. In figure 1, we show the LSSE signal for a 10 nm thin film of chromium (Cr) and 10 nm sputtered platinum (Pt) thin film both grown on a polycrystalline yttrium iron garnet (YIG) substrate under the same experimental conditions using Peltier devices to establish a thermal gradient external to the sample. Figure 2 shows the local LSSE signal for a 10 nm Cr and 25 nm Pt Hall bar utilizing a local heating method via Joule heating in a controlled vacuum cryostat environment. The high resistance of the evaporated Cr leads to very large local LSSE voltages, indicating this easily prepared film holds promise for probing thermally generated spin current phenomena in a range of magnetic insulators. 
**References** [1] Bleser, Greening, Roos, et al. J. Appl. Phys. 131, 113904 (2022).
[2] Sola, A., Bougiatioti, P., Kuepferling, M. et al. Sci Rep 7, 46752 (2017).
[3] A. Sola et al. IEEE Transactions on Instrumentation and Measurement, vol. 68, no. 6, pp. 1765-1773, June 2019.
[4] W.X. Wang, S. H. Wang, L. K. Zou, et al. Appl. Phys. Lett. 105, 182403 (2014).
[5] Michael Schreier, et al. Appl. Phys. Lett. 103, 242404 (2013). 
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Local spin Seebeck effect on polycrystalline YIG/thermally evaporated chromium bilayers

Spintronics is a prime candidate for information storage and logic devices due to its significant advantages over traditional CMOS technology, such as low-power consumption, non-volatility, and high endurance. Recently, spin-gapless semiconductors (SGSs) have been introduced for modern spintronics-based applications and are promising candidates for designing quantum computing, data storage, coding, and decoding. In SGSs, spin-polarized charge carriers or spin current are the primary functions of these magnetic materials [1]. SGS materials such as CoFeMnSi Heusler Alloy offer high spin polarization (64%), high Curie temperature (620 K), and low damping constant (0.0046) are all intriguing properties that can be used in room-temperature spintronic device applications [2]. SGS has unique features such as almost temperature-independent carrier concentration, and quantum linear magnetoresistance in a low-temperature range [3].
In this abstract, the effect of changing the sputtering power from 30W to 50W and 90W on an RF sputtered thin film of CoFeMnSi (CFMS) Heusler alloy with a nominal thickness of 30 nm with temperature-dependent electrical and magneto-transport properties has been studied. Fig. 1(a) shows Hall resistivity as a function of applied magnetic field for CFMS 90W (30nm) thin-film recorded at 10K, 50K, 100K, 200K, 250K, and 300K. Fig. 1(b) demonstrates the SGS behavior of the material in nearly temperature-independent carriers' concentrations with the same order up to 300K. Fig. 1(c) depicts magnetoresistance (MR) curves of 90W (30nm) CFMS thin film within the temperature range of 10K to 200K. The MR curves exhibit a linear field-dependent trend. In this temperature range, the observed MR is negative. The peak presence at zero magnetic fields signifies the localization and as we increase the field, the path contributing to localization is go out of the phase. 
**References** [1]. D. Rani, L, Bainsla, A. Alam, and K. G. Suresh, “Spin-gapless semiconductors: Fundamental and applied aspects”, Journal of Applied Physics, vol. 128, no. 22, 2020.
[2]. L. Bainsla, A. I. Mallick, M. Raja, A. K. Nigam, B. Varaprasad, Y. Takahashi, A. Alam, K. G. Suresh, and K. Hono “Spin gapless semiconducting behavior in equiatomic quaternary CoFeMnSi Heusler alloy”, Physical Review B, vol. 91, 2015.
[3]. X. L. Wang, “Proposal for a new class of materials: spin gapless semiconductors”, Physical review letters, vol. 100, 2008. 
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Study of Cobalt Based Spin Gapless Semiconducting Heusler Alloy Thin Film

