France



We identified and exploited a novel mechanism in an emerging branch of spintronics based on transport phenomena governed by crystal and magnetic symmetries, and its interplay with the antiferromagnetic order [1]. In this talk, we will focus on the origin of the subsequent experimental observation of a large spontaneous Hall effect in the Mn&lt;sub&gt;5&lt;/sub&gt;Si&lt;sub&gt;3&lt;/sub&gt; antiferromagnet, arising mostly by time-reversal symmetry breaking. These findings could prove essential for the development of robust large effects, vital in new device concepts.&lt;br/&gt;&lt;br/&gt;More specifically, the Zeeman effect is among the cornerstones of quantum physics that contributed to the development of spintronics. To date, the Zeeman spin-splitting of atomic energy levels or bands in crystals has been associated with the presence of a magnetic dipole. Countering the established physical picture [2-4], we identify an antiferromagnet with a band-structure comprised of separated crystal-momentum valleys with opposite Zeeman spin-splittings, which allows for their probing and exploiting by analogous electron-transport phenomena as used for the Zeeman effect in the presence of the magnetic dipole.&lt;br/&gt;&lt;br/&gt;In this talk we focus on one of the most prominent consequences of spin splitting – the spontanous Hall effect. We experimentally demonstrated its presence in Mn&lt;sub&gt;5&lt;/sub&gt;Si&lt;sub&gt;3&lt;/sub&gt; an antiferromagnet with separated Zeeman spin-split valleys [1]. We carefully disentangled various contributions to the measured transversal signal and we show that the signal is dominated by a robust spontaneous (present at zero magnetic field) Hall contribution with broad coercivity, which can only be attributed to the antiferromagnetic Zeeman effect. We further present structural, magnetization and magneto-transport results in a sample series and discuss the role of epitaxial growth on our results.

**References:**

[1] H. Reichlova, R. L. Seeger et al, under review. arXiv:2012.15651&lt;br/&gt;[2] L. Néel. Magnetism and Local Molecular Field. Science 174, 985-992 (1971).&lt;br/&gt;[3] N. J. Ghimire et al. Large anomalous Hall effect in the chiral-lattice antiferromagnet CoNb&lt;sub&gt;3&lt;/sub&gt;S&lt;sub&gt;6&lt;/sub&gt;. Nat. Com. 9, 3280 (2018).&lt;br/&gt;[4] C. Sürgers, et al. Large topological Hall effect in the non-collinear phase of an antiferromagnet. Nat. Com. 5, 3400 (2014).

**Images:**





INTERMAG 2021

 Spontaneous Hall effect in the Mn5Si3 antiferromagnet, due to antiferromagnetic Zeeman spin-splitting

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We identified and exploited a novel mechanism in an emerging branch of spintronics based on transport phenomena governed by crystal and magnetic symmetries, and its interplay with the antiferromagnetic order [1]. In this talk, we will focus on the origin of the subsequent experimental observation of a large spontaneous Hall effect in the Mn5Si3 antiferromagnet, arising mostly by time-reversal symmetry breaking. These findings could prove essential for the development of robust large effects, vital in new device concepts. More specifically, the Zeeman effect is among the cornerstones of quantum physics that contributed to the development of spintronics. To date, the Zeeman spin-splitting of atomic energy levels or bands in crystals has been associated with the presence of a magnetic dipole. Countering the established physical picture [2-4], we identify an antiferromagnet with a band-structure comprised of separated crystal-momentum valleys with opposite Zeeman spin-splittings, which allows for their probing and exploiting by analogous electron-transport phenomena as used for the Zeeman effect in the presence of the magnetic dipole. In this talk we focus on one of the most prominent consequences of spin splitting – the spontanous Hall effect. We experimentally demonstrated its presence in Mn5Si3 an antiferromagnet with separated Zeeman spin-split valleys [1]. We carefully disentangled various contributions to the measured transversal signal and we show that the signal is dominated by a robust spontaneous (present at zero magnetic field) Hall contribution with broad coercivity, which can only be attributed to the antiferromagnetic Zeeman effect. We further present structural, magnetization and magneto-transport results in a sample series and discuss the role of epitaxial growth on our results.

**References:**

[1] H. Reichlova, R. L. Seeger et al, under review. arXiv:2012.15651 [2] L. Néel. Magnetism and Local Molecular Field. Science 174, 985-992 (1971). [3] N. J. Ghimire et al. Large anomalous Hall effect in the chiral-lattice antiferromagnet CoNb3S6. Nat. Com. 9, 3280 (2018). [4] C. Sürgers, et al. Large topological Hall effect in the non-collinear phase of an antiferromagnet. Nat. Com. 5, 3400 (2014).

