France



Room temperature skyrmions have been the focus of research for development of skyrmionic devices based on thin film multilayers (MLs) with perpendicular anisotropy (PMA) and interfacial Dzyaloshinskii-Moriya interaction (iDMI)&lt;sup&gt;1&lt;/sup&gt;. The skyrmion spin texture is governed by several competing energies: iDMI, exchange energy, anisotropy energy, and magnetostatic energy. It has been shown that the skyrmion wall type and chirality determine the strength of the stray field above and below the thin film structure&lt;sup&gt;2&lt;/sup&gt;. Moreover, knowing the type and strength of the interlayer coupling is a prerequisite for designing future skyrmionic devices&lt;sup&gt;3&lt;/sup&gt;.&lt;br/&gt;Recent studies&lt;sup&gt;4&lt;/sup&gt; showed that the spin texture of the skyrmion in each ferromagnetic (F) layer depends on its position within the ferromagnet/heavy metal ML. The dependence of the skyrmion wall on the vertical position inside the multilayer was attributed to the minimization of the total energy, which included the formation of a flux-closure structure to reduce the magnetostatic energy. However, the existence of even a weak Ruderman–Kittel–Kasuya–Yosida (RKKY) interlayer exchange could significantly alter this scenario by dominating magnetostatic energy contributions. Neglecting the RKKY exchange in modelling work stems from the fact that it has not been thoroughly studied in structures supporting skyrmion formation. Therefore, it is important to investigate the role of RKKY coupling in such multilayered structures in combination with the other energies present in these systems.&lt;br/&gt;Here, we report on multilayered systems that allow the assessment of interlayer RKKY interaction relevant for systems with iDMI, thus providing the required input for the design of multilayer systems with well-defined uniform skyrmion spin textures throughout the multilayer system. Note that a similar concept has been already used to measure RKKY interactions&lt;sup&gt;5&lt;/sup&gt;, but for systems with a magnetic in-plane anisotropy without iDMI. Also, because the coercivity of the pinned layer was very small, only antiferromagnetic (AF) exchange coupling could be measured. Here we are interested in systems with PMA with iDMI supporting skyrmions, with ferromagnetic layers that can be coupled either by ferromagnetic or antiferromagnetic RKKY exchange.&lt;br/&gt;To assess RKKY interactions in such systems, a rare-earth ferrimagnet based multilayered system is proposed. The magnetically hard rare-earth amorphous ferrimagnet consisting of a Tb&lt;sub&gt;x&lt;/sub&gt;Fe&lt;sub&gt;1-x&lt;/sub&gt; alloy is exchange-coupled to a thin Co layer. The magnetization of the latter remains pinned up to reasonably high fields by the magnetically hard ferrimagnet layer. This bi-layer system is then separated from a “free” magnetic layer by an interlayer consisting of the typical noble metal used in systems with iDMI. In the simplest case the “free” layer is a 1.5nm-thick Co layer deposited on a Pt substrate to obtain PMA.&lt;br/&gt;The net magnetic moment of the rare-earth based ferrimagnet layer is governed by the composition of rare-earth and transition metal (Tb&lt;sub&gt;x&lt;/sub&gt;Fe&lt;sub&gt;1-x&lt;/sub&gt; with 15 &amp;lt; x &amp;lt; 30), such that either the magnetic moment of the rare-earth or transition metal element aligns parallel to the direction of an applied test-field &lt;i&gt;H&lt;sub&gt;ex&lt;/sub&gt;&lt;/i&gt;. Consequently, the adjacent Co layer aligns antiparallel or parallel to &lt;i&gt;H&lt;sub&gt;ex&lt;/sub&gt;&lt;/i&gt;, which permits the measurement of a ferromagnetic or antiferromagnetic RKKY exchange coupling, respectively, occurring between the “pinned” and “free” Co layers through the interlayer. The RKKY coupling energy density can be obtained from magnetometry using &lt;i&gt;E=M&lt;sub&gt;free layer&lt;/sub&gt;.t.H&lt;sub&gt;ex&lt;/sub&gt;&lt;/i&gt;.&lt;br/&gt;The situation however becomes more challenging if the “free” Co layer has asymmetric interfaces, hence the material at the top (e.g. Ir) is different from that at the bottom (Pt). In such a case the remanence of the “free” layer is suppressed by the formation of skyrmions or chiral domains arising from the net DMI generated by the asymmetric interfaces. To overcome this problem, we designed the free layer as a multilayer system with symmetric interfaces suppressing the net DMI.&lt;br/&gt;The proposed multilayer design permits to reliably measure the RKKY interactions occurring in all typical magnetic multilayer systems exhibiting iDMI, which provides the so-far missing input for micromagnetic simulations of such systems relevant for the design of future skyrmionic devices.

