Spintronics and the limitations of every day electronics⌗

In today’s society electronic devices are heavily incorporated in everyone’s daily life. The everlasting desire to make our computers run faster, necessarily leads to smaller and smaller electric components. Where in the early 70s a single computer chip could host up to a few thousands of transistors, today the number approaches tens to hundreds of billions and soon will reach a fundamental limit ( Citation: McClean, 2020 McClean (2020). The McClean Report. https://www.icinsights.com/reports/mcclean-report/. ).

At the heart of electronic devices are electronic circuits that control the charge of electrons. Besides charge, electrons however possess two spin states that can be named “up” and “down”, a degree of freedom that can be utilized in both data storage and processing. The giant magneto-resistance effect ( Citation: Binasch & al., 1989 Binasch, G., Grünberg, P., Saurenbach, F. & Zinn, W. (1989). Enhanced magnetoresistance in layered magnetic structures with antiferromagnetic interlayer exchange. Phys. Rev. B, 39(7). 4828–4830. https://doi.org/10.1103/physrevb.39.4828 ; Citation: Baibich & al., 1988 Baibich, M., Broto, J., Fert, A., Van Dau, F., Petroff, F., Etienne, P., Creuzet, G., Friederich, A. & Chazelas, J. (1988). Giant magnetoresistance of (001)Fe/(001)Cr magnetic superlattices. Phys. Rev. Lett., 61(21). 2472–2475. https://doi.org/10.1103/physrevlett.61.2472 ) for example has made a tremendous impact on data storage technologies ( Citation: Puebla & al., 2020 Puebla, J., Kim, J., Kondou, K. & Otani, Y. (2020). Spintronic devices for energy-efficient data storage and energy harvesting. Comms. Mater., 1(1). 1–9. https://doi.org/10.1038/s43246-020-0022-5 ).

Unfortunately these improvements in computer chips and data storage has led to an increase in energy consumption. Predictions say the total electricity demand of information and communication technology will be 20.9% of the total world’s electricity demand ( Citation: Jones, 2018 Jones, N. (2018). How to stop data centres from gobbling up the world’s electricity. Nature, 561(7722). 163–166. https://doi.org/10.1038/d41586-018-06610-y ) by 2030.

Spin-based electronics or “spintronics” as it is often referred to, has become an active field of research. Compared with charge-based devices, spin-based devices could in principle have higher density, lower energy cost, and faster operating speed ( Citation: Pu, 2020 Pu, Y. (2020). Charge-spin conversion in 2D systems. InLiu, W. & Xu, Y. (Eds.), Spintronic 2D materials. (pp. 125–136). Elsevier. https://doi.org/10.1016/b978-0-08-102154-5.00004-7 ; Citation: Liu & al., 2020 Liu, W., Bryan, M. & Xu, Y. (2020). Introduction to spintronics and 2D materials. InLiu, W. & Xu, Y. (Eds.), Spintronic 2D materials. (pp. 1–24). Elsevier. https://doi.org/10.1016/b978-0-08-102154-5.00001-1 ; Citation: Wang & al., 2019 Wang, X., Chen, H. & Khenata, R. (2019). Recent advances in novel materials for future spintronics (). MDPI. https://doi.org/10.3390/books978-3-03897-977-7 ). Despite active research, many open questions remain about the electron spin dynamics. These include among others understanding the effects of spin-orbit coupling, spin-valley coupling, and spin-photon interaction ( Citation: Liu & al., 2020 Liu, W., Bryan, M. & Xu, Y. (2020). Introduction to spintronics and 2D materials. InLiu, W. & Xu, Y. (Eds.), Spintronic 2D materials. (pp. 1–24). Elsevier. https://doi.org/10.1016/b978-0-08-102154-5.00001-1 ; Citation: Hellman & al., 2017 Hellman, F., Hoffmann, A., Tserkovnyak, Y., Beach, G., Fullerton, E., Leighton, C., MacDonald, A., Ralph, D., Arena, D., Dürr, H., Fischer, P., Grollier, J., Heremans, J., Jungwirth, T., Kimel, A., Koopmans, B., Krivorotov, I., May, S., Petford-Long, A., Rondinelli, J., Samarth, N., Schuller, I., Slavin, A., Stiles, M., Tchernyshyov, O., Thiaville, A. & Zink, B. (2017). Interface-induced phenomena in magnetism. Rev. Mod. Phys., 89(2). 025006. https://doi.org/10.1103/revmodphys.89.025006 ).