**Images:**

technical paper

Mechanisms for voltage control of magnetism are often based on strain or charge effects. Recently, a new approach based on electrochemical mechanisms was discovered. Due to the ionic reactions involved, it is promising especially for large and non-volatile voltage induced effects on the magnetic properties.[1,2] In the charge-based or electrochemical approach, the fast majority of publications reports on Co-based thin films with perpendicular anisotropy. In our study, we focus on a distinctly different system, namely FeOx/Fe thin films with uniaxial in-plane anisotropy. Although films with uniaxial in-plane anisotropy hold great potential for switchable artificial magnetic stray field landscapes for lab-on-a-chip or for giant magnetoresistance sensors, there are no reports of electrochemical voltage control of such films yet. We demonstrate that significant effects on their magnetic properties can be achieved via electrolytic gating. The detailed analysis of the interplay between electrochemical processes and hysteresis, anisotropy and domain changes allow us to reveal an oxygen-based tuning of the Néel wall interactions as the underlying mechanism. The thin films are composed of 3nm FeOx and 5nm Fe. In-plane angular magnetometry measurements show the presence of a uniaxial anisotropy. Along the easy axis, the shape of the magnetization curve is close to rectangular. Nevertheless, the hysteresis along the hard axis is more rounded and the coercivity (HC) is comparable with the HC along the easy axis (red curve in Figure 1 a). This behavior is known to be caused by charged Néel domain wall interactions. These interactions block the rotation of the magnetization and lead to a large hysteresis along the hard axis. Upon voltage application, HC strongly decreases along every angle. In the vicinity of the hard axis, HC almost completely vanishes (blue curve in Fig. 1 a). As HC and anisotropy are strongly correlated, we investigate the anisotropy of the thin film via anhysteretic measurements. We find an increase of the uniaxial anisotropy energy density upon the voltage-triggered oxide-metallic transformation. This is an unusual finding as it is often assumed in voltage control of magnetism that HC and anisotropy are directly proportional to another. Obviously, this simple model is not applicable here. Instead, changes in the microstructure or the magnetic domain structure dominate over direct anisotropy effects. To evaluate how the magnetic domain structure is affected, we investigated the AC-demagnetized state, which resembles the equilibrium domain state. Upon a low voltage application (1V), and thus transforming the FeOx to metallic Fe, the domain size significantly increases, see Fig. 1 b and c. In order to understand the domain coarsening, we approximated the change in the surface energy density for the Néel walls. This calculation shows an increase in domain-wall energy of 40% upon the oxide-metal transformation, which could explain the decrease in the number of domain walls and the associated increase in the domain size. In order to propose a consistent mechanism which explains the observed changes, we focused on the specific properties of the magnetically charged Néel walls. The Néel domain wall interactions becomes a significant factor, as soon as their tails overlap which is when the domain width is smaller than two times the tail width. With the extracted domain size from Fig. 1, we calculated strong interactions for the oxidized state. For the oxide to metal transformation, the interactions are significantly decreased. A comparable trend is expected and also observed in the remanent state. As a result, the tails would not overlap and we thus expect significantly fewer interactions between the walls in the reduced state. This is consistent with the observed voltage controlled deblocking. To demonstrate the technological relevance, we demonstrated that our electrochemical based switching mechanism allows for 180° magnetization reversal along the easy axis. Purely magnetic field reversal shows the nucleation and growth of magnetic domains (Fig. 2 (a) red curve and (b)). In comparison, during voltage assisted switching, the magnetization reversal occurs at a lower field within seconds (Fig. 2 (a) blue curve and (c)). Assuming a linear relation between the electrode diameter and the switching energy, we estimate the energy efficiency of this process to be 5fJ for an electrode diameter of 3nm. These value approaches the same range as for the so far lowest reported switching energies. Interestingly, the domain evolution is similar to the reversal process induced by a magnetic field. This indicates that the nucleation sites and the local distribution of pinning sites that affect the reverse domain growth do not change substantially during the reduction process. However, the E-induced switching proceeds at much lower magnetic field, which points to a substantially reduced pinning strength during the FeOx to metal Fe transformation. The reversible and low voltage (1V) control of defect sites might be transferrable to other defect-controlled materials, such as type II superconductors or materials with specific mechanical properties.[3]

**References:**

[1] C. Navarro-Senent, A. Quintana, E. Menéndez, E. Pellicer, J. Sort, APL Materials 2019, 7, 030701. [2] C. Song, B. Cui, F. Li, X. Zhou, F. Pan, Progress in Materials Science 2017, 87, 33. [3] J. Zehner, I. Soldatov, S. Schneider, R. Heller, N. B. Khojasteh, S. Schiemenz, S. Fähler, K. Nielsch, R. Schäfer, K. Leistner, Adv. Electron. Mater. 2020, 6, 2000406.

**Images:**

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/d35959871426edaba9a12be7d3a1dbc5.jpg)
Fig.1: Magnetization curves and magnetic domains in the FeOx/Fe state (red curve in (a) and domains in (b)) and in the Fe state, blue curve in (b) and domains in (c).

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/5d4968e18040b7ba8b1145609a0e0b42.jpg)
Fig.2: E-induced 180° switching of magnetization (M). (a) pathway for H- and E-induced M-reversal. (b) H-induced and (c) E-induced M-reversal.

 Voltage control of Néel domain wall interactions and pinning sites

Exchange bias is a well-known and very useful effect that occurs due to an interfacial coupling between adjacent thin films of an antiferromagnet and a ferro(ferri)magnet [1]. Controlling exchange bias in an antiferromagnet/ferro(ferri)magnet thin film system by application of a gate voltage is much sought-after for spintronic applications. However, since the exchange bias effect is related to the ordering of spins in both the antiferromagnet and the ferro(ferri)magnet, and electric fields have little influence over the spin order, electrical control of exchange bias is very hard to achieve practically. Recently, ionic gating of magnetic heterostructures, where a gate voltage is used to drive ions (O2-, H+ etc.) in or out of the active layers, has yielded very interesting and promising results. Due to the size of the H+ ion, protonic gating is potentially faster and more reversible compared to gating with other ions and is also able to cause large changes in magnetic properties in the underlying active layers, such as modulation of perpendicular magnetic anisotropy in ultra-thin Co films [2]. The utility of protonic gating was further demonstrated when it was shown that ferrimagnetic order in GdCo metal thin films can be dynamically controlled by this method [3]. GdCo is comprised of two sub-lattices, one made up of Gd atoms and one of Co atoms, and the magnetic moments in each sub-lattice point in opposite directions, hence resulting in ferrimagnetic order. Experimental and theoretical analyses show that the protons being inserted into the GdCo reduce the effective magnetic moment of the Gd atoms, and by starting from a Gd-dominated magnetic state, the overall magnetization can be switched 180 degrees through proton gating. Harnessing this functionality, we have shown, in this work, that exchange bias toggling is possible when we incorporate the GdCo ferrimagnet in an exchange biased heterostructure with NiO serving as the antiferromagnet. Using sputter deposition we have engineered a stack with the structure NiO(33)/Pd(1)/GdCo(10)/Pd(10)/GdOx(30)/Au(3) on thermalized Si, which has fully shifted loops, i.e. the exchange bias field is larger than the coercive field (HEB&gt;HC), as depicted in Fig. 1(a). When a sufficiently high (&gt;1.5V) positive voltage is applied to the Au top electrode (Pd serves as the bottom electrode), atmospheric water is split and the proton is transported through the GdOx electrolyte, into the GdCo(10)/Pd(10) layers. Starting from a Gd-dominated state of the GdCo, upon enough insertion of hydron ions after applying +1.8V, the dominant sublattice of GdCo switches from Gd to Co, as expected from previous work, but is now also accompanied by a toggling of the exchange bias direction, as shown in Fig. 1(b). The effect is fully reversible, as shown in Fig. 1(c). We can understand this phenomena when we realize that although the gating does nothing to the relative spin orientation in either the ferrimagnet or the antiferromagnet, the ferrimagnet’s magnetization direction depends not only on the spin orientation of the sublattices but also on the relative magnitude. The magnetization direction flips 180 degrees during gating but the relative spin orientation across the interface remains the same. Essentially, if initially the pinned magnetization is +Mz (meaning HEB is -ve) then after gating the pinned magnetization will be -Mz necessarily making HEB +ve. To the best of our knowledge, this is the simplest demonstration of exchange bias toggling to date, since our system does not rely on any complex materials or growth processes and works at room temperature, as opposed to some previous works [4,5]. Due to the small size of the proton, our method is highly reversible, and initially we have shown full cycling toggling of the exchange bias up to 10 times, where the hysteresis loop remains fully shifted throughout the process (Fig. 2) as evidenced by HEB/HC being over 1. We believe our simple but robust method to toggle exchange bias can serve as a platform for demonstrating more functionalities and/or devices and can have broad implications for spintronics in general. This work is supported in part by SMART, one of seven centers of nCORE, a Semiconductor Research Corporation program, sponsored by National Institute of Standards and Technology (NIST).

