Yang, Enhancement of spin Hall effect induced torques for current-driven magnetic domain wall motion: inner interface effect, Phys.. Beach, Spin-orbit torques in Ta/ TbxCo100-x ferrimagn[r]
(1)aInstitute of Materials Science, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Cau Giay, Hanoi, Vietnam bToyota Technological Institute, 2-12-1 Hisakata, Tempaku, Nagoya 468- 511, Japan
a r t i c l e i n f o
Article history:
Received June 2018 Received in revised form September 2018 Accepted September 2018 Available online 17 September 2018
Keywords:
Antiferromagnet Ferrimagnet Spin-transfer torques Spineorbit torques Magnetization switching Domain wall motion
Perpendicular magnetic anisotropy
a b s t r a c t
The current-induced spin-torques provide an efficient means of manipulating magnetization, intro-ducing the way for next generation spintronic devices During the past decades, studies have mainly focused on ferromagnetic materials In recent years, antiferromagnetically coupled structures have been found with more efficient spin-toques and robust to magnetic noises This is because they have the strongly exchange-coupled magnetic sublattice structures, and the antiferromagnetic order parameter dynamics are different from those of the ferromagnetic ones As a result, the antiferromagnetically coupled structures offer a novel approach for reducing energy consumption as well as the immunity against external magnetic perturbation in spintronic devices In this review, we discuss current-induced domain wall motion under the action of different spin torques in a wide range of antiferromagnetically coupled materials New approaches and prospective applications of the antiferromagnetic structure-based devices are also discussed
©2018 The Authors Publishing services by Elsevier B.V on behalf of Vietnam National University, Hanoi This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)
1 Introduction
Magnetic materials are a central component in many elec-tronic devices, such as data storage, sensors, motors etc After the discovery of giant magneto-resistance (GMR) by Albert Fert and Peter Grünberg in 1988[1,2]offered with the Nobel prize in physics in 2007, the research on applications in spintronics has speeded up quickly [3e12] Then the spin-polarized current excites the magnetization state and might eventually lead to the magnetization reversal in multilayered structures of a nonmag-netic (NM) layer sandwiched between two ferromagnonmag-netic (FM) layers (Fig la)[13e17]and magnetic wires (Fig 1b)[18] There-fore, continuous efforts in the spintronics field, which use the spins of conduction electrons to further reduce the size as well as energy consumption of the magnetic devices, are important for such applications.
As shown inFig 1a, a multilayered structure consists of FM1/ NM/FM2 where the in-plane FM1 is the pinned layer and supposed to have much higher coercivity than that of the FM2 one The electrons passing FM1 become spin-polarized along the direction of FM1 magnetization The misalignment between the magnetization directions of FM1 and FM2 will cause the conduction electrons to lose the transverse component of their spin momentum This mo-mentum is transferred to the local FM2 magnetization because of total angular momentum conservation[13,14] It means that the magnetization of the FM2 can be excited or even reversed by the injecting current without any applied external magnetic fields. Besides that, one of the most interesting consequences is the pos-sibility of manipulating domain walls (DWs) position in nanowires solely by an electric current: current-induced DW motion (CIDM) effect (Fig 1b)[19e24] This idea had been proposed for a long time [25], but the nanotechnology had limited its approaches such as micro-fabricating technique and effective methods for observing magnetization The advantage of electric current with respect to the effect of magneticfield is that it drives all domain walls in the direction of electron flow, whereas the magnetic field tends to expand or shrink domains of opposite magnetizations[25].
The majority of studies have been carried out for single NiFe nanowires exhibiting in-plane magnetic anisotropy (IMA) [23,26e28] One of the highest DW velocities in NiFe exceeded *Corresponding author
**Corresponding author Institute of Materials Science, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Cau Giay, Hanoi, Vietnam
E-mail addresses:dobang.tti@gmail.com(D Bang),phamthach@toyota-ti.ac.jp
(P Van Thach)
Peer review under responsibility of Vietnam National University, Hanoi
https://doi.org/10.1016/j.jsamd.2018.09.003
(2)100 m/s in zero field [29,30] This is convenient for designing magnetic storage devices based on a shift register[31,33] The DW velocity can be enhanced with increasing temperature due to a decrease of magnetization and pining strength[33] On the other hand, the DW velocity can be enhanced or suppressed depending on the mutual magnitude and orientation of thefield and current [34,35] The velocity enhancement is also dependent on thefield range However, the current density required for inducing magnetization switching and DW motion is of the order of 1012A/ m2, which justifies the need for nanometer sizes with as small cross-sections as possible, to minimize the injected current.