Spintronics in ferro- and antiferromagnets⌗

Ferromagnetic spintronics has greatly contributed to microelectronic technology in the last few decades ( Citation: Bader & al., 2010 Bader, S. & Parkin, S. (2010). Spintronics. Annu. Rev. Condens. Matter Phys., 1(1). 71–88. https://doi.org/10.1146/annurev-conmatphys-070909-104123 ; Citation: Sinova & al., 2012 Sinova, J. & Žutić, I. (2012). New moves of the spintronics tango. Nat. Mater., 11(5). 368–371. https://doi.org/10.1038/nmat3304 ; Citation: Bhatti & al., 2017 Bhatti, S., Sbiaa, R., Hirohata, A., Ohno, H., Fukami, S. & Piramanayagam, S. (2017). Spintronics based random access memory: A review. Mater. Today, 20(9). 530–548. https://doi.org/10.1016/j.mattod.2017.07.007 ). One of the practical results was the development of magnetic memories with purely electronic write-in and read-out processes as an alternative to existing solid state drive technologies ( Citation: Kent & al., 2015 Kent, A. & Worledge, D. (2015). A new spin on magnetic memories. Nat. Nanotechnol., 10(3). 187–191. https://doi.org/10.1038/nnano.2015.24 ; Citation: Sato & al., 2018 Sato, N., Xue, F., White, R., Bi, C. & Wang, S. (2018). Two-terminal spin–orbit torque magnetoresistive random access memory. Nat. Electron., 1(9). 508–511. https://doi.org/10.1038/s41928-018-0131-z ).

Ferromagnetic thin films have already entered commercial use in hard drives, magnetic field and rotation angle sensors and in similar devices ( Citation: Parkin & al., 2003 Parkin, S., Jiang, X., Kaiser, C., Panchula, A., Roche, K. & Samant, M. (2003). Magnetically engineered spintronic sensors and memory. Proc. IEEE, 91(5). 661–680. https://doi.org/10.1109/jproc.2003.811807 ; Citation: Jogschies & al., 2015 Jogschies, L., Klaas, D., Kruppe, R., Rittinger, J., Taptimthong, P., Wienecke, A., Rissing, L. & Wurz, M. (2015). Recent developments of magnetoresistive sensors for industrial applications. Sensors, 15(11). 28665–28689. https://doi.org/10.3390/s151128665 ; Citation: Gibertini & al., 2019 Gibertini, M., Koperski, M., Morpurgo, A. & Novoselov, K. (2019). Magnetic 2D materials and heterostructures. Nat. Nanotechnol., 14(5). 408–419. https://doi.org/10.1038/s41565-019-0438-6 ), while keeping high promises for technologically competitive ultrafast memory elements ( Citation: Lau & al., 2016 Lau, Y., Betto, D., Rode, K., Coey, J. & Stamenov, P. (2016). Spin–orbit torque switching without an external field using interlayer exchange coupling. Nat. Nanotechnol., 11(9). 758–762. https://doi.org/10.1038/nnano.2016.84 ) and neuromorphic chips ( Citation: Fukami & al., 2016 Fukami, S., Zhang, C., DuttaGupta, S., Kurenkov, A. & Ohno, H. (2016). Magnetization switching by spin–orbit torque in an antiferromagnet–ferromagnet bilayer system. Nat. Mater., 15(5). 535–541. https://doi.org/10.1038/nmat4566 ).