**References:**

[1]. Y. Fan et al., Nature Nanotechnology, Vol. 8, p. 438 (2013) [2]. A.J. Tan et al., Nature Materials, Vol. 18, p. 35 (2019) [3]. M. Huang et al., manuscript under review [4]. S. Wu et al., Physical Review Letters, Vol. 110, p. 067202 (2013) [5]. X. He et al., Nature Materials, Vol 9, p. 579 (2010)

**Images:**

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/36bc1892deb385267892bf4aee4bb5dd.jpg)
Fig. 1. MOKE hysteresis loops of the structures described in the text in the (a) initial state, (b) after applying +1.8V for 180s and (c) after applying 0V for 80s. The MOKE signal follows the Co magnetic moments, which is why in the Gd dominated state (a) and (c) the loops are inverted

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/ee59777b4e38f83110d076127ab1a339.jpg)
Fig. 2. Reversible toggling of exchange bias in sample with fully shifted loops, where the voltage was toggled between +1.8V and 0V with period of 40s. Note that the erratic oscillations in EB towards the latter cycles are due to noise during measurement of individual hysteresis loops

 Exchange Bias Toggling in GdCo/NiO Thin Film System by Solid-State Hydrogen Gating

Magnetic random-access memory (MRAM) has recently emerged as a promising way for next generation memory due to its nonvolatility, low power consumption and high density. How to achieve energy-efficient magnetization switching is one of the main challenges for MRAM. Recent studies propose spin orbit torque (SOT) as a promising method for data writing [1]. However, an external magnetic field along current direction is usually needed to realize deterministic switching. It can be overcome by using antiferromagnet/ferromagnet structures in which exchange bias can replace external field [2]. Voltage controll of magnetic anisotropy (VCMA) is another candidate method for lowering down the energy height by inducing electron accumulation at the ferromagnet/oxide interface[3]. Combination of VCMA and SOT effect may lead to decrease of power consumption by a gate voltage lowering the energy barrier height. For example, Yoda et.al propose a new spintronics-based memory employing the VCMA effect as a bit selecting principle and the SOT effect as a writing principle. [4]. Back et al reported that a gate voltage can be used to manipulate both perpendicular magnetic anisotropy and spin orbit torque[5]. Hence, it is essential to make it clear whether the voltage-controlled spin-orbit effective torques (VCSOT) or voltage controlled magnetic anisotropy causes the decrease of critical current, or both. In this work, we investigate VCSOT effect and VCMA effect in the IrMn/CoFeB/MgO structures. The film structures were thermally oxidized Si substrate/Ta(2)/IrMn(5)/CoFeB(0.94)/MgO(2.5)Al2O3(5), (with film thickness in nm in the parentheses). The films were patterned into Hall bar by ion beam etching (IBE) and lithography as shown in Fig. 1(a). Fig. 1(b) shows the micrograph of the Hall bar and the measurement setup. Furthermore, to explore voltage-gated SOT switching, a gate voltage is applied at the top electrode and the switching loops are obtained with no external field applied as shown in Fig. 1(d). Figure 1(f) presents critical current densities with 5mT field under different gate voltages. The critical current density Jc shows a decreasing tendency with increasing VMgO. These results indicate that a gate voltage can be used to effectively modulate SOT-driven perpendicular magnetization switching and this is a feasible writing method for low energy consumption. Next, spin-orbit effective fields at the different voltage were measured by using a second harmonic method as shown in Fig. 2 (a). The damping-like torque efficiency decreases with positive voltage increasing, whereas the field-like torque efficiency shows weaker voltage dependence. These results demonstrate that VMgO can modulate spin torques in IrMn/CoFeB/MgO system. The damping-like torque efficiency under VMgO of -0.4 V is 1.5 times larger than that under VMgO of 0.4 V. A larger JC is required for the magnetization switching under positive voltage due to the reduction of θSHE. Through VCSOT effect, positive voltage tends to increase Jc, which is reverse to the experimental results in Fig. 1(f). In-plane hysteresis loops at different gate voltages are obtained as shown in Fig. 2(b). The dependence of anisotropy energy Keff(VMgO) on gate voltage is shown in Fig.2 (c). By linear fitting, Keff decreases by 55% when VMgO changes from -0.6V to 0.6V. According to theoretical research from Ref.[6], the Jc for SOT switching is proportional to Keff. Therefore, the decrease of Keff will lead to significant reduction of Jc. Figure 2(d) shows the interfacial anisotropy coefficient Ki. We can see that the Ki changes linearly with VMgO due to VCMA effect. From the slope of the linear fitting, the VCMA coefficient ξ of 34.3 fJ/Vm is obtained for IrMn/CoFeB/MgO structure. Therefore, VCSOT effect is not the reason for the reduction of Jc in the voltage-gated SOT switching. The decrease of Jc in the voltage-gate SOT switching is mainly caused by the reduction of PMA due to VCMA effect. In summary, we demonstrate field-free switching in the IrMn/CoFeB/MgO structures and show the critical switching current can be modulated by the control voltage. Moreover, VCSOT effect and VCMA effect are explored. We measured spin-orbit effective torques under different voltage. We concluded that through VCSOT effect, positive voltage tends to increase Jc, which is reverse to the experimental results. Next, we measured anomalous Hall resistance at different voltage to explore VCMA effect. From quantitative calculation, the critical switching current at different voltage is consistent with experiments. Therefore, we concluded VCSOT effect hindered the reduction of Jc, while the VCMA effect made a main contribution to the Jc reduction. This work provides comprehensive understanding of voltage-gated spin torque switching.

