Spin-orbitronics in transition metals

Spin-orbitronics in transition metals

Details

Historical perspective

One day, a friend told me: “Whenever you have a new idea, before you start getting swamped by equations, have a look at JETP first; there’s probably a Russian or Soviet physicist who already published the idea two decades ago”. This is particularly true to spin-orbitronics. 
For instance, spin Hall effect – the separation of up and down spin currents under scattering or through band structure effects – was initially predicted by D’yakonov and Perel in 1971 [1], before being revived by Hirsch and Zhang in 1999-2000 [2]. This later revival was essential though because it was shortly followed by its observation in semiconductors [3] and metals [4] about ten years ago. Its reciprocal effect, the inverse spin Hall effect, was observed at the same time [5].
Inverse spin galvanic effect (also called the Rashba-Edelstein effect) – the electrical generation of non-equilibrium spin density – alos has an intriguing history. It was first proposed by Ivchenko and Vask’o in 1978-1979 [6] and observed in Tellurium shortly after [7]. It was then (re-)discovered by Aronov and Edelstein in 1989-1990 [8]. Between 2005 and 2009, several groups (Bernevig, Manchon & Zhang and Garate and MacDonald, Jalil & Tang) had the simultaneous idea to use this non-equilibrium spin density to torque magnetization [9]. This observation was achieved in 2009-2010 in semiconductors and metals [10].
Magnetic skyrmions and chiral magnets, which constitute the third movement of spin-orbitronics, also have a really long story. Of course, their father, Tony Skyrme proposed them as early as 1962 in the field of particle physics [11]. In magnetic materials, the occurrence of thermodynamically stable lattices of “vortices” was originally proposed in 1989 by Bogdanov [12]. In his work, the antisymmetric exchange interaction that gives rise to such entities was proposed by Dzyaloshinskii and Moriya in 1959-1960 [13], again revived by Fert and Levy in 1980 in the context of weak ferromagnets [14]. Finally magnetic skyrmions and homochiral spin spiral were beautifully evidenced by direct imaging in 2006-2010 [15].
One could ask why such awesome physical effects, predicted long ago, became important only recently. Part of the response comes from the major breakthrough in nanofabrication, materials growth and magnetic imaging that took place between 2000 and 2010. This short summary illustrates that creativity in science is quite a complex and non-linear process…and that Russian journals are definitely worth reading before starting anything new!

                                                 

A snapshot of the vast field of spin-orbitronics: See Nature Materials 14, 871–882 (2015)!​

​[1] D’yakonov and Perel’, Physics Letters 35, 459 (1971).
[2] Hirsch, Phys. Rev. Lett. 83, 1834 (1999); Zhang, Phys. Rev. Lett. 85, 393 (2000).

[3] Kato et al., Science 306, 1910 (2004); Wunderlich et al., Phys. Rev. Lett. 94, 047204 (2005).

[4] Valenzuela and Tinkham, Nature 442, 176 (2006); Kimura et al., Phys. Rev. Lett. 98, 156601 (2007).

[5] Saitoh, Appl. Phys. Lett. 88, 182509 (2006).

[6] Ivchenko and Pikus, Pis'ma Zh. Eksp. Teor. Fiz 27, 604 (1978); Vas’ko and Prima, Sov. Phys.-Solid State 21, 994 (1979).

[7] Vorobev, JETP Lett. 29, 485 (1979).

[8] Aronov et al., JETP Lett. 50, 398 (1989); Edelstein, Solid State Comm. 73, 233 (1990);  

[9] Bernevig and Vafek, Phys. Rev. B 72, 033203 (2005); Tan et al., ArXiV: 0705.3502v1 (2007); Manchon and Zhang, Phys. Rev. B 78, 212405 (2008); Garate and MacDonald, Phys. Rev. B 80, 134403 (2009).

[10] Chernyshov et al., Nature Physics 5, 656 (2009); Miron et al., Nature Materials 9, 230 (2010).

[11] Skyrme, Nuclear Physics31, 556 (1962).

[12] Bogdanov, Sov. Phys. JETP 68, 101 (1989).