It is widely known that spin-orbit interaction provides an efficient way to couple electronic and magnetic degrees of freedom. It is, therefore, no wonder that the largest torque on magnetization, which is also referred to as the spin-orbit torque, emerges in magnetic systems with strong spin-orbit interaction ( Citation: Mihai Miron & al., 2010 Mihai Miron, I., Gaudin, G., Auffret, S., Rodmacq, B., Schuhl, A., Pizzini, S., Vogel, J. & Gambardella, P. (2010). Current-driven spin torque induced by the rashba effect in a ferromagnetic metal layer. Nat. Mater., 9(3). 230–234. https://doi.org/10.1038/nmat2613 ; Citation: Haney & al., 2013 Haney, P., Lee, H., Lee, K., Manchon, A. & Stiles, M. (2013). Current induced torques and interfacial spin-orbit coupling: Semiclassical modeling. Phys. Rev. B, 87(17). 174411. https://doi.org/10.1103/physrevb.87.174411 ) as has been long anticipated ( Citation: Dyakonov & al., 1971 Dyakonov, M. & Perel, V. (1971). Current-induced spin orientation of electrons in semiconductors. Phys. Lett. A, 35(6). 459–460. https://doi.org/10.1016/0375-9601(71)90196-4 ).

The spin-orbit coupling may be enhanced by confinement potentials in effectively two-dimensional systems consisting of conducting and magnetic layers. The in-plane current may efficiently drive domain walls or switch magnetic orientation in such structures with the help of spin-orbit torque ( Citation: Awschalom & al., 2009 Awschalom, D. & Samarth, N. (2009). Spintronics without magnetism. Physics, 2. 50. https://doi.org/10.1103/physics.2.50 ; Citation: Manchon & al., 2008 Manchon, A. & Zhang, S. (2008). Theory of nonequilibrium intrinsic spin torque in a single nanomagnet. Phys. Rev. B, 78(21). 212405. https://doi.org/10.1103/physrevb.78.212405 ; Citation: Garate & al., 2009 Garate, I. & MacDonald, A. (2009). Influence of a transport current on magnetic anisotropy in gyrotropic ferromagnets. Phys. Rev. B, 80(13). 134403. https://doi.org/10.1103/physrevb.80.134403 ; Citation: Manchon & al., 2009 Manchon, A. & Zhang, S. (2009). Theory of spin torque due to spin-orbit coupling. Phys. Rev. B, 79(9). 094422. https://doi.org/10.1103/physrevb.79.094422 ), which is present even for uniform magnetization, or with the help of spin-transfer torque, which requires the presence of magnetization gradient (due to e.g. domain wall) ( Citation: Slonczewski, 1996 Slonczewski, J. (1996). Current-driven excitation of magnetic multilayers. J. Magn. Magn. Mater., 159(1-2). L1–L7. https://doi.org/10.1016/0304-8853(96)00062-5 ; Citation: Berger, 1996 Berger, L. (1996). Emission of spin waves by a magnetic multilayer traversed by a current. Phys. Rev. B, 54(13). 