**References:**

[1] M. Miron, K.Garello and G. Gaudin., Nature, vol. 476, no. 7359, pp. 189–193. (2011). [2] S.Z. Peng, D. Q. Zhu and W S Zhao., Adv. Electron. Mater. Vol. 5 pp. 1100134. (2019). [3] W.G. Wang, M. Li and C.L.Chien., Nat.Mater, vol. 11, no. 1, pp. 64–68. (2012). [4] H. Yoda, N. Shimomura and A. Kurobe., IEEE Electron Devices Meet. (IEDM). pp. 27.6.1-27.6.1. (2016). [5] L. Chen, M.Gmitra and C.H.Back., Nat. Electron., vol. 1, no. 6, pp. 350–355, (2018). [6] K.S. Lee, S.W. Lee and K.J. Lee., Appl. Phys. Lett. vol.102, pp. 112410. (2013).

**Images:**

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/1ed57da223949489824ad933c4957076.jpg)
Fig.1 (a) Schematic of IrMn/CoFeB/MgO structures. (b) Micrograph of the Hall bar and the measurement setup. (c) SOT-driven magnetization switching with various in-plane external field. Voltage-gated SOT switching under different gate voltages with (d)no external field and (e)5 mT in-plane external field. (f) Critical current density Jc dependence on voltage applied to MgO (VMgO) with 5 mT field applied.

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/177e5ff0550d0f2846103ad2879572c8.jpg)
Fig.2 (a) The dependence of spin-orbit effective torques on voltage in MgO layer (VMgO). The error bars are standard deviations. (b) Anomalous Hall resistance (RHall) under different gate voltages (VMgO) (c) Keff and (d) Ki dependence on VMgO.

 Experimental demonstration of voltage-gated spin-orbit torque switching in antiferromagnet/ferromagnet structure

The voltage control of magnetic anisotropy (VCMA) is an active field of research, as it is a promising route towards the realization of low power spintronic devices. Among a few proposed VCMA mechanisms, voltage-induced oxygen migration (i.e., magneto-ionic effect) has demonstrated large modulation of magnetic anisotropy. In this work, we study the voltage control of the interfacial perpendicular magnetic anisotropy (PMA) in a series of Pt/Co/MOx (M=Al and Tb) trilayers [1]. The stacks were patterned by electron beam lithography and ion beam etching into stripes (1 – 50 µm width) then covered with a 10 nm thick ZrO2 dielectric layer and a 6 nm thick Pt top electrode to form capacitor-like structures. We show a large modification of interfacial magnetic anisotropy (β&gt;2000fJ(Vm)) accompanied by a non-volatile effect at room temperature (RT). This modification is explained in terms of voltage-induced oxygen migration towards/away from the Co/MOx interface. The Co films can be reversibly switched from an under-oxidized state with in-plane anisotropy (IPA) to an optimal oxidized state with maximum PMA, to an over-oxidized state under applied voltage (see figure). The switching time depends on the amplitude of the applied voltage. Here, we demonstrate that the switching time can be reduced from several seconds down to few milliseconds at RT by adjusting the voltage amplitude.

**References:**

[1] A. Fassatoui, S. Pizzini, Phys. Rev. Appl. 14, 064041 (2020).

**Images:**

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/9867cc6713f62186cd8b1b84462308ad.jpg)
Variation of the coercivity of a Pt/Co/TbOx/ZrOx/Pt device during the application of different gate voltages: (a) for positive voltages showing the transition from an over-oxidised state, to max PMA, to under-oxidised state with in-plane anisotropy; (b) transition from under-oxidised to over-oxidised state with negative voltage. In both cases, increasing slightly the voltage gives rise to large acceleration of the electric-field effect.

 Large Reversible Voltage Manipulation of Interfacial Magnetic Anisotropy in Pt/Co/Oxide Multilayers

Controlling magnetic properties of materials with electric fields (EFs) is of remarkable importance in spintronics applications due to its potential for much lower power consumption devices. Much like the power efficiency, two other sought-after features to incorporate are non-volatility and reversibility. This has been demonstrated with magneto-ionics, where EFs induce the migration of mobile ionic-species towards/away from the magnetic interface [1–4]. However, several works conducted in a variety of magneto-ionic materials have revealed important issues like irreversibility, the need of elevated temperatures to recover the initial states and chemical and structural degradation [4–6]. Recent studies have also focused on the differences in magneto-ionic reversibility between various oxides [7], pointing out the importance of the mechanisms governing ionic conduction. In this study, we unravel a higher degree of complexity in an HfO2 based device and demonstrate the coexistence of two distinct magneto-ionic regimes. For this purpose, we chose amorphous Ta/CoFeB/HfO2 thin films grown by magnetron sputtering with an ionic-liquid gate. It is shown that a gate voltage drives the anisotropy of the system from an underoxidized state exhibiting in-plane anisotropy (IPA) to an optimum oxidation level resulting in perpendicular anisotropy (PMA) and further into an overoxidized state resulting IPA in a non-volatile manner. The IPA (underoxidized) to PMA regime is found to be highly irreversible and is significantly faster than the PMA to IPA (overoxidized) regime which is fully reversibile under the same gate voltages. In addition, the effective damping parameter also shows a marked dependence with the anisotropy evolution in different regimes; IPA to PMA regime going from 0.029 to 0.012 and only a modest increase to 0.014 in the PMA to IPA regime. The existence of two magneto-ionic regimes has been linked to a difference in the chemical environment of oxygen species added to under/over oxidized layers. Our results show that different magneto-ionic regimes can coexist and that their identification is of great importance for tuning the properties and the design of high performance spintronics devices based on magneto-ionics.