Growing interest has recently been devoted to the systems with perpendicular magnetic anisotropy (PMA)[36e44] The magnetic wires contained very narrow Bloch walls, which contributed to high spin transfer efficiency, as the DWs were displaced with a current density of one order smaller than that of the in-plane magnetic one Some systems with PMA, like Pt/Co/AlOx [36], exhibited larger DW velocities compared to NiFe, up to 400 m/s [37] Recently, a lot of papers have reported on current-induced DW motion in PMA systems composed of different materials such as FePt [38], Co/Ni [39e41], and Co/Pt [42,44] However, the high current density is still needed to drive DWs in the PMA wires, thus limiting its practical applications Very low critical current densities of the order of l09A/m2 have been reported for magnetic semi-conductors, such as GaMnAs[45,46] This is attributed to the low spontaneous magnetization and high-carrier spin polarization of this material[47] But this approach is only achieved at low tem-peratures due to the low Curie temperature of the semiconductor. In the last seven years, an asymmetric (ASY) bilayer of a perpendicular anisotropy FM and heavy metal (HM) with strong spineorbit coupling has attracted considerable interest for their potential utility in spintronic elements In these systems, current-induced spineorbit torques (SOTs)[48,49] on the magnetization can be induced by the Rashba effect at the interface (Fig 2a)[37,50] and by spin currents injected from the heavy metal due to the spin Hall effect (SHE) (Fig 2b)[49,51e56] SOTs have been identified and quantified by a variety of techniques, including spin-torque ferro-magnetic resonance[53], quasistatic magnetization tilting probed through harmonic voltage measurements [54], and
current-induced hysteresis loop shift measurements [57] In the bilayer wires, DWs can be moved with high speed up to a few hundreds m/ s under current densities of the order of 1011A/m2in the opposite direction to the direction of DWs motion in a single layer under the effect of conventional spin-transfer torques (STTs) Unlike the FM system, in antiferromagnetically (AF) coupled structures, their angular momentum is not associated with the order parameter so that spin dynamics in these structures is intrinsically much faster than in FMs Up to now, a maximum DW velocity of up to 750 m/s has been reported for Co/Ni/Co/Ru (t)/Co/Ni/Co wires with a syn-thetic antiferromagnetic (SAF) structure Such a high DW velocity can be achieved owing to the SAF structure that gives rise to a novel torque associated with the antiferromagnetic exchange coupling
field [58] Current efforts are to optimize material structures for realizing a high-speed and low-power magnetic memory based on the CIDM Recently, current-driven relativistic Neel orderfield as well as DW motion in AFs where magnetic atoms have a local environment with broken inversion symmetry have been predicted theoretically and experimentally [59e65] It has been demon-strated that the antiferromagnetic DW can be moved in these AFs with very high velocities which are orders of magnitude greater than those in FMs due to the efficiency of the staggered spineorbit
fields to couple to the order parameter and the exchange-enhanced phenomena in AF texture dynamics Furthermore, the absence of a Walker breakdown limit can keep the velocity of the antiferro-magnetic DW up to values of few km/s[61] Besides that, rare-earth (RE) transition-metal (TM) alloys named ferrimagnetic alloys in which the moments of RE sublattices are anti-ferromagnetically coupled with those of TM sublattices are potential candidates for realizing such high speed devices[66e73] In ferrimagnetic alloys, a negative exchange interaction between the RE and TM sublattices can induce much faster DW motion at low current densities[74] and magneticfields[75] Therefore, the AFs have led to the recent development of spintronic-based devices with the ultimate speed of magnetic dynamics[59,76e79].
2 Current induced domain wall motion in wires based on antiferromagnetically coupled structures
2.1 Synthetic antiferromagnetic bilayer wires
A synthetic antiferromagnetic structure composes of two mag-netic sublayers of upper magmag-netic (UM) and lower magmag-netic (LM) layers which are exchange-coupled via an ultrathin spacer layer
Fig 1.Schematic of an injecting current induces (a) in-plane magnetization exciting and magnetization switching in a multilayered structure of FM1/NM/FM2 and (b) domain wall (DW) motion in an in-plane magnetic wire
(3)DMI derived from the strong spineorbit coupling and the proximity-induced moment in Pt[81e84] WhenJ¼0, the DW with the magnetizations ofMUandMLin the centre of the SAF structure respectively, exhibits an anticlockwise Neel structure. WhenJs0,MUandMLare rotated towards the spin accumulation direction denoted by the magenta arrows (Fig 3b) and are sub-jected to longitudinalfieldsHUlg andHLlg, respectively, which are composed of the corresponding DMIfields andHx, and exchange-couplingfieldsHUexandHLex, respectively (Fig 3c and d) Each of
magnetic coupling of bilayers also can be attributed to a change in the DW velocity in a SAF wire by changing the thickness of the spacer (Fig 5c) For the antiferromagnetically coupled wires with Ru thicknesses of about and Å, the DW velocities are much higher than those of the ferromagnetically coupled ones.
As mentioned above, theoretical estimations suggest the possi-bility to substantially reduce the critical currents and tailor the domain structure of antiferromagnetically -coupled wires at critical currents above 109A/m2, which are about one order of magnitude below the highest value reported for the ferromagnetic structures. However, most recent studies on the SAF wire have been focused on only Co/Ni system[85,86]due to its strong coupling in the ultrathin regime To optimize effectively the current-induced DW motion in AFs, one must control the thickness and magnetization by changing their compositions As such, antiferromagnetic compounds such as Mn2Au and CuMnAs[61]and ferrimagnetic alloys such as the RE-TM alloys offer additional advantages.
Fig 3.Schematic illustration of (a) DWs in a SAF wire and (b) Spin Hall current from an HM layer induced DWs motion in the SAF wire (c, d) Directions offields and torques in the SAF bilayer, upper and lower panels correspond to the UF and LF, respectively Replotted from Ref 58 (Copyright 2015 Macmillan Publisher Limited)
(4)2.2 Current-induced DW motion in ferrimagnetic alloys
In the RE-TM alloys, where RE element (e.g., Tb, Gd, etc.) and TM element (e.g., Co, Fe, etc.) sublattices are antiferromagnetically coupled, the net magnetic moment can be tuned easily by varying the RE-TM composition as shown in Fig RE-TM alloy such as TbeCofilms can be simply fabricated from a single target of TbCo alloys or co-sputtering of two Co and Tb targets by using RF or DC magnetron sputtering at room temperature without any
post-annealing processes At room temperature, pure Tb and Co are paramagnetic and in-plane anisotropy ferromagnetic, respectively. In form of an alloy or multilayers with alternating thin layers of Tb and Co, however, the Tb and Co sublattices show a ferrimagnetic order (Fig 6a)[87,88] This ferrimagnetic order between the Tb and Co sublattices may be confirmed by observation of the compensa-tion points (Fig 6b).