**References:**

1. M. Bacani, M. A. Marioni, J. Schwenk, H. J. Hug, &lt;i&gt;Scientific Reports &lt;/i&gt;9, 3114 (2019).&lt;br/&gt;2. M. A. Marioni, M. Penedo, M. Bacani, J. Schwenk, H. J. Hug, &lt;i&gt;Nano Letters&lt;/i&gt; &lt;i&gt;18&lt;/i&gt;, 4, 2263-2267 (2018).&lt;br/&gt;3. D. Suess, C. Vogler, F. Bruckner, P. Heistracher, C. Abert, &lt;i&gt;Aip Advances &lt;/i&gt;&lt;i&gt;8, &lt;/i&gt;11 (2018).&lt;br/&gt;4. W. Legrand, J. Y. Chauleau, D. Maccariello, N. Reyren, S. Collin, K. Bouzehouane, N. Jaouen, V. Cros, A. Fert, &lt;i&gt;Science Advances&lt;/i&gt; &lt;i&gt;4,&lt;/i&gt; 7 (2018).&lt;br/&gt;5. S. S. P. Parkin, &lt;i&gt;Physical Review Letters &lt;/i&gt;&lt;i&gt;67&lt;/i&gt; (25), 3598-3601 (1991).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/080ec7629d5cbd156a14f958d9f4fde5.jpg)




INTERMAG 2021

 The effect of RKKY exchange coupling through heavy metal interlayers on future skyrmionic devices

## Dr. Nishikant (Nish) Sonwalkar: Academician, Scientist, Musician

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Dr. Sonwalkar is regarded as a leading expert in the application of computers in education. He has extensive research and development experience in hypermedia authoring, mobile learning, adaptive learning, and brain-based synaptic learning, advanced scientific visualization, database management systems, and computer simulation.

After receiving doctoral degree from MIT in the area of Molecular Dynamics of Nano-interfaces, he joined MIT as faculty in Mechanical Engineering, but his passion for technology enabled education led him become the founding director of Hypermedia Teaching Facility (Hypermedia Lab) at MIT and later he was appointed as the Principal Educational Architect of MIT.

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NISH 2021

Room temperature skyrmions have been the focus of research for development of skyrmionic devices based on thin film multilayers (MLs) with perpendicular anisotropy (PMA) and interfacial Dzyaloshinskii-Moriya interaction (iDMI)1. The skyrmion spin texture is governed by several competing energies: iDMI, exchange energy, anisotropy energy, and magnetostatic energy. It has been shown that the skyrmion wall type and chirality determine the strength of the stray field above and below the thin film structure2. Moreover, knowing the type and strength of the interlayer coupling is a prerequisite for designing future skyrmionic devices3. Recent studies4 showed that the spin texture of the skyrmion in each ferromagnetic (F) layer depends on its position within the ferromagnet/heavy metal ML. The dependence of the skyrmion wall on the vertical position inside the multilayer was attributed to the minimization of the total energy, which included the formation of a flux-closure structure to reduce the magnetostatic energy. However, the existence of even a weak Ruderman–Kittel–Kasuya–Yosida (RKKY) interlayer exchange could significantly alter this scenario by dominating magnetostatic energy contributions. Neglecting the RKKY exchange in modelling work stems from the fact that it has not been thoroughly studied in structures supporting skyrmion formation. Therefore, it is important to investigate the role of RKKY coupling in such multilayered structures in combination with the other energies present in these systems. Here, we report on multilayered systems that allow the assessment of interlayer RKKY interaction relevant for systems with iDMI, thus providing the required input for the design of multilayer systems with well-defined uniform skyrmion spin textures throughout the multilayer system. Note that a similar concept has been already used to measure RKKY interactions5, but for systems with a magnetic in-plane anisotropy without iDMI. Also, because the coercivity of the pinned layer was very small, only antiferromagnetic (AF) exchange coupling could be measured. Here we are interested in systems with PMA with iDMI supporting skyrmions, with ferromagnetic layers that can be coupled either by ferromagnetic or antiferromagnetic RKKY exchange. To assess RKKY interactions in such systems, a rare-earth ferrimagnet based multilayered system is proposed. The magnetically hard rare-earth amorphous ferrimagnet consisting of a TbxFe1-x alloy is exchange-coupled to a thin Co layer. The magnetization of the latter remains pinned up to reasonably high fields by the magnetically hard ferrimagnet layer. This bi-layer system is then separated from a “free” magnetic layer by an interlayer consisting of the typical noble metal used in systems with iDMI. In the simplest case the “free” layer is a 1.5nm-thick Co layer deposited on a Pt substrate to obtain PMA. The net magnetic moment of the rare-earth based ferrimagnet layer is governed by the composition of rare-earth and transition metal (TbxFe1-x with 15 &lt; x &lt; 30), such that either the magnetic moment of the rare-earth or transition metal element aligns parallel to the direction of an applied test-field Hex. Consequently, the adjacent Co layer aligns antiparallel or parallel to Hex, which permits the measurement of a ferromagnetic or antiferromagnetic RKKY exchange coupling, respectively, occurring between the “pinned” and “free” Co layers through the interlayer. The RKKY coupling energy density can be obtained from magnetometry using E=Mfree layer.t.Hex. The situation however becomes more challenging if the “free” Co layer has asymmetric interfaces, hence the material at the top (e.g. Ir) is different from that at the bottom (Pt). In such a case the remanence of the “free” layer is suppressed by the formation of skyrmions or chiral domains arising from the net DMI generated by the asymmetric interfaces. To overcome this problem, we designed the free layer as a multilayer system with symmetric interfaces suppressing the net DMI. The proposed multilayer design permits to reliably measure the RKKY interactions occurring in all typical magnetic multilayer systems exhibiting iDMI, which provides the so-far missing input for micromagnetic simulations of such systems relevant for the design of future skyrmionic devices.