9353–9358. https://doi.org/10.1103/physrevb.54.9353 ; Citation: Ralph & al., 2008 Ralph, D. & Stiles, M. (2008). Spin transfer torques. J. Magn. Magn. Mater., 320(7). 1190–1216. https://doi.org/10.1016/j.jmmm.2007.12.019 ; Citation: Stiles & al., 2002 Stiles, M. & Zangwill, A. (2002). Anatomy of spin-transfer torque. Phys. Rev. B, 66(1). 014407. https://doi.org/10.1103/physrevb.66.014407 ).

On the other hand, antiferromagnets have received a great deal of attention due to their high temperature magnetic order in a large variety of materials. The study of antiferromagnets have uncovered many interesting properties. For example, the antiferromagnet has zero magnetic moment, is insensitive to external fields and contains no internal stray fields. Furthermore, ultrafast switching of the antiferromagnetic order has been observed ( Citation: Gomonay & al., 2016 Gomonay, O., Jungwirth, T. & Sinova, J. (2016). High antiferromagnetic domain wall velocity induced by néel spin-orbit torques. Phys. Rev. Lett., 117(1). 017202. https://doi.org/10.1103/physrevlett.117.017202 ; Citation: Olejník & al., 2018 Olejník, K., Seifert, T., Kašpar, Z., Novák, V., Wadley, P., Campion, R., Baumgartner, M., Gambardella, P., Němec, P., Wunderlich, J., Sinova, J., Kužel, P., Müller, M., Kampfrath, T. & Jungwirth, T. (2018). Terahertz electrical writing speed in an antiferromagnetic memory. Sci. Adv., 4(3). eaar3566. https://doi.org/10.1126/sciadv.aar3566 ; Citation: Jungwirth & al., 2018 Jungwirth, T., Sinova, J., Manchon, A., Marti, X., Wunderlich, J. & Felser, C. (2018). The multiple directions of antiferromagnetic spintronics. Nat. Phys., 14(3). 200–203. https://doi.org/10.1038/s41567-018-0063-6 ; Citation: MacDonald & al., 2011 MacDonald, A. & Tsoi, M. (2011). Antiferromagnetic metal spintronics. Proc. R. Soc. A, 369(1948). 3098–3114. https://doi.org/10.1098/rsta.2011.0014 ; Citation: Gomonay & al., 2014 Gomonay, E. & Loktev, V. (2014). Spintronics of antiferromagnetic systems (Review article). Low Temp. Phys., 40(1). 17–35. https://doi.org/10.1063/1.4862467 ; Citation: Železný & al., 2014 Železný, J., Gao, H., Výborný, K., Zemen, J., Mašek, J., Manchon, A., Wunderlich, J., Sinova, J. & Jungwirth, T. (2014). Relativistic néel-order fields induced by electrical current in antiferromagnets. Phys. Rev. Lett., 113(15). 157201. https://doi.org/10.1103/physrevlett.113.157201 ). In spintronic devices these properties translate to storing magnetic data at high densities, fast reading and writing, and, in addition to low energy consumption, make the antiferromagnet an ideal candidate for further study.