**References:**

[1] U. Bauer, S. Emori, and G. S. D. Beach, Nat. Nanotech. 8, 411 (2013) [2] U. Bauer, L. Yao, A. J. Tan, and G. S. D. Beach, Nat. Mater. 14, 174 (2015) [3] A. J. Tan, M. Huang, C. O. Avci, and G. S. D. Beach, Nat. Mater. 18, 35 (2019) [4] L. Herrera Diez, Y. Liu, D. Gilbert, M. Belmeguenai, J. Vogel, S. Pizzini, E. Martinez, A. Lamperti, J. Mohammedi, A. Laborieux, et al., Phys. Rev. Appl. 12, 034005 (2019) [5] C. Bi, Y. Liu, T. Newhouse-Illige, M. Xu, M. Rosales, J. W. Freeland, O. Mryasov, S. Zhang, S. G. E. te Velthuis, and W. G. Wang, Phys. Rev. Lett. 113, 267202 (2014) [6] D. A. Gilbert, A. J. Grutter, E. Arenholz, K. Liu, B. J. Kirby, J. A. Borchers, and B. B. Maranville, Nat. Commun. 7, 12264 (2016) [7] A. Fassatoui, Phys. Rev. Appl. 14, 064041 (2020)

**Images:**

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/739c64ac3b9dc0fe2b2d809ba80bb186.jpg)
Fig. 1: Graphic representation of the Ta/CoFeB/HfO2 magneto-ionic stack covered with an [EMI-TFSI] ionic liquid gate. The gate voltage induces motion of oxygen species in HfO2 that drive anisotropy changes in the CoFeB layer.

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/a9cfb45146f55322b6c3cafa5270f8f3.jpg)
Fig. 2: A progressive oxidation is induced upon exposure to a gate voltage GV=-2V. Different exposure times t drive the system from IPA (a, initial state) through regime I (IPA to PMA) (b) into PMA (c) and back to IPA through regime II (PMA to IPA) (d).

 Reversible and Irreversible Magneto-ionic Regimes in Ta/CoFeB/HfO2

The Hall effect is one of the best known effects in (solid-state) physics. Conventionally, this phenomenon describes the occurrence of charge currents that are perpendicular to an externally applied electric field due to a time-reversal symmetry breaking magnetic field. Besides, in ferromagnetic systems, the net magnetization can break time-reversal symmetry even in the absence of a magnetic field which allows the so-called anomalous Hall effect. This effect originates from extrinsic and intrinsic contributions that are both related to the existence of spin-orbit coupling [1]. Moreover, another contribution to the Hall effect, which is known as the topological Hall effect, can exist even if spin-orbit coupling is negligible. It may occur in certain noncollinear noncoplanar magnetic textures with a nonzero scalar spin chirality like skyrmions [2, 3]. However, recent works [4, 5] reported the occurrence of an anomalous Hall effect in several compensated kagome magnets (cf. Fig. 1). These materials are coplanar antiferromagnets with vanishing net magnetization, and still, a group theoretical analysis allows the existence of the effect. The large conductivities obtained via first-principle calculations have been confirmed in experiments for Mn3Sn [6] and Mn3Ge [7]. However, a straightforward microscopic picture for this phenomenon was still missing. In this talk, we present an explanation on a microscopic level based on tight-binding calculations and analytical considerations [8]. For coplanar kagome magnets, we show the equivalence of spin-orbit coupling and an out-of-plane tilting of the magnetic moments. The existence of spin-orbit interaction does not only break a combined time-reversal and mirror symmetry of the Hamiltonian but can be transformed to a magnetic texture that is virtually canted, whereas, the original texture remains coplanar [cf. Fig. 2(a)]. Consequently, the ‘new’ anomalous Hall effect can be interpreted as a combination of an effective anomalous and topological Hall effect due to the net magnetic moment and the net scalar spin chirality of this virtual magnetic texture, respectively. Furthermore, as we demonstrate, a noncoplanar kagome magnet with spin-orbit coupling is able to behave like a system that is virtually coplanar and with compensated spin-orbit coupling [cf. Fig. 2(b)]. In this case, the combination of mirror and time-reversal symmetry of the Hamiltonian that was broken before has been restored. A critical out-of-plane tilting angle of the real texture can be found, where the virtual texture is coplanar and the Hall effect is absent for all energies. As we show in detail, the electronic properties are determined by this virtual texture that is hidden in the Hamiltonian. In consequent investigations, the calculations have been repeated for other transport quantities like the spin Hall effect where charge currents are converted into spin currents. These results can again be related to the virtual spin texture which has, however, different consequences for the spin Hall effect. Besides, in order to simulate the experimental situation, the investigated model was extended from a two-dimensional kagome lattice, as considered here, to a more realistic model including d-orbitals and kagome planes that are stacked along the out-of-plane direction.

**References:**

[1] N. Nagaosa, J. Sinova, S. Onoda, et al. "Anomalous Hall effect". Rev. Mod. Phys. 82, 1539 (2010). [2] P. Bruno, V. K. Dugaev, and M. Taillefumier. "Topological Hall Effect and Berry Phase in Magnetic Nanostructures". Phys. Rev. Lett. 93, 096806 (2004). [3] N. Nagaosa and Y. Tokura. "Topological properties and dynamics of magnetic skyrmions". Nat. Nanotechnol. 8, 899 (2013). [4] H. Chen, Q. Niu, and A. H. MacDonald. "Anomalous Hall Effect Arising from Noncollinear Antiferromagnetism". Phys. Rev. Lett. 112, 017205 (2014). [5] Y. Zhang, Y. Sun, H. Yang, et al. "Strong anisotropic anomalous Hall effect and spin Hall effect in the chiral antiferromagnetic compounds Mn3X (X=Ge, Sn, Ga, Ir, Rh, and Pt)". Phys. Rev. B 95, 075128 (2017). [6] S. Nakatsuji, N. Kiyohara, and T. Higo. "Large anomalous Hall effect in a non-collinear antiferromagnet at room temperature". Nature (London) 527, 212 (2015). [7] A. K. Nayak, J. E. Fischer, Y. Sun, et al. "Large anomalous Hall effect driven by a nonvanishing Berry curvature in the noncolinear antiferromagnet Mn3Ge". Sci. Adv. 2, e1501870 (2016). [8] O. Busch, B. Göbel, and I. Mertig. "Microscopic origin of the anomalous Hall effect in noncollinear kagome magnets". Phys. Rev. Research 2, 033112 (2020).