**References:**

1. M. Bacani, M. A. Marioni, J. Schwenk, H. J. Hug, Scientific Reports 9, 3114 (2019). 2. M. A. Marioni, M. Penedo, M. Bacani, J. Schwenk, H. J. Hug, Nano Letters 18, 4, 2263-2267 (2018). 3. D. Suess, C. Vogler, F. Bruckner, P. Heistracher, C. Abert, Aip Advances 8, 11 (2018). 4. W. Legrand, J. Y. Chauleau, D. Maccariello, N. Reyren, S. Collin, K. Bouzehouane, N. Jaouen, V. Cros, A. Fert, Science Advances 4, 7 (2018). 5. S. S. P. Parkin, Physical Review Letters 67 (25), 3598-3601 (1991).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/080ec7629d5cbd156a14f958d9f4fde5.jpg)

technical paper

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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://assets.underline.io/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://assets.underline.io/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

Electrical manipulation of the magnetization and exchange bias in antiferromagnet (AFM)/ferromagnet (FM) heterostructures[1,2] is expected to be of use in several high performance spintronic devices. An efficient method for electrical switching of the FM magnetization is to use the spin–orbit torque (SOT) generated from a heavy metal layer in AFM/FM/heavy metal structures[3]. The in-plane exchange field generated at the AFM/FM interface enables field-free switching of the perpendicular magnetization[4,5]. However, manipulation of the exchange bias is usually achieved by field cooling, which requires an external magnetic field and high temperature, hindering its application in practical devices. It has been demonstrated that the exchange bias field at the AFM/FM interface can be switched by the SOT generated in the Pt layer in a Pt/Co/IrMn structure, passing through the thin Co layer[2]. Strong SOTs can also be generated in certain AFM thin films (such as IrMn and PtMn) due to their giant spin Hall angle[6,7], allowing simpler spintronic devices to be created. Here, we report the current-induced switching of exchange bias field in a perpendicularly magnetized IrMn/CoFeB bilayer structure using a spin-orbit torque generated in the antiferromagnet IrMn layer[8]. By manipulating the current direction and amplitude, independent and repeatable switching of the magnetization and exchange bias field below the blocking temperature can be achieved. Figure 1a illustrates four states for the CoFeB magnetization and the interfacial IrMn spins. By applying a negative pulse current in the presence of an in-plane magnetic field ofμ0Hx = 100 mT, switching of the magnetization from up to down can be realized, as shown in Fig. 1c. Interestingly, the exchange bias field before the magnetization switching is -1.3 mT (Fig. 1b), but it changes to 1.6 mT after the magnetization switching (Fig. 1d), indicating reversal of the exchange bias field from negative to positive driven by the SOT current. Next, we find that when a relatively small current (e.g. 7 mA) is applied to a sample with DP state, only the magnetization switches, while the exchange bias field remains unchanged, leading to a transition from DP to UAP state, as shown in Fig. 1e. Then, when a pulse current with amplitude of 8 mA is applied to the samples with UAP state, the exchange bias field is reversed alone, but the magnetization remains unswitched, resulting in a transition from UAP to UP state (see Fig. 1f-h). X-ray magnetic circular dichroism (XMCD), polarized neutron reflectometry (PNR) measurements and micromagnetic simulations show that a small net magnetization within the IrMn interface plays a crucial role in these phenomena. Figure 2 illustrates the micromagnetic simulation results of exchange bias and its manipulation by SOT. Figure 2a shows the schematic of the AFM/FM exchange bias system. Initially, a positive exchange bias field is obtained, as shown in Fig. 2b. When we apply a SOT current of JSOT = 90 MA●cm-2, the FM magnetization can be switched while the exchange bias field is still positive, as indicated in Fig. 2c. Moreover, Fig. 2c also shows that a large SOT current ( JSOT= 270 MA●cm-2) can be used to reverse the exchange bias field. Figure 2d and 2e are snapshots of the z component of FM magnetization at selected times upon the application of different SOT currents. Through sweeping the SOT current density, it is clearly shown in Fig. 2f that the critical switching current density for the exchange bias is larger than that for the magnetization. Furthermore, to confirm the different critical current densities for magnetization and exchange bias field, temperature- and thickness-dependent switching are explored. In summary, we have reported current-induced exchange bias switching via the SOT originating from the AFM layer in an IrMn/CoFeB bilayer. The independent switching of magnetization and exchange bias field in a repeatable manner is demonstrated by manipulating the current direction and amplitude in the presence of an in-plane magnetic field. Experimental results from PNR and XMCD indicate a small net magnetization exists at the IrMn interface, comprised primarily of rotatable uncompensated Mn spins and a much smaller fraction (&lt;10%) of pinned spins. Micromagnetic simulations and temperature-dependent measurements show that the critical current density to switch the interfacial pinned spins, and hence the exchange bias field, is larger than that of magnetization reversal, and this difference allows the FM layer and exchange bias to be individually manipulated by SOT currents, rather than via perpendicular magnetic fields.

