Role of Micromagnetic States on Spin–Orbit Torque-Switching Schemes

Letter Cite This: Nano Lett. XXXX, XXX, XXX−XXX

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Role of Micromagnetic States on Spin−Orbit Torque-Switching Schemes Jie Zhang,†,‡,∥ Chirag Garg,‡,§,∥ Timothy Phung,*,‡ Charles Rettner,‡ Brian P. Hughes,‡ See-Hun Yang,‡ Yong Jiang,† and Stuart S. P. Parkin*,‡,§ †

School of Materials Science and Engineering, University of Science & Technology Beijing, Beijing 100083, China IBM Almaden Research Center, San Jose, California 95120, United States § Max Planck Institute for Microstructure Physics, Halle (Saale) D06120, Germany Downloaded via UNIV OF SUSSEX on June 15, 2018 at 20:30:11 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

‡

S Supporting Information *

ABSTRACT: Three-terminal spintronic memory devices based on the controlled manipulation of the proximate magnetization of a magnetic nanoelement using spin−orbit torques (SOTs) have attracted growing interest recently. These devices are nonvolatile, can operate at high speeds with low error rates, and have essentially infinite endurance, making them promising candidates for high-speed cache memory. Typically, the magnetization and spin polarization in these devices are collinear to one another, leading to a finite incubation time associated with the switching process. While switching can also be achieved when the magnetization easy axis and spin polarization are noncollinear, this requires the application of an external magnetic field for deterministic switching. Here, we demonstrate a novel SOT scheme that exploits non-uniform micromagnetic states to achieve deterministic switching when the spin polarization and magnetic moment axis are noncollinear to one another in the absence of external magnetic field. We also explore the use of a highly efficient SOT generator, oxygen-doped tungsten in the three-terminal device geometry, confirming its −50% spin Hall angle. Lastly, we illustrate how this scheme may potentially be useful for nanomagnetic logic applications. KEYWORDS: Spintronics, spin−orbit torque, MRAM, magnetic tunnel junctions, nanomagnetic logic, magnetization dynamics

T

mechanisms in conventional STT−MRAM MTJ devices is the breakdown of the tunnel barrier, which occurs when large voltages needed for high-speed operation are applied across the tunnel barrier during the write process.19 In three-terminal devices, this wear-out mechanism is eliminated because the read and write paths are separated. Typically, the efficiency of the SOT is quantified by the spin Hall angle (θSH) and is defined as the ratio of spin to charge current.4,6,20,21 For device applications, the SOT generating material should have a high θSH as well as a low resistivity to reduce power consumption. Previously, we investigated oxygen doped tungsten (W(O)) as a SOT generator and reported a θSH = −0.5, which is the highest θSH obtained so far to date for a conventional metal-based system.22 This work was motivated by the analogy of the spin Hall effect23 to the anomalous Hall effect, in which large Hall angles have been observed in glassy

here has been considerable recent interest in threeterminal magnetic memory devices in which the writing mechanism is based on the controlled manipulation of magnetic moments using spin-transfer torque1,2 (STT) generated through spin−orbit interactions.3−6 One approach to a three-terminal magnetic memory device is based on the current-induced motion of a magnetic domain wall in a nanoscopic wire.7−10 A second approach is by using spin−orbit torques (SOTs) to switch the magnetization of an adjacent magnetic nanoelement.4,6,11−13 The readout of the magnetic state in both types of devices uses a magnetic tunnel junction (MTJ) based on the tunneling magnetoresistance (TMR) effect. While these are larger in overall footprint than conventional two-terminal spin-transfer torque−magnetic random access memory (STT−MRAM) MTJ devices,14 these three-terminal devices may be advantageous for high-speed memory applications.11,15−18 The separation of the read and write paths in the three terminal devices makes optimization of materials and the individual reading and writing schemes considerably more tractable. In addition, one of the wear-out © XXXX American Chemical Society

Received: December 13, 2017 Revised: May 9, 2018

A

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Nano Letters metallic systems.24 Indeed, the introduction of oxygen in W at high oxygen concentrations (greater than ∼12%) stabilizes a nanocrystalline phase of the W(O), while at lower oxygen concentrations, it gives rise to β-W, an A15 phase. In this work, we demonstrate that switching takes place with high efficiency when W(O) is used as the SOT generating layer in a threeterminal MTJ device. The devices considered in this work are composed of a thin film stack grown by magnetron sputtering on oxidized Si substrates, and is as follows, with the thickness of each film layer in Angstroms: substrate | 60 W(O) | 20 Co40Fe40B20 | 0.50 Co70Fe30 | 16 MgO | 25 Co70Fe30 | 5 Ru | 25 Co70Fe30 | 50 Ta | 50 Ru. The W(O) layer is grown by reactive sputtering using a gas mixture composed of 98.8% Ar and 0.3% O2. The incorporation of oxygen is estimated to be 12.1% based on Rutherford backscattering spectrometry analysis. In this study, the resistivity of the W(O) layer was ∼175 μΩ−cm, while the resistance area product of the MTJs was ∼100 Ω−μm2. The MTJs were patterned by e-beam lithography and ion-milling, and the surface of the underlying W(O) layer was etched to a depth of ∼2 nm to ensure that the MTJ free layer adjacent to the W(O) layer is fully patterned. Figure 1a shows a schematic of a typical three-terminaldevice configuration for switching a magnetic nanoelement with SOT. The current (Iy) flowing in the W(O) layer and the magnetization easy axis (along the x direction) lie in plane and