**Images:**

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/5ba5815bd43591c766a0d90db120a54b.jpg)
Fig. 1. Overview of the discussed coplanar kagome magnets. The arrows indicate the magnetic moments that are located at the basis atoms of the unit cell. The configurations can be characterized by their vector spin chiralities [(a), (b) positive, and (c), (d) negative]. Besides, each magnetic texture has different symmetry planes (time reversal T, mirror M or a combination of both) as indicated by the red lines.

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/93336328e4e3193aa019ed2b5bbc3832.jpg)
 
Fig. 2. Within the considered model, spin-orbit coupling gives rise to a virtual magnetic texture (red arrows) that is tilted out of the kagome plane with respect to the original magnetic texture (black arrows). (a) The virtual texture of a coplanar configuration can be noncoplanar resulting in the occurrence of an effective anomalous and topological Hall effect. (b) At a critical out-of-plane canting angle of the real magnetic texture, spin-orbit coupling is compensated and the virtual magnetic texture is coplanar. In this case, the anomalous Hall effect is absent.

 Interpretation of the anomalous Hall effect as an effective topological Hall effect in noncollinear kagome magnets

Antiferromagnetic spintronic devices have the potential to greatly outperform their current ferromagnetic counterparts due to their robustness to external fields, ultrafast dynamics and potential for high data density storage. Mn2Au is one of the most promising materials for antiferromagnetic spintronics due to its very high Néel temperature, moderate in-plane anisotropy and layered two sublattice spin structure [1]. Here we present atomistic spin simulations that allow us to estimate the temperature dependent magnetic properties of Mn2Au single crystals. We introduce a thermodynamically consistent spin Hamiltonian guided by previous ab-initiocalculations [3], which includes easy plane and rotational anisotropy terms. Temperature scaling of the anisotropy parameters is crucial for the performance optimization of antiferromagnetic devices, from the scale of magnetic domains to stability under thermal activation [2]. However, scaling in antiferromagnet has been barely studied due to the inherent difficulties to measure antiferromagnetic order parameter, n. We find a scaling of the easy plane anisotropy with the sublattice magnetization of n2.32. This is consistent with its two-ion origin [4], whereas the rotational anisotropy presents a n10dependence, consistent with the Callen-Callen scaling in ferromagnets of a 4thorder anisotropy. The crystal structure is shown in Fig. 1 showing two distinct Mn sites with a 180 degree relative orientation. We obtain quantitative agreement with experimental measurements of the temperature dependence of the order parameter by using a thermal-bath temperature rescaling, which has been demonstrated to work in ferromagnets. Our model provides a critical temperature (Neel) of 1256 K from the ab initiovalues of the exchange interactions. Due to the presence of four easy directions, the domain wall structure of 90 degrees and 180 degrees are stable in Mn2Au. We find a narrow domain wall width of 23.13 +/- 0.085 nm at zero temperature in both cases as shown in Fig. 2. Applying thermal spin fluctuations yields a domain wall width that increases with temperature, up to 25 +/- 2 at 300K and to 53 +/- 18 nm at 800K, matching well with experimental results of Sapozhnik et al[5]. In the case of a 180 degree wall the two separate 90 degree walls are weakly bound and separate at high temperatures. Further analysis of the domain wall width could provide information about the scaling of the exchange stiffness in antiferromagnets, a pivotal parameter for the construction of hierarchical multiscale models in magnetism, which are missing for antiferromagnets. When an electrical current is applied to the system along the [110]direction a spin orbit torque (SOT) is generated by the flow of electrons through the system interacting with the Au atoms. These SOTs cause the domain wall to move. For a Neel anti-damping SOT field of 0.05 T we find a domain wall velocity of 250 m/s at 0K, which is different to the usually fast dynamics displayed by anti-ferromagnetic materials.This is because the SOT applied is precessional in nature and both sublattices have precessional motion in the same direction. Applying a field-like SOT yields the usual fast motion of the domain walls. The atomistic spin model [6] used here to compute thermal properties of Mn2Au provide new insights on the temperature dependent magnetic properties – magnetic order and anisotropies and domain wall widths in Mn2Au. The understanding of the macroscopic parameters is necessary for the developments of multiscale models of Mn2Au that could greatly help to the development of novel antiferromagnetic spintronic devices.

**References:**

[1] V. Barthem et al Nature comminucations 4 (2013) [2] L Rózsa, S Selzer, T Birk, U Atxitia, U Nowak Physical Review B 100, 064422 (2019) [3] A. B. Shick et al. Phys. Rev. B 81, 212409 (2010) [4] R.F.L. Evans et al. Phys. Rev. B 102, 020412(2020) [5] A. A. Sapozhnik, Phys. Rev. B 97, 134429 (2018)

**Images:**

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/c38d47266d2475804a86e9579cb756b5.jpg)
Magnetic unit cell of Mn2Au. The Mn atoms (atoms with arrows) form two anti-parallel sublattices aligned along the [110] and [-1-10] crystal directions. The gold coloured atoms represent Gold.

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/22f100ca89efd90f63a1ac9868813590.jpg)
90 degree and 180 degree domain wall profiles.

 Temperature-dependent magnetic properties and domain wall width of the antiferromagnet Mn2Au