**References:**

[1] D.R. Xiong, S.Z. Peng and W.S. Zhao, Appl. Phys. Lett. Vol. 117, no. 21, pp. 212401 (2020). [2] P.H. Lin, B.Y. Yang and C.H. Lai, Nat. Mater. Vol. 18, pp. 335–341 (2019). [3] S.Z. Peng, D.Q. Zhu and W.S. Zhao, Adv. Electron. Mater. Vol. 5, pp.1900134 (2019). [4] Y.W. Oh, S.C. Baek and B.G. Park, Nat. Nanotechnol, Vol. 11, pp.878–884 (2016). [5] S.Z. Peng, J.Q. Lu and W.S. Zhao, IEEE Int. Electron Devices Meet. (IEDM), p. 28.6.1-28.6.4 (2019). [6] D. Wu, G.Q. Yu and K.L. Wang, Appl. Phys. Lett., Vol. 109, pp.222401 (2016). [7] Y.X. Ou, S.J. Shi and R.A. Buhrman, Phys. Rev. B, Vol. 93, pp. 220405(R) (2016). [8] S.Z. Peng, D.Q. Zhu and W.S. Zhao, Nat. Electron. Vol. 3, pp. 757–764 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/80a05ae9b4e976a9e973c73b4ec889d9.jpg)
Fig.1 Exchange bias and magnetization switching driven by current-induced SOT. a, Schematic configurations of four states for the CoFeB magnetization and interfacial IrMn spins and transitions among them. b-h, Concurrent switching of the magnetization and exchange bias field (b-d), independent switching of magnetization (e) and independent switching of exchange bias field (f-h) by a pulse current in the presence of an in-plane magnetic field.

![](https://assets.underline.io/uploads/markdown_image/1/image/2832a31a51b3b77bf9dccc9d8b4fd9ee.jpg)
Fig.2 Micromagnetic simulation results of exchange bias and its manipulation by SOT. a, Schematic of the AFM/FM exchange bias system. b,c, Hysteresis loops (b) before and (c) after application of SOT currents. d,e, Snapshots of the z component of the FM magnetization configuration (mz) at selected times. f, Switching of the exchange bias and magnetization under different SOT current densities.

 Exchange bias switching in an antiferromagnet/ferromagnet bilayer driven by spin–orbit torque

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:**

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

Antiferromagnets (AF) have many potential applications in spintronics such as data storage or long-range spin transport devices. The control of spins in AF by electrical current is proven to be possible by different mechanisms [1,2] but it remains challenging to verify experimentally [3]. Such detection can be unambiguously performed with the use of magnetic imaging techniques [4]. However, they are typically sensitive to the topmost layer and cannot be applied in more complex structures where the AF is buried far from the top interface. To mitigate this problem, we present a study of electrical signals in switching experiment in various temperatures for CoO. Basing on this temperature dependence of electrical data for AF CoO thin film we extract patterns that do not follow the trend expected for thermal effects but are probably fingerprints of magnetic changes. In characterization experiments for CoO, magnetoresistance studies for CoO reveal clear spin-flop transitions and pronounced antiferromagnetic hysteresis loops due to strong in-plane anisotropy. Magnetoresistance shows abrupt changes in Rxy around 7 T (240K) when the magnetic field is aligned along [110] axes (easy axes). They can be attributed to spin-flop transitions observed by means of Spin Hall Magnetoresistance. This behavior is hysteretic and absent when the field is aligned along [100] directions (hard axes) or in T = 304 K (above Néel temperature TN). It confirms the presence of biaxial anisotropy in CoO and easy axes along [110] in agreement with literature [5]. Hysteresis loops in Rxy when the magnetic field is rotated with respect to crystalline axes are observed up to the highest tested magnetic fields due to the strong in-plane anisotropy. In the actual switching experiments of CoO (Fig. 1), the temperature dependence of the transverse resistance Rxy variations after current pulses applied in alternating directions in a CoO | Pt device is examined. Resistivity variations due to thermal effects (such as asymmetric heating) increase with increasing temperature or current pulse amplitude and persist above TN of CoO. However, at lower current magnitudes we find a pattern that decreases with increasing temperature and vanishes above TN suggesting its magnetic origin (Fig. 2). In conclusion, we demonstrate that manipulation of temperature may help to gain more insight into the nature of electrical signals variations in experiments with antiferromagnets. These presented experimental findings can be important for current research acitivities towards using antiferromagnets in real spintronic devices.