[13] Dzyaloshinskii, Sov. Phys. JETP 5, 1259 (1957); Miroya, Phys. Rev. 120, 91 (1960).

[14] Fert and Levy, Phys. Rev. Lett. 44, 1538 (1980).

[15] Bode et al., Nature 447, 190 (2007); Muhlbauer et al., Science 323, 915 (2009); Yu et al., Nature 465, 901 (2010).


Spin-orbit torques

In magnetic materials lacking inversion symmetry, such as in ZnS or B20 crystals or at metallic interfaces such as Pt/CoFeB/MgO, flowing charge currents are accompanied by non-equilibrium spin density, aligned along a direction determined by the symmetry of the structure. Such a non-equilibrium spin density can torque the magnetization and result in current-driven excitation or switching without the need of an external polarizer.
The simplest model system one can start from when modeling spin-orbit torque is the two-dimensional ferromagnetic Rashba gas. Indeed, Rashba spin-orbit coupling is a form that emerges in asymmetrically grown two-dimensional gases and that support a wide variety of fascinating phenomena. See our reviews on this topic [1,2].
So, starting from the simplest ferromagnetic Rashba gas, we demonstrated that Rashba spin-orbit coupling can generate both field-like and damping-like torque, the latter being related to extrinsic spin scattering [3,4] and intrinsic interband transition [5] (see also [6]) and results in quite a complex angular dependence due to band structure effects and anisotropic D’yakonov-Perel’s spin relaxation [7,8]. Noticeably, these results do not only hold in the context of the Rashba gas, but also apply in realistic system, as demonstrated by first principles calculations [9]. The latter was a very important achievement until then, it remained quite unclear how realistic was the Rashba spin-orbit coupling model. Ref. [9] exploits density functional theory and demonstrates that the spin-orbit torques are indeed sizable in systems that are far more complicated than a two-dimensional free electron gas. All these exciting results are summarized in Ref. [10].
We have also worked along a different line to better understand the nature of the spin Hall torque that emerges from adjacent heavy metals using Boltzmann approach and drift-diffusion equations [11]. We also discovered that a new effect, called spin swapping, can substantially contribute to the torque – it creates a field-like torque – in the case where the thickness of the heavy metal is of the order of the mean free path [12,13].
Finally, we have regular collaborations with experimentalists in the field and investigated spin-orbit torques in various configurations. Among the most prominent results, spin-orbit torque was achieved in thick Pd/Co magnetic multilayers, which was attributed to the presence of local inversion symmetry breaking between Pd/Co and Co/Pd interfaces [14,15]. In another work, our experimentalists colleagues demonstrated a significant increase of spin torque efficiency by capping the magnet with a Ru layer, which we interpreted as arising from enhanced interfacial spin dephasing [16]. Finally, a recent study of spin-orbit torque arising from Cu-Au substrate suggests that the spin swapping torque predicted above might be sizable in this system [17].
Several reviews are available on these topics [18,19,20].

Dzyaloshinskii-Moriya interaction

Magnetic materials lacking inversion symmetry can host chiral magnets and present a unique platform for the exploration and control of chiral objects. A crucial ingredient for the generation of such chiral textures is the Dzyaloshinskii-Moriya antisymmetric magnetic interaction (DMI) arising from spin-orbit coupling in inversion asymmetric magnets. Originally proposed in the context of Mott insulators by Dzyaloshinskii and Moriya, as well as weak metallic ferromagnets and spin glasses by Fert and Levy, major attention has been recently drawn toward the nature of the DMI at transition-metal interfaces. In these systems, the interfacial DMI gives rise to several exotic magnetic phases such as Néel domain walls, spin spirals, and skyrmions with a defined chirality. 
In fact, the high complexity of interfacial hybridization hinders the development of qualitative and quantitative predictions in these material combinations. For instance, we performed a systematic calculation of the magnetic and spin-orbit properties of transition metal interfaces, highlighting the evolution of the Rashba-like spin splitting across the heavy metal substrate [21]. We were able to connect this splitting with the induced orbital moment at the interface. Inspired by these results, we then conducted the first systematic and comprehensive theoretical analysis of the DMI for a large series of 3d transition metals (V, Cr, Mn, Fe, Co, Ni) as overlayers on 5d transition metals (W, Re, Os, Ir, Pt, Au) substrates. We demonstrated that the sign and magnitude of the DMI are directly correlated to the degree of 3d-5d orbital hybridization around the Fermi energy, which can be controlled by the intra-atomic Hund’s rule [22]. Hence, Hund’s rule on 3d metal and crystal field considerations on the 5d substrate can serve as guideline to design DMI. We also demonstrated that DMI can be significantly modified by doping the interface with oxygen, paving the way towards interfacial control of DMI [23].