Antiferromagnets (AFMs) are promising materials for spintronics, that compared to ferromagnets exhibit faster dynamics, enhanced stability with respect to interfering magnetic fields and higher bit packing density, thanks to the absence of long-range magnetic coupling via stray fields. However, the absence of a net magnetic moment makes manipulation using conventional magnetic fields challenging [1]. For the use of AFMs, one requires efficient electrical writing and reading. Recently, there have been reports on the current-induced switching of the Néel vector orientation [2-5]. In particular, we demonstrated that in the insulating antiferromagnet NiO/heavy metal Pt thin film system there are multiple effects contributing to the electrical signal [6]. These include the switching of the magnetic Néel order, whose mechanism is debated in terms of origin and efficiency [2-6], but also non-magnetic signals possibly related to annealing or electromigration in the Pt layer [7]. While NiO has been intensively studied, key information such as the torque strength is missing so far. Using a different AFM such as CoO, that we study here [8], entails a number of advantages: we first show that, due to the compressive strain by the MgO substrate, a fourfold in-plane magnetic anisotropy of the CoO layer with two easy axes of the Néel order in the (001) plane is favored, and the spin flop field is accessible (around 7 T at 200 K). Such a system with two orthogonal stable states (along the [110] and [-110] directions) is ideal for applications where the orientation of n is read by spin Hall magnetoresistance (SMR) [4, 9, 10]. Furthermore, we achieve electrical switching and probe its symmetry, where the accessible spin flop field allows us to directly compare the effects of fields and currents. By looking at the switching above and below the Neél temperature in the CoO/Pt bilayer, we can show that this switching is of magnetic origin, as the signal related to the antiferromagnetism disappears above the Néel temperature, which in CoO is easily accessible around room temperature. For the switching, 8-arms Hall stars devices are used, made of Pt 2 nm thick, with the pulsing arms orientated along the [110] and [-110] easy axes directions (Fig.1). Before the pulses, the Néel vector n is aligned along [110]. When current pulses are applied along the orientation given by the contact combination 3-2 (initial state n∥jpulse), the transverse resistance drops in a step-like fashion, indicating a current-induced 90° n rotation (Fig. 1a). Performing a MR scan with field along the contact combination 4-1 after the current pulses, shown in Fig. 1b, yields a field-induced spin flop transition of n back to the initial state (along [110]). No background was subtracted to the data in Fig. 1, meaning that at this temperature (200 K), pulse length (1 ms), average current density (jpulse = 1.15x1012 A m−2) and in this switching configuration (straight pulses), where the effect of hot corners is not important, the non-magnetic effects are negligible and the electrical signal is dominated by a step-like magnetic contribution. At higher current densities the non-magnetic signal, possibly related to a local annealing process and electromigration in the Pt layer, can be observed and does not disappear above the Néel temperature, in contrast to the magnetic one. Finally, one can see how the threshold and saturation current density of the switching vary as a function of the magnetic field applied during the switching. By doing this, we find a linear relation between the current and the magnetic field and we ascertain a current-field equivalence ratio of value 4x10−11 T A−1 m2, that is orders of magnitude higher than for ferromagnets. The Néel vector final state (n⊥j) in the center of the device and the linear current-field dependence are in line with a thermomagnetoelastic switching mechanism for a negative magnetoelastic constant of the CoO, whose sign is at the moment not known for CoO thin films. With this we show that, for the switching of AFMs, currents are much more efficient than magnetic fields.

**References:**

[1] V. Baltz et al., Rev. Mod. Phys., Vol. 90, p. 015005 (2018); [2] L. Baldrati et al., Phys. Rev. Lett., Vol. 123, p. 177201 (2019); [3] T. Moriyama et al., Sci. Rep., Vol. 8, p. 14167 (2018); [4] X. Z. Chen et al., Phys. Rev. Lett., Vol. 120, p. 207204 (2018); [5] H. Meer et al., Nano Lett. 10.1021/acs.nanolett.0c03367, (2020); [6] F. Schreiber et al., Appl. Phys. Lett., Vol. 117, p. 082401 (2020); [7] T. Matalla-Wagner et al., Phys. Rev. Research, Vol. 2, p. 033077 (2020); [8] L. Baldrati et al., Phys. Rev. Lett., Vol. 125, p. 077201 (2020); [9] H. Nakayama et al., Phys. Rev. Lett., Vol. 110, p. 206601 (2013); [10] L. Baldrati et al., Phys. Rev. B, Vol. 98, p. 024422 (2018).

**Images:**

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/2450f831dc6eff9ad0429b7fc8ecf987.jpg)
Figure 1: Symmetry of the current-induced switching. (a) Current-induced spin flop transition. (b) Field-induced spin flop, resetting n. Adapted from Ref. [8].

 Quantifying spin torques in CoO(001)/Pt bilayers by comparing field- and current-induced switching

Magnetic skyrmions, topologically stabilized quasi-particles, have attracted much attention not only from fundamental physics but also from device applications1. Ferromagnetic skyrmions can be easily stabilized at room temperature by an interfacial Dzyaloshinskii-Moriya interaction (DMI) and can be efficiently controlled electrically through spin-orbit torques (SOT)2. However, problems arise from a large gyrotropic force due to the skyrmion Hall effect (SkHE)3, which is a diagonal motion along with current flow direction, that is easily able to surpass repulsive force from device edge. Thus, ferrimagnetic/antiferromagnetic skyrmions, which consist of two skyrmions antiferromagnetically coupled at each sublattice4,5, have received much attention due to a SkHE-free motion. Formation of ferrimagnetic6/synthetic antiferromagnetic (SyAFM) skyrmions7 has lately been demonstrated. Also, the SkHE-free motion of a half skyrmion is observed in a ferrimagnetic system at a specific temperature where angular momentum is compensated8. Earlier theoretical work has also predicted intriguing thermal characteristics of AF skyrmion including topology-dependent diffusive dynamics5,9. Nevertheless, the thermal effect on AF skyrmion is hitherto experimentally unexplored. Our work comprises two parts to comprehensively cover the full dynamics range. The first one is about the current-induced deterministic motion10, where we show the current-induced motion of skyrmions with suppressed SkHE even at room temperature in a SyAFM system. In the second part, we demonstrate the first observation of thermal diffusive dynamics for SyAFM skyrmions, which allows us to uncover the thermal effect on AF-coupled skyrmions. Ir-based SyAFM system whose ferromagnetic elements are composed of CoFeB is used for this work. The second peak of oscillation of the interlayer exchange coupling is used for maximizing antiferromagnetic exchange coupling as well as stabilizing perpendicular easy axis. Figure 1 shows the current density dependence of average velocity and SkHE for the skyrmion in the FM and SyAFM systems. We find that skyrmions in both systems are driven by current, indicating topological stabilization stemming from the skyrmion spin structure. More importantly, the skyrmions in the SyAFM system are driven by an order-of-magnitude smaller current density than those in the ferromagnetic system at comparable velocities. Based on an extended Thiele’s equation with a separately quantified SOT strength, it is shown that the achieved efficient motion of SyAFM skyrmions can be attributed to the enhanced SOTs by Pt, Ir, and W, compensated magnetic moments, and the reduction of effective topological charge. Figure 1 also shows that monotonically increasing SkHE with velocity for the FM skyrmions as in previous studies that consider an effect of pinning and/or field-like torque on SkHE3. Meanwhile, for a SyAFM skyrmion, no noticeable SkHE is observed, even in the depinning and flow regime10. Such inhibition of SkHE should be primarily caused by a reduction of the effective topological charge due to opposite magnetization at each sub-lattice. The achieved favorable properties are attributed to the employed stack structure which is engineered so that the interlayer exchange coupling, DMI, and SOT act in a concerted way10. Figure 2 shows the trajectories of SyAFM skyrmion under μ0|H| = 0.1 mT at 297.2 K measured for 1 hour. We observe that some of SyAFM skyrmions are displaced from an original position through the trajectory even though there is no bias current. The thermal diffusive dynamics of AF coupled skyrmions have been observed for the first time. We measure mean squared displacement to characterize the diffusion constant as previously conducted for FM skyrmions11. We find that the temperature dependence of diffusion constant of SyAFM skyrmions behaves approximately linear in log scale but more sensitive compared to that of FM skyrmions due to possibly suppressing gyrotropic force which stems from finite topological charge. Also, large size fluctuation of SyAFM skyrmions is observed with the thermal diffusive dynamics, which is consistent with the observed uneven sizes of skyrmions during the current induced motion. The origin could be intrinsic large thermal fluctuation of spins, relatively small interlayer exchange coupling, and/or differences in the magnetic properties between ferromagnets. In conclusion, we find that SyAFM skyrmions can be efficiently driven by currents with suppressed SkHE at room temperature, which has been a challenge of skyrmion research so far. Also, we show the first observation of the thermal diffusive dynamics of AF coupled skyrmions, which indicates that AF skyrmions would be promising to realize not only deterministic skyrmionic devices such as race-track memory12 but also unconventional computing e.g. the skyrmion-based token computing11,13. This work was supported in part by JSPS KAKENHI 19H05622.