We report a large spin-current generation from the interface of the Ti/Pt bilayer. By doing the spin-torque ferromagnetic resonance (ST-FMR)1 in Ti(5)/Pt(1.5)/Py(5)/Pt(1.5) heterostructure, we observe a large enhancement of the damping-like torque that cannot be explained by the spin Hall effect (SHE) of Pt due to the cancellation of the spin-current generated from the symmetrically placed Pt layers on either side of the ferromagnet. We observe that the sign of damping-like torque generated in Ti/Pt/Py/Ti heterostructure is opposite as compared to Pt/Py bilayers which rule out the possibility of the conversion of orbital-current generated by Ti into the spin-current using the spin-orbit coupling of Pt2–5. This effect is reproduced for different thicknesses of Py (4 -8 nm). We confirm that this effect disappears when Pt is substituted by Cu. All these pieces of evidence together suggest a possible formation of the Rashba surface at the Ti/Pt interface due to their work function difference (approximately 1.3 eV). This could be a way to boost up the generated spin-current by exploiting the interfacial Rashba-Edelstein effect and bulk spin hall effect together for practical applications. 
**References** 1 L. Liu, T. Moriyama, D.C. Ralph, and R.A. Buhrman, Phys. Rev. Lett. 106, 1 (2011).
2 D. Go, F. Freimuth, J.P. Hanke, F. Xue, O. Gomonay, K.J. Lee, S. Blügel, P.M. Haney, H.W. Lee, and Y. Mokrousov, Phys. Rev. Res. 2, 1 (2020).
3 Y. Choi, D. Jo, K. Ko, D. Go, and H. Lee, ArXiv:2109.14847v1 1 (2021).
4 S. Lee, M.G. Kang, D. Go, D. Kim, J.H. Kang, T. Lee, G.H. Lee, J. Kang, N.J. Lee, Y. Mokrousov, S. Kim, K.J. Kim, K.J. Lee, and B.G. Park, Commun. Phys. 4, 3 (2021).
5 S. Ding, A. Ross, D. Go, L. Baldrati, Z. Ren, F. Freimuth, S. Becker, F. Kammerbauer, J. Yang, G. Jakob, Y. Mokrousov, and M. Kläui, Phys. Rev. Lett. 125, (2020). 
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Large spin current generation from the Rashba surface at Ti/Pt interface

Transition metal dichalcogenides (TMDs) are potential materials for exerting efficient spin-orbit torque (SOT) on the adjacent ferromagnetic (FM) layer due to their high spin-orbit coupling (SOC) and broken inversion symmetry at the interface [1]. An unconventional SOT is recently observed in WTe2/NiFe heterostructures due to low symmetry in WTe2 [2]. PtSe2 is one of the TMDs having high SOC [3]. In this work, we measured the effective spin Hall efficiency (SHE) in PtSe2/NiFe/Pt heterostructure using spin-torque ferromagnetic resonance (STFMR). PtSe2 was synthesized by salinization of a sputtered Pt (3 nm) film. The growth of PtSe2 was confirmed using Raman measurements, which shows two peaks at 176 cm-1 (Eg) and 206 cm-1 (A1g). Subsequently, a 6 nm thick NiFe (Py) layer followed by Pt (3 nm) capping layer was deposited on PtSe2 using magnetron sputtering. For STFMR measurements, RF current of frequency varying from 3 GHz to 7 GHz was applied to the device in the presence of an external magnetic field (H). The mixing voltage (Vmix) across the device was measured and the symmetric & anti-symmetric components (VS, VA) of Vmix, linewidth (ΔH), and resonance field (Hr) were extracted (Fig.1) from the fitting of STFMR spectra. Effective SHE was calculated using the ratio of VS and VA and found to be increased 33% for PtSe2/Py/Pt compared to reference (Py/Pt). This change in SHE is due to the presence of PtSe2, which was further confirmed by making a stack with Pt/Py/Pt structure. STFMR signal of all three stacks has been compared in Fig. 1 (a). No clear signal was observed for Pt/Py/Pt which confirms the presence of SOT due to PtSe2. Damping parameter was extracted by the fitting of linewidth (ΔH) vs. frequency (f) curve (Fig. 2) and was found to be enhanced by 131% in the case of PtSe2/Py/Pt compared to its reference Py/Pt. Large enhancement in damping parameter indicates large spin pumping into PtSe2. These results indicate the suitability of using PtSe2 as a potential material for spin-orbit torque. 
**References** [1] Q. Shao et al., Nano Letter 16, 7514-7520 (2016)
[2] D. MacNeill et. al., Nature Physics, 13, 300-305 (2017)
[3] Marcin Kurpas and Jaroslav Fabian, Physical Review B, 103, 125409 (2017)
 
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