It has been reported that the critical current density to drive domain wall motion strongly depends on the layered structure as well as its composition[68] The lowest critical current density of about 1.51011A/m2and the highest slope of domain wall velocity curve are obtained for the wire having thin Co sublayers and more inner Tb/Co interfaces, while the largest critical current density of 2.61011A/m2is required to drive domain walls in the TbeCo alloy magnetic wire (Fig 7).
An enhancement of the antidamping torques by extrinsic spin Hall effect due to Tb rare-earth impurity-induced skew scattering is suggested to explain the high efficiency of current-induced domain wall motion in the Co/Tb multilayer with more number of inner interfaces (n) This study indicates an efficient way to reduce the critical current density for DW motion through inner interface engineering.
As discussed above, the effective SAFfilms are mostly limited in ultrathin sublayers of a few Å and total film thickness of few nanometers due to the dominance of interfacial effects Recently, ultrafastfield-induced DW motion has been observed in GdFeCo-based ferrimagnets at the angular momentum compensation temperature[75,89,90] Because of different Lande g-factors be-tween the RE and TM elements, below the Curie temperature these ferrimagnets have two special temperatures of the magnetization compensation temperature (TM), at which the two magnetic mo-ments cancel each other, and the angular momentum compensa-tion temperature (TA), at which the net angular momentum vanishes[91,92] As a result, the nature of the dynamics of the ferrimagnets changes from ferromagnetic to antiferromagnetic on
Fig 5.DW velocity as functions of (a) longitudinalfield (Left and right panels: measured and calculated result), (b) current pulse densities for different thicknesses and (c) Ru spacer thickness (the orange and blue shaded regions correspond to ferromagnetic and antiferromagnetic couplings) Replotted from ref 56 (Copyright 2015 Macmillan Publisher Limited)
(5)approaching the TA Furthermore, the net magnetic moment of ferrimagnets is nonzero atTAand can thus couple to an external magneticfield as well as the efficiencies offield-induced DW mo-tion As shown inFig 8, the DW velocity can reach up to over km/s under around 100 mTfield at temperature aroundTA However, it will be rapidly reduced when the temperature is far from theTA.
In the following, a theory for thefield-driven DW dynamics in ferrimagnets is discussed briefly The low-energy dynamics of a DW in quasi-one-dimensional magnets is generally described by
Fig 7.(a) Schematic illustration of TbeCo basedfilms with different layered structures (b) Current density dependence of DW velocity for different magnetic wires (1.1-mm width) of A-, B-, and C-stack structures Replotted from Ref 68 (Copyright 2016 American Physical Society)
Fig 8.DW velocity in a GdFeCo ferrimagnetic wire as a function of temperature under different applied in-planefields Replotted from ref 75 (Copyright 2017 Macmillan Publisher Limited)
(6)two collective coordinates, its position (X) and angle (4), which capture the translational and spin-rotational degrees of freedom of the DW, respectively In ferromagnets, the force onXinduces the dynamics of4and vice versa Due to this coupling, the mo-tion of a DW is limited by the Walker breakdown [93] In contrast, in antiferromagnets the dynamics of X and 4 are in-dependent due to vanishing of the net spin density The DW dynamics can be fast and be free from the Walker breakdown In RE-TM alloys, the RE and TM moments can be easily controlled by varying the composition or temperature, so that the TA can be designed for appropriate applications To date, the effect of angular momentum compensation point on magnetization dy-namics has attracted to studies of ferrimagnetic systems [67,94,95] The lower threshold current density of one order of magnitude, smaller power consumption, and higher speed than those of FM systems would be a key to realizing spintronic de-vices Finally, The improvement of DW velocity and reduction of critical current density (Jc) by optimizing magnetic materials and layered structures as functions of year are shown in Fig It
clearly shows that the DW velocity is rapidly increased, while the Jcis reduced by a few orders of magnitude at room temperature without applying any externalfields.
2.3 Prospective applications of the current-induced DW motion based spintronic devices
Recently, magnetic nanostructures have been at the heart of a multitude of devices ranging from applications of sensors to data storage Probably the best known concept device is the racetrack memory, which was proposed by IBM[31,32,96]based on the CIDM effect As shown inFig 10, the racetrack memory can be designed along lines in two and three dimensions or even in circular loops. One of the key problems of the conventional hard drive is the mechanical motion of the media, which can lead to failure in the case of a mechanical shock In the case of the racetrack memory, positions of domains as well as coded information can be moved without using any mechanical motors On the other hand, the racetrack only comprises one write or read element which can
(7)to the symmetry of the Y-shape, the two domains from inputs arrive at the confluence point at same time and then are combined each other to continue moving to the output gate as a signal“l”for the case of input (1, 1) For the case of input (1, 0) or (0, l), a single domain will be trapped at the confluence points due to the different widths of the branches of inputs and output, so that the output signal is“0” By using this concept device, memory and logic can be
netic process) and data processing (electronic transistors) It means that these devices can potentially work faster with higher energy-efficiency Additionally, other solutions such as magneticfield and heat can be utilized to assist the CIDM for reducing theJc Therefore, it is believed that the new structures can be very promising to build up future memory and logic devices performing ultra-high density and speed.