**References:**

[1] P. Wadley, B. Howells, J. Zelezny et al., Science, 351, 587 (2016). [2] L. Baldrati, O. Gomonay, A. Ross et al., Phys. Rev. Lett., 123, 177201 (2019). [3] C. C. Chiang, S. Y. Huang, D. Qu, et al., Phys. Rev. Lett., 123, 227203 (2019). [4] M. J. Grzybowski, P. Wadley, K. W. Edmonds et al., Phys. Rev. Lett., 118, 057701 (2017). [5] L. Baldrati, C. Schmitt, O. Gomonay et al., Phys. Rev. Lett., 125, 077201 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/dc1c0c50382cc7fa878e0b12ff757dcd.jpg)
Fig. 1 The switching experiment for CoO (5 nm) | Pt (5 nm) thin films device where the transverse resisitivity Rxy is measured after each pulse of high current (the direction of the pulsing current is changed to perpendicular one after each 5 pulses). Interestingly, above TN the pattern visible in 240K is not present.

![](https://assets.underline.io/uploads/markdown_image/1/image/151b408e9acc0384e83f5b04392a240d.jpg)
Fig. 2 The magnitude of Rxy variations after pulsing in orthogonal directions in CoO for 24 mA current diminishes with increasing temperature and is practically invisible in room temperature (above TN). This trend is different for higher currents where Rxy variations increases with T as expected for thermal effects.

 Switching experiment of antiferromagnetic CoO in different temperatures

The spin-1/2 of an electron makes it an archetypal two-level system and inspires the description of other two-level systems using an analogous pseudospin. The quantized spin excitations of an ordered antiferromagnet are such pairs of spin-up and -down magnons and can be characterized by a magnonic pseudospin. The similarity between electronic spin and magnonic pseudospin has triggered the prediction of exciting phenomena like emergent spin-orbit coupling and topological states in antiferromagnetic magnonics. An experimental observation of the associated dynamics of antiferromagnetic pseudospin, however, has eluded experiments thus far. As a first step we will introduce the concept of magnon pseudospin and the description of magnon pseudospin dynamics, as well as briefly discuss similarities to electron spin transport [1]. In the second part, we show our recent experiments demonstrating control of magnon spin transport and pseudospin dynamics in a 15 nm thin film of the antiferromagnetic insulator hematite (α-Fe2O3) utilizing two Pt strips for all-electrical magnon injection and detection [2] (c.f. Fig. 1 (a)). We observe an oscillation in polarity of the magnon spin signal at the detector as a function of the externally applied magnetic field (see Fig. 1 (b)), which we quantitatively explain in terms of diffusive magnon transport. In particular, we observe a coherent precession of the magnon pseudospin caused by the easy-plane anisotropy and the Dzyaloshinskii-Moriya interaction. This observation can be viewed as the magnonic analogue of the electronic Hanle effect and the Datta-Das transistor, unlocking the high potential of antiferromagnetic magnonics towards the realization of electronics-inspired phenomena. Financial support from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy - EXC-2111 - 390814868 and project AL2110/2-1, and the Research Council of Norway through its Centers of Excellence funding scheme, project 262633, "QuSpin" is gratefully acknowledged.

**References:**

[1] A. Kamra et al., Physical Review B 102, 174445 (2020) [2] T. Wimmer et al., Physical Review Letters 125, 247204 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ec8627bd4d1b243e84613268af7a73af.jpg)
Fig. 1: (a) Sketch of the device geometry, the electrical wiring, and the coordinate system. The canting of the magnetic sublattices m1 and m2 and the corresponding net moment mnet as well as the Néel order parameter n are illustrated. Upon applying a charge current Iinj to the injector, a spin current Is with spin polarization s is generated via the SHE and injected into the hematite (α-Fe2O3) with thickness t = 15 nm. The emerging antiferromagnetic magnon current is then detected via the inverse SHE induced current at the detector by measuring the electrical voltage drop Veldet. (b) Magnon transport signal Veldet as a function of the external magnetic field magnitude. The signal oscillates between positive and negative values. The qualitative behaviour is very similar to the electronic Hanle effect.