Chiral Damping

Symmetry and symmetry breaking are extremely powerful concepts in physics. They allow insightful hand-waving arguments, as well as rigorous theoretical predictions. One of the most beautiful demonstration of the predictive power of symmetry concepts, in my view, is the study of phase transitions by Kosterlitz, Thouless and Haldane, Physics Nobel prize 2016, as well as the mind-blowing burst of topological materials that have overwhelmed the field of condensed matter physics and beyond in the past ten years.
On a much more humble – but not less influential – scale, an application of symmetry concepts in condensed matter is the Neumann’s principle: “Any physical properties of a system possess the symmetry of that system.” Hence, in a heterostructure possessing inversion symmetry breaking (here we go again), the energy landscape should also display such a symmetry breaking. This is the origin of Dzyaloshinskii-Moriya interaction.
However, since Neumann’s principle is general, it also apply to energy dissipation; in other words, in non-centrosymmetric system, the energy should dissipate differently depending on the chirality of the system considered. Concretely, it means that domain walls with different chiralities possess different damping: this is the idea behind chiral damping. In a recent experiment, our colleagues from SPINTEC identified such a chiral damping in the asymmetric expansion of magnetic bubbles [24]. We subsequently proposed a phenomenological theory to explain such an effect [25]. We are now working on a microscopic theory to obtain a much finer understanding of this effect and compare it with DMI.


Collaborators

M. Miron, G. Gaudin, V. Baltz, CEA/CNRS SPINTEC, Grenoble, France
H. Yang, National University of Singapore, Singapore
X. Qiu, Tongji University, Shanghai, China

Publications

[1] New Perspectives for Rashba Spin-Orbit Coupling, A. Manchon, H.C. Koo, J. Nitta, S.M. Frolov, R.A. Duine, Nature Materials 14, 871–882 (2015). Listed hot paper by Web of Science. 

[2] Rashba spin-orbit coupling in two dimensional systems, in SPINTRONIC 2D MATERIALS: FUNDAMENTALS AND APPLICATIONS, Eds. Yongbing Xu and Wenqing Liu, Elsevier, A. Manchon (2017)

[3] Diffusive spin dynamics in ferromagnetic thin films with a Rashba Interaction X. Wang and A. Manchon, Physical Review Letters 108, 117201 (2012). Published in Virtual Journal of Nanoscale Science and Technology.

[4] Spin-orbit coupled transport and spin torque in a ferromagnetic heterostructure, X. Wang, C. Ortiz Pauyac, and A. Manchon, Phys. Rev. B 89, 054405 (2014).

[5] Intraband and interband spin-orbit torques in noncentrosymmetric ferromagnets, H. Li, H. Gao, L.P. Zarbo, K. Vyborny,  X. Wang , I. Garate, F. Dogan, A. Cejchan, J. Sinova, T. Jungwirth, and A. Manchon, Phys. Rev. B 91, 134402 (2015).

[6] Spin-Orbitronics: A new moment for Berry (News & Views), A. Manchon, Nature Physics 10, 340 (2014).

[7] Angular dependence and symmetry of Rashba spin torque in ferromagnetic heterostructures, C. Ortiz Pauyac, X. Wang, M. Chshiev, and A. Manchon, Appl. Phys. Lett. 102, 252403 (2013).

[8] Angular dependence of spin-orbit spin transfer torques, K.-S. Lee , D. Go , A. Manchon, P.M. Haney , M.D. Stiles, H.-W. Lee,  and K.-J. Lee, Phys. Rev. B 91, 144401 (2015).