(8)3 Conclusion
We have shown the key distinctions in current-induced dynamics in ferromagnetic, antiferromagnetic and ferrimag-netic structures As compared to the FM-ordered materials, the AF-ordered ones have more efficient spin-toques, as well as high DW motion speeds of up to few hundreds m/s and are robust to magnetic noises This is because the AF materials have a strongly exchange-coupled magnetic sublattice struc-ture, and the antiferromagnetic order parameter dynamics are different from those of the ferromagnetic ones However, these effective SAFfilms are mostly limited to the ultrathin sublayers of a few Å and the total film thickness of a few nanometers due to the dominance of interfacial effects such as Rashba ef-fect and DMI Alternatively, the RE-TM ferrimagnetic alloys are not limited in these thin thickness regions The DW velocity can reach over km/s under around 100 mT field at temper-ature around the angular compensated tempertemper-ature The RE and TM moments can be easily controlled by varying compo-sition or temperature, so that the angular compensated tem-perature can be designed for appropriate applications The RE-TM ferrimagnetic alloys are therefore expected to provide a
new approach for reducing energy consumption as well as the immunity against external magnetic perturbation in spintronic devices, such as racetrack memories and spin logic gates.
Acknowledgments
This research was partially supported by the Ministry of Edu-cation, Culture, Sport, Science and Technology, Japan - Supported Program for Strategic Research Foundation at Private University (2014e2020) and KAKENHI (Nos 17H03240 and 18K14128).
References
[1] M.N Baibich, J.M Proto, A Fert, F Nguyen Van Dau, F Petroff, P Etienne, G Creuzet, A Friederich, L Chazelas, Giant magnetoresistance of (001)Fe/ (001)Cr magnetic superlattices, Phys Rev Lett 61 (1988) 2472e2475.https:// doi.org/10.1103/PhysRevLett.61.2472
[2] G Binasch, P Gr'unberg, F Saurenbach, W Zinn, Enhanced magnetoresistance in layered magnetic structures with antiferromagnetic interlayer exchange, Phys Rev B 39 (1989) 4828e4830.https://doi.org/10.1103/PhysRevB.39.4828 [3] J Daughton, J Brown, E Chen, R Beech, A Pohm, W Kude, Magneticfield sensors using GMR multilayer, IEEE Trans Magn 30 (1994) 4608e4610
https://doi.org/10.1109/20.334164
(9)[9]] H Dery, P Dalal, L Cywinski, L.J Sham, Spin-based logic in semiconductors for reconfigurable large-scale circuits, Nature 447 (2007) 573e576.https:// doi.org/10.1038/nature05833[9]
[10] Stuart Parkin, See-Hun Yang, Memory on the racetrack, Nat Nanotechnol 10 (2015) 195e198.https://doi.org/10.1038/nnano.2015.41
[11] Zhiyong Qiu, Dazhi Hou, Joseph Barker, Kei Yamamoto, Olena Gomonay, Eiji Saitoh, Spin colossal magnetoresistance in an antiferromagnetic insu-lator, Nat Mater 17 (2018) 577e580 https://doi.org/10.1038/s41563-018-0087-4
[12] Seung-heon Chris Baek, Kyung-Woong Park, Deok-Sin Kil, Yunho Jang, Jongsun Park, Kyung-Jin Lee, Byong-Guk Park, Complementary logic operation based on electric-field controlled spineorbit torques, Nat Electron (2018), 398-340,https://doi.org/10.1038/s41928-018-0099-8
[13] J.C Slonczewski, Current-driven excitation of magnetic multilayers, J Magn Magn Mater 159 (1996) L1eL7 https://doi.org/10.1016/0304-8853(96) 00062-5
[14] L Berger, Emission of spin waves by a magnetic multilayer traversed by a current, Phys Rev B 54 (1996) 9353e9358.https://doi.org/10.1103/PhysRevB 54.9353
[15] M Tsoi, A.G Jansen, J Bass, W.-C Chiang, M Seck, V Tsoi, P Wyder, Excitation of a magnetic multilayer by an electric current, Phys Rev Lett 80 (1998) 4281e4284.https://doi.org/10.1103/PhysRevLett.80.4281
[16] J.A Katine, F.J Albert, R.A Buhrman, E.B Myers, D.C Ralph, Current-driven magnetization reversal and spin-wave excitations in Co/Cu/Co pillars, Phys Rev Lett 84 (2000) 3149e3152.https://doi.org/10.1103/PhysRevLett.84.3149 [17] S Zhang, P.M Lery, A Fert, Mechanisms of spin-polarized current-driven magnetization switching, Phys Rev Lett 88 (2002) 236601.https://doi.org/ 10.1103/PhysRevLett.88.236601
[18] L Thomas, S Parkin, in: H Kronmtller, S Parkin (Eds.), Nanowires in Hand-book of Magnetism and Advanced Magnetic Materials, vol 2, John Wiley&
Sons, Ltd., 2007