 Observation of Antiferromagnetic Magnon Pseudospin Dynamics and the Magnon Hanle effect



Antiferromagnets (AFMs) have the potential to push spintronic devices from the static or gigahertz frequency range to the terahertz (THz) range for the sake of the high-speed processing. However, the insensitivity of AFMs to magnetic fields also makes it hard to manipulate spin currents. While the ultrafast generation of the spin current in ferromagnet/heavy metal (FM/HM) structures has received a lot of attention in recent years, it is still unknown as to whether a similar scenario can be observed in an AFM/HM system. Here we show the optical generation of ultrafast spin current in an AFM/HM heterostructure at zero external magnetic field and at room temperature by detecting the associated THz emission [1]. We believe this is a common phenomenon in antiferromagnets with strong nonlinear optical effects. Our results open an avenue of fundamental research into antiferromagnetism and a route to AFM spintronic devices.

**References:**

[1] H. Qiu, et al., Nature Physics (https://doi.org/10.1038/s41567-020-01061-7).

**Images:**





 Ultrafast Spin Current Generated from an Antiferromagnet INVITED

Introduction: Compensated ferrimagnets possess two or more inequivalent, antiferromagnetically-coupled sublattices such that the net magnetization is zero. The detailed compensation conditions can be typically tuned by varying the temperature, chemical composition or strain. These materials do not only possess the advantages of an antiferromagnet, i.e. faster switching, higher storage density and being immune to external field perturbation, but also, they are compatible with the commonly employed reading and writing schemes for conventional ferromagnets. A prototypal compensated ferrimagnet is Mn2RuxGa which was first identified as a half metallic compensated ferrimagnet in 2014 [1]. Mn2RuxGa crystallizes in the inverse Heusler structure (Space group No. 216), where Mn atoms occupy 4a and 4c sites of distinct chemical environment. Compensation is achieved when the moments from the two antiferromagnetically coupled Mn sites cancel each other. Ru of composition x then act as a knob for tuning the compensation temperature Tcomp. Previous works have demonstrated high spin polarization [1], large anomalous Hall effect (AHE) [2], finite tunnel magnetoresistance [3], efficient spin-orbit torque switching [4] and all-optical toggle switching [5] in nearly compensated Mn2RuxGa. Here we unveil the potential of exploiting Mn2RuxGa with perpendicular magnetic anisotropy for spontaneous thermoelectric generation at room temperature via anomalous Nernst effect (ANE) with no stray field coupling to the surrounding. Experimental Methods and Results: Epitaxial Mn2RuxGa (001) films with thicknesses ~ 27 nm and x ranging from 0.26 to 0.73 were grown on MgO (001) substrates at a substrate temperature of ~350oC by magnetron co-sputtering Mn2Ga and Ru targets. The unit cell of Mn2RuxGa makes a 45-degree rotation with respect to that of MgO such that the in-plane epitaxial relationship is MgO [100] // Mn2RuxGa [110]. The substrate induced in-plane biaxial compressive strain leads to ~1% of the tetragonal distortion along the out-of-plane c-axis, which defines the easy axis of the magnetization. Millimeter-scale Hall bar devices were fabricated for characterizing the transport and thermoelectric response of Mn2RuxGa films with varying x. An electrical current or a heat current was applied along the long axis of the Hall bar, along the [110] axis of Mn2RuxGa. The in-plane temperature gradient was monitored by measuring the resistance change of two on-chip Pt wires. Vibrating sample magnetometry at room temperature shows that adding Ru from x = 0.26 to x = 0.60 reduces monotonically the saturation magnetization Ms from ~90 kA/m to below 5 kA/m, followed by a slight upturn of MS upon further increasing x to 0.73. This reflects the magnetic compensation of Mn2RuxGa is achieved at room temperature for x ~ 0.6. We also found that the AHE signal for films with x = 0.51 and x = 0.73 are of opposite sign whereas for x = 0.60 the coercivity diverges, which corroborates this interpretation. Concerning the thermoelectric properties of Mn2RuxGa at room temperature, both the Seebeck coefficient Sxx and the anomalous Nernst coefficient Sxy change sign across the compensation. |Sxx| for all the samples are relatively small (&lt;1 μV/K) whereas their transverse counterpart |Sxy| are around 0.3 μV/K, which is comparable to many 3d ferromagnets but with orders of magnitude smaller Ms for Mn2RuxGa. The small |Sxx| also leads to relatively large anomalous Nernst angle |Sxy/Sxx| of the order of 0.5. Sxy can be expressed as Sxy = ρxxαxy + Sxxρxy/ρxx where αxy denotes the transverse thermoelectric conductivity. We found the second term, referring to the collective contribution of AHE and Seebeck effect, is negligible. ANE in Mn2RuxGa is therefore governed by the first term, i.e. the direct conversion from a thermal gradient to a transverse charge current. We obtain αxy = +0.12 A/(K●m) for x = 0.26 which reduces to αxy = +0.07 A/(K●m) and αxy = -0.07 A/(K●m) for x = 0.51 and x = 0.73, respectively. αxy reverses its sign across the compensation suggesting that it depends on the magnetization direction of a Mn sublattice and not on the net moment, in analogy with ρxy of AHE. Finally, it is worth noting that |αxy| and |Sxy| of Mn2RuxGa near the compensation are comparable to those of the chiral antiferromagnetic Mn3Sn [6] with an additional advantage of high tunability. We expect further enhancement of the thermoelectric performance of compensated Heusler compounds by improving the chemical ordering and/or by tuning the Fermi level via substitutional alloying [7]. This work was partly supported by JSPS KAKENHI (No. JP20K15156, JP20K05296).