An increasing demand for ever higher performance computation and ever faster big data analytics has therefore sparked the interest to antiferromagnetic spintronics ( Citation: MacDonald & al., 2011 MacDonald, A. & Tsoi, M. (2011). Antiferromagnetic metal spintronics. Proc. R. Soc. A, 369(1948). 3098–3114. https://doi.org/10.1098/rsta.2011.0014 ; Citation: Gomonay & al., 2014 Gomonay, E. & Loktev, V. (2014). Spintronics of antiferromagnetic systems (Review article). Low Temp. Phys., 40(1). 17–35. https://doi.org/10.1063/1.4862467 ; Citation: Wadley & al., 2016 Wadley, P., Howells, B., elezny, J., Andrews, C., Hills, V., Campion, R., Novak, V., Olejnik, K., Maccherozzi, F., Dhesi, S., Martin, S., Wagner, T., Wunderlich, J., Freimuth, F., Mokrousov, Y., Kune, J., Chauhan, J., Grzybowski, M., Rushforth, A., Edmonds, K., Gallagher, B. & Jungwirth, T. (2016). Electrical switching of an antiferromagnet. Science, 351(6273). 587–590. https://doi.org/10.1126/science.aab1031 ; Citation: Jungwirth & al., 2016 Jungwirth, T., Marti, X., Wadley, P. & Wunderlich, J. (2016). Antiferromagnetic spintronics. Nat. Nanotechnol., 11(3). 231–241. https://doi.org/10.1038/nnano.2016.18 ; Citation: Baltz & al., 2018 Baltz, V., Manchon, A., Tsoi, M., Moriyama, T., Ono, T. & Tserkovnyak, Y. (2018). Antiferromagnetic spintronics. Rev. Mod. Phys., 90(1). 015005. https://doi.org/10.1103/revmodphys.90.015005 ; Citation: Jungwirth & al., 2018 Jungwirth, T., Sinova, J., Manchon, A., Marti, X., Wunderlich, J. & Felser, C. (2018). The multiple directions of antiferromagnetic spintronics. Nat. Phys., 14(3). 200–203. https://doi.org/10.1038/s41567-018-0063-6 ; Citation: Jungfleisch & al., 2018 Jungfleisch, M., Zhang, W. & Hoffmann, A. (2018). Perspectives of antiferromagnetic spintronics. Phys. Lett. A, 382(13). 865–871. https://doi.org/10.1016/j.physleta.2018.01.008 ), i.e. to the usage of the much more subtle antiferromagnetic order parameter to store and process information. This idea is driven primarily by the expectation that antiferromagnetic materials may naturally allow for up to THz operation frequencies ( Citation: Gomonay & al., 2016 Gomonay, O., Jungwirth, T. & Sinova, J. (2016). High antiferromagnetic domain wall velocity induced by néel spin-orbit torques. Phys. Rev. Lett., 117(1). 017202. https://doi.org/10.1103/physrevlett.117.017202 ; Citation: Olejník & al., 2018 Olejník, K., Seifert, T., Kašpar, Z., Novák, V., Wadley, P., Campion, R., Baumgartner, M., Gambardella, P., Němec, P., Wunderlich, J., Sinova, J., Kužel, P., Müller, M., Kampfrath, T. & Jungwirth, T. (2018). Terahertz electrical writing speed in an antiferromagnetic memory. Sci. Adv., 4(3). eaar3566. https://doi.org/10.1126/sciadv.aar3566 ; Citation: Jungwirth & al., 2018 Jungwirth, T., Sinova, J., Manchon, A., Marti, X., Wunderlich, J. & Felser, C. (2018). The multiple directions of antiferromagnetic spintronics. Nat. Phys., 14(3). 200–203. https://doi.org/10.1038/s41567-018-0063-6 ; Citation: MacDonald & al., 2011 MacDonald, A. & Tsoi, M. (2011). Antiferromagnetic metal spintronics. Proc. R. Soc. A, 369(1948). 3098–3114. https://doi.org/10.1098/rsta.2011.0014 ; Citation: Gomonay & al., 2014 Gomonay, E. & Loktev, V. (2014). Spintronics of antiferromagnetic systems (Review article). Low Temp. Phys., 40(1). 17–35. https://doi.org/10.1063/1.4862467 ; Citation: Železný & al., 2014 Železný, J., Gao, H., Výborný, K., Zemen, J., Mašek, J., Manchon, A., Wunderlich, J., Sinova, J. & Jungwirth, T. (2014). Relativistic néel-order fields induced by electrical current in antiferromagnets. Phys. Rev. Lett., 113(15). 157201. https://doi.org/10.1103/physrevlett.113.157201 ) in sharp contrast to ferromagnets whose current-induced magnetization dynamics is fundamentally limited to GHz frequency range.