[19] A Thiaville, Y Nakatani, J Miltat, N Vernier, Domain wall motion by spin-polarized current: a micromagnetic study, J Appl Phys 95 (2004) 7049e7051.https://doi.org/10.1063/1.1667804
[20] G Tatara, H Kohno, Theory of current-driven domain wall motion: spin transfer versus momentum transfer, Phys Rev Lett 92 (2004) 086601
https://doi.org/10.1103/PhysRevLett.92.086601
[21] Z.Liand S Zhang, Domain-wall dynamics driven by adiabatic spin-transfer torques, Phys Rev 70 (2004) 024417.https://doi.org/10.1103/PhysRevB.70 024417
[22] A Thiaville, Y Nakatani, F.F Piechon, J Miltat, T Ono, Transient domain wall displacement under spin-polarized current pulses, Eur Phys J B 60 (2007) 15e27.https://doi.org/10.1140/epjb/e2007-00320-3
[23] N Vernier, D.A Allwood, D Atkinson, M.D Cooke, R.P Cowburn, Domain wall propagation in magnetic nanowires by spin-polarized current injection, Europhys Lett 65 (2004) 526.https://doi.org/10.1209/epl/i2003-10112-5 [24] G.S.D Beach, C Knutson, M Tsoi, J.L Erskine, Field- and current-driven
domain wall dynamics: an experimental picture, J Magn Magn Mater 310 (2007) 2038e2040.https://doi.org/10.1016/j.jmmm.2006.10.946
[25] L Berger, Dragging of domains by an electric current in very pure, non-compensated, ferromagnetic metals, Phys Lett 46 (1973) 3e4.https://doi org/10.1016/0375-9601(73)90658-0
[26] J Grollier, D Lacour, V Cros, A Hamzi, A Vaur'es, A Fert, D Adam, G Faini, Switching the magnetic configuration of a spin valve by current-induced domain wall motion, J Appl Phys 92 (2002) 4825e4827.https://doi.org/10 1063/1.1507820
[27] A Yamaguchi, S Nasu, H Tanigawa, T Ono, K Miyake, K Mibu, T Shinjo, Effect of Joule heating in current-driven domain wall motion, Appl Phys Lett 86 (2005) 012511.https://doi.org/10.1063/1.1847714
[28] M Kl€aui, P.-O Jubert, R Allenspach, A Bischof, J.A.C Bland, G Faini, U Ri idiger, C.A.F Yaz, L Vila, C Vouille, Direct observation of domain-wall configurations transformed by spin currents, Phys Rev Lett 95 (2005) 026601.https://doi.org/10.1103/PhysRevLett.95.026601
[29] M Hayashi, L Thomas, C Rettner, R Moriya, Y.B Bazaliy, S.S.P Parkin, Current driven domain wall velocities exceeding the spin angular momentum transfer
1103/PhysRevLett.96.197207
[36] T.A Moore, I.M Miron, G Gaudin, G Serret, S Auffret, B Rodmacq, A Schuhl, S Pizzini, J Vogel, M Bonfim, High domain wall velocities induced by current in ultrathin Pt/Co/AlOx wires with perpendicular magnetic anisotropy, Appl Phys Lett 93 (2008) 262504.https://doi.org/10.1063/1.3062855
[37] I.M Miron, G Gaudin, S Auffret, B Rodmacq, A Schuhl, S Pizzini, J Vogel, P Gambardella, Current-driven spin torque induced by the Rashba effect in a ferromagnetic metal layer, Nat Mater (2010) 230e234.https://doi.org/10 1038/nmat2613
[38] C Burrowes, A.P Mihai, D Ravelosona, J.-V Kim, C Chappert, L Vila, A Maffy, Y Samson, F Garcia-Sanchez, L.D Buda-Prejbeanu, I Tudosa, E.E Fullerton, J.-P Affane, Non-adiabatic spin-torques in narrow magnetic domain walls, Nat Phys (2010) 17e21.https://doi.org/10.1038/nphys1436
[39] C Burrowes, D Ravelosona, C Chappert, S Mangin, E.E Fullerton, J.A Katine, B.D Terris, Role of pinning in current driven domain wall motion in wires with perpendicular anisotropy, Appl Phys Lett 93 (2008) 172513.https://doi org/10.1063/1.2998393
[40] T Koyama, G Yamada, H Tanigawa, S Kasai, N Ohshima, S Fukami, N Ishiwata, Y Nakatani, T Ono, Control of domain wall position by electrical current in structured Co/Ni wire with perpendicular magnetic anisotropy, Appl Phys Express (2008) 101303 https://doi.org/10.1143/APEX.1 101303
[41] H Tanigawa, T Koyama, G Yamada, D Chiba, S Kasai, S Fukami, T Suzuki, N Ohshima, N Ishiwata, Y Nakatani, T Ono, Domain wall motion induced by electric current in a perpendicularly magnetized Co/Ni nano-wire, Appl Phys Express (2009) 053002.https://doi.org/10.1143/APEX.2.053002
[42] S Fukami, Y Nakatani, T Suzuki, K Nagahara, N Ohshima, N Ishiwata, Relation between critical current of domain wall motion and wire dimension in perpendicularly magnetized Co/Ni nanowires, Appl Phys Lett 95 (2009) 232504.https://doi.org/10.1063/1.3271827