**References:**

[1] H. Kurt et al., Phys. Rev. Lett. 112, 027201 (2014) [2] N. Thiyagarajah et al., Appl. Phys. Lett. 106, 122402 (2015) [3] K. Borisov et al., Appl. Phys. Lett. 108, 192407 (2016) [4] J. Finley et al., Adv. Mater. 31, 1805361 (2019) [5] C. Banerjee et al., Nat. Commun. 11, 4444 (2020) [6] M. Ikhlas et al., Nat. Phys. 13, 1085 (2017) [7] Y. Sakuraba et al., Phys. Rev. B 101, 134407 (2020)

**Images:**

 Anomalous Nernst effect in compensated ferrimagnetic Mn2RuxGa

Antiferromagnetic spintronics is on the rise as it could provide advantages over ferromagnetic-based conventional spintronics in terms of scalability, reliability and speed, opening the route to extend the working frequency of memory and logic devices from the current GHz range up to THz [1]. The electrical read-out of the magnetic state in antiferromagnetic materials, however, presents additional challenges due to the lack of a net magnetization which prevents the use of the typical detection schemes employed for ferromagnets. The possibility to access the magnetic configuration state in antiferromagnets by electrical methods would then provide a versatile characterization tool and is fundamental for the development of spintronic devices. At variance with ferromagnets, only few antiferromagnetic conductors have been demonstrated to show anisotropic magnetoresistance [2,3] allowing for a direct electric detection of the magnetic configuration by resistive measurements. In IrMn, the most widely used metallic antiferromagnet in applications, a small anisotropic magnetoresistance [4] has been demonstrated, whereas tunneling anisotropic magnetoresistance has been used to infer its magnetic state [5]. Here we follow a different approach exploiting interfacial effects between the antiferromagnet and a suitable neighboring metal layer. This approach, already employed for the insulating antiferromagnet Cr2O3 [6,7], underlines the critical role of interfaces in the determination of the transport properties related to the antiferromagnetic state. In this contribution we report the electrical detection of the antiferromagnetic state of IrMn through anomalous Hall measurements in Ta/IrMn heterostructures, grown by DC magnetron sputtering on a SiO2/Si substrate. The magnetic state is set in the antiferromagnet through out-of-plane field cooling and detected electrically by transverse resistance measurements in Hall bar structures, without the need of any ferromagnetic layer. An offset compensation system has been used to isolate the transverse resistance from spurious contributions (longitudinal resistance and magnetoresistance) [8]. The signal goes to zero at the Néel temperature of the antiferromagnet (TN), above which the system becomes paramagnetic. TN is found out to be 110 K for our 4 nm thick IrMn film, smaller than in the bulk (650 K) because of the finite thickness. The amplitude of the signal increases with the magnetic field applied during the cooling (whereas the value of TN is not affected) and is enhanced by the proximal interface with the Ta layer. We ascribe this enhancement to spin Hall magnetoresistance at room temperature and above, and to magnetic proximity which is the leading term at lower temperatures. From the temperature dependence of the effect and the comparison between Ta/IrMn and Ru/IrMn interfaces, we propose an explanation of such readout based on the simultaneous occurrence of spin-Hall magnetoresistance and magnetic proximity effect in Ta. These findings highlight how interface effects could be generally employed for the investigation of antiferromagnetic materials as well as for the electrical readout of the antiferromagnetic state.