Recently, spin-orbit-torque-driven electric switching of the Néel vector orientation has been predicted ( Citation: Železný & al., 2014 Železný, J., Gao, H., Výborný, K., Zemen, J., Mašek, J., Manchon, A., Wunderlich, J., Sinova, J. & Jungwirth, T. (2014). Relativistic néel-order fields induced by electrical current in antiferromagnets. Phys. Rev. Lett., 113(15). 157201. https://doi.org/10.1103/physrevlett.113.157201 ) and discovered in non-centrosymmetric crystals such as CuMnAs ( Citation: Wadley & al., 2016 Wadley, P., Howells, B., elezny, J., Andrews, C., Hills, V., Campion, R., Novak, V., Olejnik, K., Maccherozzi, F., Dhesi, S., Martin, S., Wagner, T., Wunderlich, J., Freimuth, F., Mokrousov, Y., Kune, J., Chauhan, J., Grzybowski, M., Rushforth, A., Edmonds, K., Gallagher, B. & Jungwirth, T. (2016). Electrical switching of an antiferromagnet. Science, 351(6273). 587–590. https://doi.org/10.1126/science.aab1031 ; Citation: Fina & al., 2016 Fina, I. & Marti, X. (2016). Electric control of antiferromagnets. IEEE Trans. Magn., 53(2). 1–1. https://doi.org/10.1109/tmag.2016.2606561 ; Citation: Železný & al., 2018 Železný, J., Wadley, P., Olejník, K., Hoffmann, A. & Ohno, H. (2018). Spin transport and spin torque in antiferromagnetic devices. Nat. Phys., 14(3). 220–228. https://doi.org/10.1038/s41567-018-0062-7 ; Citation: Saidl & al., 2017 Saidl, V., Němec, P., Wadley, P., Hills, V., Campion, R., Novák, V., Edmonds, K., Maccherozzi, F., Dhesi, S., Gallagher, B., Trojánek, F., Kuneš, J., Železný, J., Malý, P. & Jungwirth, T. (2017). Optical determination of the néel vector in a CuMnAs thin-film antiferromagnet. Nat. Photon., 11(2). 91–96. https://doi.org/10.1038/nphoton.2016.255 ) and Mn$_2$Au ( Citation: Barthem & al., 2013 Barthem, V., Colin, C., Mayaffre, H., Julien, M. & Givord, D. (2013). Revealing the properties of Mn2Au for antiferromagnetic spintronics. Nat. Commun., 4(1). 1–7. https://doi.org/10.1038/ncomms3892 ; Citation: Jourdan & al., 2015 Jourdan, M., Bräuning, H., Sapozhnik, A., Elmers, H., Zabel, H. & Kläui, M. (2015). Epitaxial Mn2Au thin films for antiferromagnetic spintronics. J. Phys. D: Appl. Phys., 48(38). 385001. https://doi.org/10.1088/0022-3727/48/38/385001 ; Citation: Bhattacharjee & al., 2018 Bhattacharjee, N., Sapozhnik, A., Bodnar, S., Grigorev, V., Agustsson, S., Cao, J., Dominko, D., Obergfell, M., Gomonay, O., Sinova, J., Kläui, M., Elmers, H., Jourdan, M. & Demsar, J. (2018). Néel spin-orbit torque driven antiferromagnetic resonance in Mn2Au probed by time-domain THz spectroscopy. Phys. Rev. Lett., 120(23). 237201. https://doi.org/10.1103/physrevlett.120.237201 ). Even though many antiferromagnetic compounds are electric insulators ( Citation: Pandey & al., 2017 Pandey, S., Mahadevan, P. & Sarma, D. (2017). Doping an antiferromagnetic insulator: A route to an antiferromagnetic metallic phase. EPL, 117(5). 57003. https://doi.org/10.1209/0295-5075/117/57003 ), which limits the range of their potential applications, e.g., for spin injection ( Citation: Tshitoyan & al., 2015 Tshitoyan, V., Ciccarelli, C., Mihai, A., Ali, M., Irvine, A., Moore, T., Jungwirth, T. & Ferguson, A. (2015). Electrical manipulation of ferromagnetic NiFe by antiferromagnetic IrMn. Phys. Rev. B, 92(21). 214406. https://doi.org/10.1103/physrevb.92.214406 ), the materials like CuMnAs and Mn$_2$Au possess semi-metal and metal properties, inheriting strong spin-orbit coupling and sufficiently high conductivity. These materials also give rise to collective mode excitations in THz range ( Citation: Bhattacharjee & al., 2018 Bhattacharjee, N., Sapozhnik, A., Bodnar, S., Grigorev, V., Agustsson, S., Cao, J., Dominko, D., Obergfell, M., Gomonay, O., Sinova, J., Kläui, M., Elmers, H., Jourdan, M. & Demsar, J. (2018). Néel spin-orbit torque driven antiferromagnetic resonance in Mn2Au probed by time-domain THz spectroscopy. Phys. Rev. Lett., 120(23). 237201. https://doi.org/10.1103/physrevlett.120.237201 ).