[43] O Boulle, J Kimmling, P Warnicke, M Kl"aui, U R'udiger, G Malinowski, H.J.M Swagten, B Koopmans, C Ulysse, G Faini, Nonadiabatic spin transfer torque in high anisotropy magnetic nanowires with narrow domain walls, Phys Rev Lett 101 (2008) 216601.https://doi.org/10.1103/PhysRevLett.101.216601 [44] M Cormier, A Mougin, J Ferr'e, A Thiaville, N Charpentier, F Pi'echon, R Weil, V Baltz, B Rodmacq, Effect of electrical current pulses on domain walls in Pt/Co/Pt nanotracks with out-of-plane anisotropy: spin transfer tor-que versus Joule heating, Phys Rev B 81 (2010) 024407.https://doi.org/10 1103/PhysRevB.81.024407
[45] M Yamanouchi, D Chiba, F Matsukura, H Ohno, Current-induced domain-wall switching in a ferromagnetic semiconductor structure, Nature 428 (2004) 539e542.https://doi.org/10.1038/nature02441
[46] M Yamanouchi, J Ieda, F Matsukura, S.E Barnes, S Maekawa, H Ohno, Universality classes for domain wall Motion in the ferromagnetic semi-conductor (Ga,Mn)As, Science 317 (2007) 1726 https://doi.org/10.1126/ science.1145516
[47] H Ohno, T Dietl, Spin-transfer physics and the model of ferromagnetism in (Ga,Mn)As, J Magn Magn Mater 320 (2008) 1293e1299.https://doi.org/10 1016/j.jmmm.2007.12.016
[48] M Miron, K Garello, G Gaudin, P.-J Zermatten, M.V Costache, S Auffret, S Bandiera, B Rodmacq, A Schuhl, P Gambardella, Perpendicular switching of a single ferromagnetic layer induced by in-plane current injection, Nature 476 (2011) 189e193.https://doi.org/10.1038/nature10309
[49] L Liu, C.-F Pai, Y Li, H.W Tseng, D.C Ralph, R.A Buhrman, Spin-torque switching with the giant spin Hall effect of tantalum, Science 336 (2012) 555
https://doi.org/10.1126/science.1218197
[50] S Emori, T Nan, A.M Belkessam, X Wang, A.D Matyushov, C.J Babroski, Y Gao, H Lin, N.X Sun, Interfacial spin-orbit torque without bulk spin-orbit coupling, Phys Rev B 93 (2016) 180402.https://doi.org/10.1103/PhysRevB.93.180402 [51] L Liu, O.J Lee, T.J Gudmundsen, D.C Ralph, R.A Buhrman, Current-Induced
switching of perpendicularly magnetized magnetic layers using spin torque from the apin Hall effect, Phys Rev Lett 109 (2012) 096602.https://doi.org/ 10.1103/PhysRevLett.109.096602
(10)vector in TajCoFeBjMgO, Nat Mater 12 (2013) 240e245.https://doi.org/10 1038/nmat3522
[53] C.-F Pai, L Liu, Y Li, H.W Tseng, D.C Ralph, R.A Buhrman, Spin transfer torque devices utilizing the giant spin Hall effect of tungsten, Appl Phys Lett 101 (2012) 122404.https://doi.org/10.1063/1.4753947
[54] K Garello, I.M Miron, C.O Avci, F Freimuth, Y Mokrousov, S Bliigel, S Auffret, O Boulle, G Gaudin, P Gambardella, Symmetry and magnitude of spineorbit torques in ferromagnetic heterostructures, Nat Nanotechnol (2013) 587e593.https://doi.org/10.1038/nnano.2013.145
[55] C.O Avci, K Garello, C Nistor, S Godey, B Ballesteros, A Mugarza, A Barla, M Valvidares, E Pellegrin, A Ghosh, I.M Miron, O Boulle, S Auffret, G Gaudin, P Gambardella, Fieldlike and antidamping spin-orbit torques in as-grown and annealed Ta/CoFeB/MgO layers, Phys Rev B 89 (2014) 214419
https://doi.org/10.1103/PhysRevB.89.214419
[56] C.O Avci, K Garello, M Gabureac, A Ghosh, A Fuhrer, S.F Alvarado, P Gambardella, Interplay of spin-orbit torque and thermoelectric effects in ferromagnet/normal-metal bilayers, Phys Rev B 90 (2014) 224427.https:// doi.org/10.1103/PhysRevB.90.224427
[57] Chi-Feng Pai, Maxwell Mann, Aik Jun Tan, S.D Geoffrey, Beach, Determination of spin torque efficiencies in heterostructures with perpendicular magnetic anisot-ropy, Phys Rev B 93 (2016) 144409.https://doi.org/10.1103/PhysRevB.93.144409 [58] See-Hun Yang, Kwang-Su Ryu, Stuart Parkin, Domain-wall velocities of up to 750 m s1driven by exchange-coupling torque in synthetic antiferromagnets, Nat Nanotechnol 10 (2014) 221e226.https://doi.org/10.1038/nnano.2014.324 [59] P Wadley, B Howells, J.Zelezný, C Andrews, V Hills, R.P Campion, V Novak, K Olejník, F Maccherozzi, S.S Dhesi, S.Y Martin, T Wagner, J Wunderlich, F Freimuth, Y Mokrousov, J Kunes, J.S Chauhan, M.J Grzybowski, A.W Rushforth, K.W Edmonds, B.L Gallagher, T Jungwirth, Electrical switching of an antiferromagnet, Science 351 (2016) 587e590.https://doi org/10.1126/science.aab1031
[60] J Zelezný, H Gao, K Výborný, J Zemen, J Ma sek, Aurelien Manchon, J Wunderlich, Jairo Sinova, T Jungwirth, Relativistic neel-orderfields induced by electrical current in antiferromagnets, Phys Rev Lett 113 (2014) 157201
https://doi.org/10.1103/PhysRevLett.113.157201