**References:**

[1] T. Jungwirth, J. Sinova, A. Manchon et al, Nat. Phys, Vol. 14, p. 200 (2018) [2] S.Y. Bodnar, L. Smejkal, I. Turek et al, Nat. Commun., Vol. 9, p. 348 (2018) [3] P. Wadley, B. Howells, J. Zelezný et al, Science, Vol. 351, p. 587 (2016) [4] T. Kosub, M. Kopte, F. Radu et al, Phys. Rev. Lett., Vol. 115, p. 097201 (2015) [5] D. Petti, E. Albisetti, H. Reichlová et al, Appl. Phys. Lett., Vol. 102, p. 192404 (2013) [6] J.M. Taylor, E. Lesne, A. Markou et al, Appl. Phys. Lett., Vol. 115, p. 062403 (2019) [7] M. Asa, C. Autieri, R. Pazzocco, et al., Phys. Rev. Research, vol. 2, p. 043394 (2020) [8] M. Asa, C. Rinaldi, R. Pazzocco, et al., J. Appl. Phys., Vol. 128, p. 053904 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/32c3006792ed14c06dba33f4b5099a58.jpg)
(a) Transverse resistance (RXY) in Ta (2 nm)/IrMn (4 nm) /Ta (2 nm) Hall cross at remanence resulting from different field cooling processes. In the inset a sketch of the sample is reported. (b) Anomalous Hall resistance difference (ΔRXY) at remanence between states set with upward (+Bset) and downward (-Bset) field cooling. The value of Bset is reported beside each curve. The inset reports the value of ΔRXY at 10 K as function of the absolute value of the writing field Bset. The red line is a guide for the eye.

 Electrical Readout of the Antiferromagnetic State of IrMn through Anomalous Hall Effect

Recently, manipulation of antiferromagnetic (AFM) order has been gaining the attention of the spintronics community. Magnetic switching of AFM spin axis has been reported in thin films based on electronic transport methods, which provide only spatially averaged information on AFM states. Other techniques, such as x-ray magnetic linear dichroism (XMLD), can provide local information on AFM domains. In this study, we report direct observation of spin reorientation in response to current pulses in (0001) α-Fe2O3/Pt heterostructures. Our experiment combines the application of current pulses and spatially resolved photoemission electron microscopy (PEEM) with XMLD to detect AFM contrast. Pulses were applied in two different configurations A and B (Fig. 1a), and XMLD images were interleaved with current pulse sequences to reveal changes in the AFM domains in the center of the cross (Fig. 1c). Our polarization dependent analysis reveals that the Néel vector of our α-Fe2O3 films have an out-of-plane component in their equilibrium state, contrary to what previous work indicate. Finally, we show clear evidence of AFM domains reorientation outside of the current path, which leads us to the conclusion that spin-orbit torque may not be the only driven effect in the electrical switching process.

**References:**

E. Cogulu, N. Statuto and A. D. Kent, “X-ray Magnetic Linear Dichroism Studies of Electrical Switching of Antiferromagnetic Order in α-Fe2O3 Epitaxial Films” (2020), arXiv:2012.04127 [cond-mat.mes-hall].

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/2634b4eabc849ecf23e77da37868ea40.jpg)
FIG1. (a) PEEM image of the 6-legged Hall cross with schematic representation of the circuit. Dark regions correspond to α-Fe2O3 (30 nm thickness) and bright region correspond to Pt (2 nm thickness). The Pt leads are aligned with the 3 easy axes of Fe2O3. Plus and minus signs represent the connections to the two pulse generator outputs, where the minus sign indicates a connection to ground. (b) Resistance data showing switching between two states after sequential current pulses applied along both current paths showed at panel a. (c) XMLD-PEEM images (4 μm field of view) before and after a 4 mA current pulse along the pulse A & B configurations.

 X-Ray Magnetic Linear Dichroism Studies of Electrical Switching of Antiferromagnetic Order in α-Fe2O3 Epitaxial Films

Antiferromagnets have always been overshadowed by ferromagnets in real-life applications based on magnetism or spintronics. This is primarily due to that antiferromagnet order parameters, in contrast to the ferromagnetic magnetization, are only weakly coupled to magnetic fields, and are hence difficult, in conventional view, to be manipulated. I will discuss several recent theoretical and experimental developments that counter this conventional wisdom, in a class of antiferromagnets that have stable noncollinear magnetic order. I will first explain a theory for the time-reversal-symmetry-breaking counterparts of the conventional SHE and ISHE in the noncollinear antiferromagnet Mn3Sn, which are named as the magnetic spin Hall effect (MSHE) and the magnetic inverse spin Hall effect (MISHE), respectively [1]. I will then discuss the concept of spin density polarization, and how to use it to describe spin-Hall effects in a magnetic insulator as bulk effects, without using the spin current language [2]. I will finally present an exploration on the nontrivial orbital coupling between chiral antiferromagnets and external magnetic fields [3,4], and the potential detection of the elusive itinerant orbital magnetization by magnetic neutron scattering.

**References:**

[1] M. Kimata, H. Chen, et al. Nature 565, 627 (2019). [2] H. Chen, Q. Niu, and A. H. MacDonald, arXiv:1803.01294 [3] H. Chen et al., PRB 101, 104418 (2020). [4] X. Li, A. H. MacDonald, and H. Chen, arXiv:1902.10650

**Images:**

The effect of RKKY exchange coupling through heavy metal interlayers on future skyrmionic devices

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The effect of RKKY exchange coupling through heavy metal interlayers on future skyrmionic devices

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

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