[9] Current-induced torques and interfacial spin-orbit coupling, P. M. Haney, H.-W. Lee, K.-J. Lee, A. Manchon, and M.D. Stiles, Phys. Rev. B 88, 214417 (2013).

[10] Theory of Rashba and Dirac Torques, in “Spin Current”, Oxford University Press (2016), Ed. S. Maekawa, A. Manchon and S. Zhang (2016).

[11] Current induced torques and interfacial spin-orbit coupling: Semiclassical modeling, P. M. Haney, H.-W. Lee, K.-J. Lee, A. Manchon, and M. D. Stiles, Phys. Rev. B 87, 174411 (2013).

[12] Crossover between spin swapping and Hall effect in disordered systems, Hamed Ben Mohamed Saidaoui, Y. Otani, and A. Manchon, Phys. Rev. B 92, 024417 (2015).

[13] Spin swapping transport and torques in ultrathin magnetic bilayers, H. Saidaoui and A. Manchon, Phys. Rev. Lett. 117, 036601 (2016).

[14] Spin-orbit torques in Co/Pd multilayer nanowires, M. Jamali, K. Narayanapillai, X. Qiu, A. Manchon, H. Yang, Phys. Rev. Lett. 111, 246602 (2013).

[15] Enhancement of spin Hall effect induced torques for current-driven magnetic domain wall motion: Inner interface effect, D. Bang, J. Yu, X. Qiu, Y. Wang, H. Awano, A. Manchon and H. Yang, Phys. Rev. B 93, 174424 (2016).

[16] Enhanced spin-orbit torque via modulation of spin current absorption, X. Qiu, W. Legrand, P. He, Y. Wu, J. Yu, R. Ramaswamy, A. Manchon, and H. Yang, Phys. Rev. Lett. 117, 217206 (2016).

[17] Temperature dependence of spin-orbit torques in Cu-Au alloys, Y. Wen, J. Wu, P. Li, Q. Zhang, Y. Zhao, A. Manchon, J. Q. Xiao, and X.X. Zhang, Phys. Rev. B 95, 104403 (2017).

[18] Spin-Orbitronics at Transition Metal Interfaces, in Robert E. Camley and Robert L. Stamps, editors: Solid State Physics, Vol 68, SSP, UK: Academic Press, 2017, pp. 1-89, A. Manchon and A. Belabbes (2017).

[19] Spin Orbit-Torques, in “Handbook of Spin Transport and Magnetism”, CRC Press (2016), Eds. E.Y. Tsymbal & I. Zutic, A. Manchon and H. Yang (2016).

[20] Spin Torque in Magnetic Systems: Theory, in “Handbook of Spin Transport and Magnetism”, CRC Press (2011), Eds. E.Y. Tsymbal & I. Zutic, A. Manchon and S. Zhang (revised in 2016).

[21] k-asymmetric spin-splitting at the interface between transition metal ferromagnets and heavy metals, S. Grytsyuk, A. Belabbes, P. M. Haney, H.-W. Lee, K.-J. Lee, M. D. Stiles, U. Schwingenschlogl,  and A. Manchon, Phys. Rev. B 93, 174421 (2016).

[22] Hund's rule-driven Dzyaloshinskii-Moriya interaction at 3d-5d interfaces, A. Belabbes, G. Bihlmayer, F. Bechstedt, S. Blugel, and A. Manchon, Phys. Rev. Lett. 117, 247202 (2016).

[23] Oxygen-enabled control of Dzyaloshinskii-Moriya Interaction in ultra-thin magnetic films, A. Belabbes, G. Bihlmayer, S. Blugel and A. Manchon, Scientific Reports 6:24634 (2016).

[24] Chiral damping of magnetic domain walls, E. Jué, C.K. Safeer, M. Drouard, A. Lopez, P. Balint, L. Buda-Prejbeanu, O. Boulle, S. Auffret, A. Schuhl, A. Manchon, I.M. Miron, G. Gaudin, Nature Materials 15, 272 (2016).

[25] Phenomenology of chiral damping in noncentrosymmetric magnets, C.A. Akosa, I.M. Miron, G. Gaudin, A. Manchon, Phys. Rev. B 93, 214429 (2016).