[61] O Gomonay, T Jungwirth, J Sinova, High antiferromagnetic domain wall velocity induced by Neel spin-orbit torques, Phys Rev Lett 117 (2016) 017202.https://doi.org/10.1103/PhysRevLett.117.017202
[62] Takayuki Shiino, Se-Hyeok Oh, Paul M Haney, Seo-Won Lee, Gyungchoon Go, Byong-Guk Park, Kyung-Jin Lee, Antiferromagnetic domain wall motion driven by spin-orbit torques, Phys Rev Lett 117 (2016) 087203.https://doi org/10.1103/PhysRevLett.117.087203
[63] Lili Lang, Xuepeng Qiu, Shiming Zhou, Anomalous Hall-like efect probe of antiferromagnetic domain wall, Sci Rep (2018) 329.https://doi.org/10 1038/s41598-017-18514-4
[64] Ziyang Yu, Yue Zhang, Zhenhua Zhang, Ming Cheng, Zhihong Lu, Xiaofei Yang, Jing Shi, Rui Xiong, Domain-wall motion at an ultrahigh speed driven by spineorbit torque in synthetic antiferromagnets, Nanotechnology 29 (2018) 175404.https://doi.org/10.1088/1361-6528/aaaf35
[65] Z.Y Chen, Z.R Yan, Y.L Zhang, M.H Qin, Z Fan, X.B Lu, X.S Gao, J.-M Liu, Mi-crowavefields driven domain wall motions in antiferromagnetic nanowires, N J Phys 20 (2018) 063003.https://doi.org/10.1088/1367-2630/aac68e [66] M Gottald, M Hehn, F Montaigne, D Lacour, G Lengaigne, S Suire, S Mangin,
Magnetoresistive effects in perpendicularly magnetized Tb-Co alloy based thinfilms and spin valves, J Appl Phys 111 (2012) 083904.https://doi.org/10 1063/1.3703666
[67] T Liu Tolley, Y Xu, S Le Gall, M Gottwald, T Hauet, M Hehn, F Montaigne, E E' Fullerton, S Mangin, Generation and manipulation of domain walls using a thermal gradient in a ferrimagnetic TbCo wire, Appl Phys Lett 106 (2015) 242403.https://doi.org/10.1063/1.4922603
[68] Bang Do, Hiroyuki Awano, Current-induced domain wall motion in perpen-dicular magnetized TbeFeeCo Wire with different interface structures, Appl Phys Express (2012) 125201.https://doi.org/10.1143/APEX.5.125201 [69] J Finley, L Liu, Spin-orbit-torque efficiency in compensated ferrimagnetic
cobalt-terbium alloys, Phys Rev Appl (2016) 054001.https://doi.org/10 1103/PhysRevApplied.6.054001
[70] D Bang, J Yu, X Qiu, Y Wang, H Awano, A Manchon, H Yang, Enhancement of spin Hall effect induced torques for current-driven magnetic domain wall motion: inner interface effect, Phys Rev B 93 (2016) 174424.https://doi.org/ 10.1103/PhysRevB.93.174424
[71] K Ueda, M Mann, C.-F Pai, A.-J Tan, G.S.D Beach, Spin-orbit torques in Ta/ TbxCo100-xferrimagnetic alloyfilms with bulk perpendicular magnetic anisot-ropy, Appl Phys Lett 109 (2016) 232403.https://doi.org/10.1063/1.4971393 [72] Masaaki Tanaka, Sho Sumitomo, Noriko Adachi, Syuta Honda, Hiroyuki Awano,
Mibu Ko, Electric-current-induced dynamics of bubble domains in a ferrimag-netic Tb/Co multilayer wire below and above the magferrimag-netic compensation point, AIP Adv (2017) 055916.https://doi.org/10.1063/1.4974067
[73] Tsukasa Asari, Ryosuke Shibata, Hiroyuki Awano, Novel magnetic wire fabrica-tion process by way of nanoimprint lithography for current induced magneti-zation switching, AIP Adv (2017) 055930.https://doi.org/10.1063/1.4977769 [74] Rahul Mishra, Jiawei Yu, Xuepeng Qiu, M Motapothula, T Venkatesan, Hyunsoo Yang, Anomalous current-induced spin torques in ferrimagnets near compensation, Phys Rev Lett 118 (2017) 167201.https://doi.org/10.1103/ PhysRevLett.118.167201
[75] Kab-Jin Kim, Se Kwon Kim, Yuushou Hirata, Se-Hyeok Oh, Takayuki Tono,
Duck-Ho Kim, Takaya Okuno, Woo Seung Ham, Sanghoon Kim,
Gyoungchoon Go, Yaroslav Tserkovnyak, Arata Tsukamoto,
Takahiro Moriyama, Kyung-Jin Lee, Teruo Ono, Fast domain wall motion in the vicinity of the angular momentum compensation temperature of ferri-magnets, Nat Mater 16 (2017) 1187e1192 https://doi.org/10.1038/ nmat4990
[76] T Jungwirth, T Jungwirth, X Marti, P Wadley, J Wunderlich, et al., Antifer-romagnetic spintronics, Nat Nanotechnol 11 (2016) 231e241.https://doi org/10.1038/nnano.2016.18
[77] C.-H Marrows, Addressing an antiferromagnetic memory, Science 351 (2016) 558.https://doi.org/10.1126/science.aad8211
[78] Lan Jin, Weichao Yu, Xiao Jiang, Antiferromagnetic domain wall as spin wave polarizer and retarder, Nat Commun (2017) 178.https://doi.org/10.1038/ s41467-017-00265-5
[79] V Baltz, A Manchon, M Tsoi, T Moriyama, T Ono, Y Tserkovnyak, Antifer-romagnetic spintronics, Mod Phys 90 (2018) 015005 https://doi.org/10 1103/RevModPhys.90.015005