**References:**

[1] N. Nagaosa and Y. Tokura, Nat. Nanotechnol. 8, 899 (2013). [2] S. Woo et al., Nat. Mater. 15, 501 (2016). [3] K. Litzius et al., Nat. Electron. 3, 30 (2020). [4] X. Zhang et al., Nat. Commun. 7, 10293 (2016). [5] J. Barker and O. A. Tretiakov, Phys. Rev. Lett. 116, 147203 (2016). [6] S. Woo et al., Nat. Commun. 9, 959 (2018). [7] W. Legrand et al., Nat. Mater. 19, 34 (2020). [8] Y. Hirata et al., Nat. Nanotechnol. 14, 232 (2019). [9] C. Schütte et al., Phys. Rev. B 90, 174434 (2014). [10] T. Dohi et al., Nat. Commun. 10, 5153 (2019). [11] J. Zázvorka et al., Nat. Nanotechnol. 14, 658 (2019). [12] A. Fert et al., Nat. Nanotechnol. 8, 152 (2013). [13] Y. Jibiki et al., Appl. Phys. Lett. 117, 082402 (2020).

**Images:**

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/fd236c5719509720fd04249ef1c920ad.jpg)
Figure 1 Average velocity of skyrmions (black, rectangle) and skyrmion Hall angle (red, circle) as a function of current density in FM (Left) and SyAFM (Right) system.

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/39bd75d01aa63d0d8c44ac35c2d7efe2.jpg)
Figure 2 Trajectories of SyAFM skyrmions for 1hour under |μ0H| = 0.1 mT at 297.2 K. Skyrmions have alloted color, respectively. The motion of skyrmions is traced by using trackpy.

 Dynamics of synthetic antiferromagnetic skyrmion from current-induced deterministic motion to thermally-activated diffusive motion

Efficient electrical read-out and writing of antiferromagnetic (AFM) insulators is a key prerequisite in view of using this class of materials as active elements in spintronic applications. The understanding of the electrical manipulation of the antiferromagnetic order n is a crucial aspect to exploit the advantages these materials exhibit compared to ferromagnets, such as THz dynamics, enhanced stability with respect to interfering magnetic fields and higher bit packing densities due to the absence of stray fields [1]. The absence of a net magnetic moment in antiferromagnets makes manipulation using conventional magnetic fields challenging. Recently, several reports demonstrated current-induced writing of the Néel order orientation in antiferromagnets and different switching mechanisms have been put forward [2-5]. The mechanisms depend on the type of domains present in AFM thin films. So far, however, it is largely unknown between which types of domains electrical switching occurs and in which direction the Néel vector is pointing. There are reports stating that in MgO//NiO the tensile strain induces a preferential out-of-plane orientation of n with respect to the sample plane [2] and on the other hand the Néel vector switching is detected electrically by spin Hall magnetoresistance (SMR) measurements, sensitive to the in-plane components of n, thus indicating the presence of an in-plane component of the Néel vector [6]. In our work [7] we focus on collinear insulating antiferromagnetic NiO/Pt thin films as a materials platform, and we image reversible electrical switching by photoemission electron microscopy (PEEM) employing the x-ray magnetic linear dichroism (XMLD) effect (Fig.1). By varying the x-ray polarization, energy and sample azimuthal angle, we identify the crystallographic orientation of the domains that can be switched by currents and quantify the Néel vector direction changes, showing that the switching occurs between different T-domains. The Néel vector orientation in these domains shows an enlarged out-of-plane component pointing along [±1 ±1 3.8], different from the bulk &lt;112&gt; directions. The final state of the in-plane component of the Néel vector n after switching in a Hall cross geometry by current pulses j along the [1 ±1 0] directions is n||j in the centre of the device.

**References:**

[1] V. Baltz, et al., Rev. Mod. Phys. 90, 015005 (2018). [2] T. Moriyama, et al., Sci. Rep. 8, 14167 (2018). [3] X. Z. Chen, et al., Phys. Rev. Lett. 120, 207204 (2018). [4] L. Baldrati, et al., Phys. Rev. Lett. 123, 177201 (2019). [5] P. Zhang, et al., Phys. Rev. Lett. 123, 247206 (2019). [6] S. Altieri, et al., Phys. Rev. Lett. 91, 137201 (2003). [7] C. Schmitt, et al., arXiv:2008.08507 (2020)

**Images:**

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/61bda7be24d63a6809e26b078ae55a48.jpg)
Fig. 1: The application of current pulses alternating between [100] and [010] reveals reversible switching of three different T-domains (Figure adapted from Ref. 7).

Spontaneous Hall effect in the Mn5Si3 antiferromagnet, due to antiferromagnetic Zeeman spin-splitting

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Spontaneous Hall effect in the Mn5Si3 antiferromagnet, due to antiferromagnetic Zeeman spin-splitting

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