Despite a lack of clarity concerning the microscopic mechanisms of the Néel vector switching, these experiments have been widely regarded as a breakthrough in the emerging field of THz spintronics ( Citation: Bhattacharjee & al., 2018 Bhattacharjee, N., Sapozhnik, A., Bodnar, S., Grigorev, V., Agustsson, S., Cao, J., Dominko, D., Obergfell, M., Gomonay, O., Sinova, J., Kläui, M., Elmers, H., Jourdan, M. & Demsar, J. (2018). Néel spin-orbit torque driven antiferromagnetic resonance in Mn2Au probed by time-domain THz spectroscopy. Phys. Rev. Lett., 120(23). 237201. https://doi.org/10.1103/physrevlett.120.237201 ; Citation: Gomonay & al., 2016 Gomonay, O., Jungwirth, T. & Sinova, J. (2016). High antiferromagnetic domain wall velocity induced by néel spin-orbit torques. Phys. Rev. Lett., 117(1). 017202. https://doi.org/10.1103/physrevlett.117.017202 ; Citation: Olejník & al., 2018 Olejník, K., Seifert, T., Kašpar, Z., Novák, V., Wadley, P., Campion, R., Baumgartner, M., Gambardella, P., Němec, P., Wunderlich, J., Sinova, J., Kužel, P., Müller, M., Kampfrath, T. & Jungwirth, T. (2018). Terahertz electrical writing speed in an antiferromagnetic memory. Sci. Adv., 4(3). eaar3566. https://doi.org/10.1126/sciadv.aar3566 ; Citation: Jungwirth & al., 2018 Jungwirth, T., Sinova, J., Manchon, A., Marti, X., Wunderlich, J. & Felser, C. (2018). The multiple directions of antiferromagnetic spintronics. Nat. Phys., 14(3). 200–203. https://doi.org/10.1038/s41567-018-0063-6 ; Citation: Wadley & al., 2016 Wadley, P., Howells, B., elezny, J., Andrews, C., Hills, V., Campion, R., Novak, V., Olejnik, K., Maccherozzi, F., Dhesi, S., Martin, S., Wagner, T., Wunderlich, J., Freimuth, F., Mokrousov, Y., Kune, J., Chauhan, J., Grzybowski, M., Rushforth, A., Edmonds, K., Gallagher, B. & Jungwirth, T. (2016). Electrical switching of an antiferromagnet. Science, 351(6273). 587–590. https://doi.org/10.1126/science.aab1031 ; Citation: Jungwirth & al., 2016 Jungwirth, T., Marti, X., Wadley, P. & Wunderlich, J. (2016). Antiferromagnetic spintronics. Nat. Nanotechnol., 11(3). 231–241. https://doi.org/10.1038/nnano.2016.18 ; Citation: Baltz & al., 2018 Baltz, V., Manchon, A., Tsoi, M., Moriyama, T., Ono, T. & Tserkovnyak, Y. (2018). Antiferromagnetic spintronics. Rev. Mod. Phys., 90(1). 015005. https://doi.org/10.1103/revmodphys.90.015005 ; Citation: Jungfleisch & al., 2018 Jungfleisch, M., Zhang, W. & Hoffmann, A. (2018). Perspectives of antiferromagnetic spintronics. Phys. Lett. A, 382(13). 865–871. https://doi.org/10.1016/j.physleta.2018.01.008 ). It has been suggested that current-induced Néel vector dynamics in an AFM is driven primarily by the so-called Néel spin-orbit torques ( Citation: Brataas & al., 2012 Brataas, A., Kent, A. & Ohno, H. (2012). Current-induced torques in magnetic materials. Nat. Mater., 11(5). 372–381. https://doi.org/10.1038/nmat3311 ; Citation: Hals & al., 2013 Hals, K. & Brataas, A. (2013). Phenomenology of current-induced spin-orbit torques. Phys. Rev. B, 88(8, 8). 085423. https://doi.org/10.1103/physrevb.88.085423 ; Citation: Železný & al., 2014 Železný, J., Gao, H., Výborný, K., Zemen, J., Mašek, J., Manchon, A., Wunderlich, J., Sinova, J. & Jungwirth, T. (2014). 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The Néel spin-orbit torque originates in a non-equilibrium staggered polarization of conduction electrons on AFM sublattices ( Citation: Železný & al., 2014 Železný, J., Gao, H., Výborný, K., Zemen, J., Mašek, J., Manchon, A., Wunderlich, J., Sinova, J. & Jungwirth, T. (2014). Relativistic néel-order fields induced by electrical current in antiferromagnets. Phys. Rev. Lett., 113(15). 157201. https://doi.org/10.1103/physrevlett.113.157201 ; Citation: Šmejkal & al., 2017 Šmejkal, L., Železný, J., Sinova, J. & Jungwirth, T. (2017). Electric control of Dirac quasiparticles by spin-orbit torque in an antiferromagnet. Phys. Rev. Lett., 118(10). 106402. https://doi.org/10.1103/physrevlett.118.106402 ; Citation: Železný & al., 2018 Železný, J., Wadley, P., Olejník, K., Hoffmann, A. & Ohno, H. (2018). Spin transport and spin torque in antiferromagnetic devices. Nat. Phys., 14(3). 220–228. https://doi.org/10.1038/s41567-018-0062-7 ; Citation: Manchon & al., 2019 Manchon, A., Železný, J., Miron, I., Jungwirth, T., Sinova, J., Thiaville, A., Garello, K. & Gambardella, P. (2019). Current-induced spin-orbit torques in ferromagnetic and antiferromagnetic systems. Rev. Mod. Phys., 91(3). 035004. https://doi.org/10.1103/revmodphys.91.035004 ). Characteristic magnitude of the non-equilibrium staggered polarization and its relevance for the experiments with CuMnAs and Mn$_2$Au remain, however, debated.

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