[80] S Parkin, Xin Jiang, C Kaiser, A Panchula, K Roche, Magnetically engineered spintronic sensors and memory, Proc IEEE 91 (2003) 661e680, in:https://doi org/10.1109/JPROC.2003.811807
[81] I.E Dryaloshinskii, Thermodynamical theory of 'weak"ferromagnetism in antiferromagnetic substances, Sov Phys JETP (1957) 1259
[82] I.E Dzyaloshinskii, Theory of helicoidal structures in antiferromagnets I nonmetals, Sov Phys JETP 19 (1964) 960
[83] K.-S Ryu, S.-H Yang, L Thomas, S.S.P Parkin, Chiral spin torque arising from proximity-induced magnetization, Nat Commun (2014) 3910.https://doi org/10.1038/ncomms4910
[84] Je Soong-Geun, Juan-Carlos Rojas-Sanchez, Thai Ha Pham, Pierre Vallobra, Gregory Malinowski, Daniel Lacour, Thibaud Fache, Marie-Claire Cyrille,
Dae-Yun Kim, Sug-Bong Choe, Belmeguenai Mohamed, Michel Hehn,
Stephane Mangin, Gilles Gaudin, Boulle Olivier, Spin-orbit torque-induced switching in ferrimagnetic alloys: experiments and modeling, Appl Phys Lett 112 (2018) 062401.https://doi.org/10.1063/1.5017738
[85] Takashi Kominea, Tomosuke Aono, Micromagnetic analysis of current-induced domain wall motion in a bilayer nanowire with synthetic antiferromagnetic coupling, AIP Adv (2016) 056409.https://doi.org/10.1063/1.4944769 [86] S Krishnia, P Sethi, W.L Gan, F.N Kholid, I Purnama, M Ramu, T.S Herng,
J Ding, W.S Lew, Role of RKKY torque on domain wall motion in synthetic antiferromagnetic nanowires with opposite spin Hall angles, Sci Rep (2017) 11715.https://doi.org/10.1038/s41598-017-11733-9
[87] P Hansen, C Clausen, G Much, M Rosenkranz, K Witter, Magnetic and magneto-optical properties of rare-earth transition-metal alloys containing Gd, Tb, Fe, Co, J Appl Phys 66 (1989) 756e767.https://doi.org/10.1063/1.343551 [88] L Ertl, G Endl, H Hoffmann, Structure and magnetic properties of sputtered Tb/Co multilayers, J Magn Magn Mater 113 (1992) 227e237.https://doi.org/ 10.1016/0304-8853(92)91271-T
[89] Yuichiro Kurokawa, Masaya Kawamoto, Hiroyuki Awano, Current-induced domain wall motion attributed to spin Hall effect and DzyaloshinskyeMoriya interaction in Pt/GdFeCo (100 nm) magnetic wire, Jap J Appl Phys 55 (2016) 07MC02.http://doi.org/10.7567/JJAP.55.07MC02
[90] Yuichiro Kurokawa, Akihiro Shibata, Hiroyuki Awano, Enhancement of spin orbit torques in a Tb-Co alloy magnetic wire by controlling its Tb composition, AIP Adv (2017) 055917.https://doi.org/10.1063/1.4974280
[91] C.D Stanciu, A.V Kimel, F Hansteen, A Tsukamoto, A Itoh, A Kirilyuk, T.h Rasing, Ultrafast spin dynamics across compensation points in ferrimag-netic GdFeCo: the role of angular momentum compensation, Phys Rev B 73 (2006) 220402.https://doi.org/10.1103/PhysRevB.73.220402
[92] M Binder, Weber, O Mosendz, G Woltersdorf, M Izquierdo, I Neudecker, J.R Dahn, T.D Hatchard, J.-U Thiele, C.H Back, M.R Scheinfein, Magnetization dynamics of the ferrimagnet CoGd near the compensation of magnetization and angular momentum, Phys Rev B 74 (2006) 134404.https://doi.org/10 1103/PhysRevB.74.134404
[93] N.L Schryer, L.R Walker, The motion of 180 domain walls in uniform dc
magneticfields, J Appl Phys 45 (1974) 5406e5421
[94] Kohei Ueda, Maxwell Mann, W Paul, P de Brouwer, David Bono, S.D Geoffrey, Beach, Temperature dependence of spin-orbit torques across the magnetic compensation point in a ferromagnetic TbCo alloy film, Phys Rev B 96 (2017) 064410.https://doi.org/10.1103/PhysRevB.96.064410
[95] Se Kwon Kim, Yaroslav Tserkovnyak, Fast vortex oscillations in a ferrimag-netic disk near the angular momentum compensation point, Appl Phys Lett 111 (2017) 032401.https://doi.org/10.1063/1.4985577
[96] Yue Zhang, Xueying Zhang, Jingtong Hu, Nan Jiang, Zhenyi Zheng, Zhizhong Zhang, Youguang Zhang, Nicolas Vernier, Dafine Ravelosona, Weisheng Zhao, Ring-shaped Racetrack memory based on spin orbit torque driven chiral domain wall motions, Sci Rep (2016) 35062.https://doi.org/ 10.1038/srep35062
[97] Y Kurokawa, H Awano, Multilayered current-induced domain wall motion in Pt/Tb-Co/Ta/Tb-Co/Pt magnetic wire, AIP Adv (2018) 025309.https://doi org/10.1063/1.5017814
[98] Hiroyuki Awano, Investigation of domain wall motion in RE-TM magnetic wire towards a current driven memory and logic, J Magn Magn Mater 383 (2015) 50e55.https://doi.org/10.1016/j.jmmm.2014.12.081