are orthogonal to each other. We shall denote this configuration as type Dxy, where the first subscript denotes the magnetization easy axis, and the second subscript denotes the current direction. The Dxy devices in this study are ellipses that are 150 nm × 300 nm in size. The magnetic state of the magnetic nanoelement is interrogated through the resistance (R) of the MTJ. Figure 1b shows a representative resistance versus magnetic field (RH) loop of a typical Dxy device. Current induced switching of the same device is shown in the resistance versus current (RI) loop (Figure 1c). In this measurement, the resistance is read post facto with a small bias of ±1 μA (delta mode) after application of current pulses of 1 ms for writing the state of MTJ. A field of Hx = −9 Oe is also applied to symmetrize the switching currents between the antiparallel to parallel (AP → P) and P → AP states. The current induced switching behavior is opposite to the direction of the Oersted field, which is consistent with a negative θSH of W(O). Figure 1d shows the switching-phase diagram of the device, which is obtained from measurements of the RH loops at different DC bias current values Iy. To quantify θSH, we examined the critical current to switch the device as a function of pulse length from 1 to 10 ms (Figure 1e). The critical current in this type of measurement can be

(

fitted to the following equation Ic = Ic0 1 −

( )),

τp k bT ln τ Eb 0

which originates from a macrospin model that takes into account thermal fluctuations.25 Ic is the pulse-length dependent critical current, Ic0, is the critical current in the limit of no thermal fluctuations, kb is the Boltzmann constant, T is the temperature, Eb is the energy barrier for switching the magnetic moment of the MTJ between its two easy axis directions, τp is the pulse length, and τ0 is the characteristic thermal fluctuation time (∼1 ns). By fitting the data with the equation above, we obtain Ic0 = 4 ± 0.3 mA, and a thermal stability factor of Δ = Eb/kbT = 38 ± 4.5. The resistance of the W(O) strip is ∼280 Ω for a strip that is 2 μm × 4 μm. The spin Hall angle4,6 is given by θSH =

(

2eμ0 Mstα Hc + ℏJco

Meff 2

)

, where e is the electron charge, μ0 is

the magnetic permeability of free space, Ms is the saturation magnetization, t is the thickness of the free layer of the MTJ to be switched, α is the Gilbert damping parameter, Hc is the coercivity of the MTJ free layer, Meff is the effective magnetization of the MTJ free layer, and ℏ is Planck’s constant. In the device under study, Ms = 1234 emu/cm3, α = 0.021 ± 0.001, Hc = 10 Oe, t = 2.5 nm, and Meff = 896 emu/cm3. α and Meff are determined by stripline ferromagnetic resonance and vibrating sample magnetometry, respectively (Supporting Information 1). Thus, we obtain θSH = −0.50 ± 0.04, which is consistent with our previous measurements using spintransfer torque ferromagnetic resonance technique.22 Let us now consider the Dxx configuration, shown in Figure 2a, where current and the magnetization easy axis are collinear to one another and oriented along the x-direction. In this device type, the magnetization and spin polarization are orthogonal to each other when the SOT is initially applied. In contrast, for the Dxy device (Figure 1a), the magnetization and spin polarization in the incipient state are collinear to one another. One does not expect that switching should occur in the Dxx device because the SOT only rotates the magnetization toward the in-plane hard axis direction (±y direction). Upon removing current through the W(O) layer in the Dxx device, the magnetization rotates back toward its initial direction. Figure 2b

Figure 1. (a) Schematic diagram of the three-terminal SOT device studied in the Dxy configuration in which the easy axis of the magnetic nanoelement is along the x direction and the current, Iy, is orthogonal to the easy axis direction. (b) RH loop measured for a representative Dxy device with field applied along the x axis. (c) RI loop measured with current applied along the y axis and magnetic field applied along x to symmetrize the switching currents. (d) Switching-phase diagram measured from RH loops measured at different applied currents to the W(O) layer. (e) Pulse-length dependence of critical current for switching between P → AP (red) and AP→ P (blue) states. B

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Figure 2. (a) Schematic diagram of the three-terminal SOT device studied in the Dxx configuration in which the easy axis of the magnetic nanoelement is along the x direction and the current, Ix, is collinear to the easy axis direction. (b) Time-resolved magnetization maps from micromagnetic simulations showing the absence of switching in the Dxx configuration when a 500 ps long positive current pulse is applied to the W(O) layer. (c) Current pulses used in micromagnetic simulations. (d,e) Time-resolved magnetization maps from micromagnetic simulations showing current-induced switching in right trapezoid patterned elements with a negative sloped left leg (Dxx−). Current-induced switching from the +x and −x state occurs with a positive and negative current, respectively, following the application of a 500 ps current pulse.

illustrates this by time-resolved micromagnetic simulations26 of SOT switching of a 200 nm × 100 nm element in the Dxx configuration under a 500 ps long positive current pulse that is shown in Figure 2c. In this simulation, the SOT is modeled as a damping-like torque originating from the spin Hall effect. As expected, the micromagnetic simulation shows that the magnetization rotates toward the in plane hard axis direction of the device (±y direction for ± Ix current, respectively; Figure 2b, top-right panel). Furthermore, the magnetization has effectively attained a steady-state configuration within the duration of the 500 ps pulse (Supporting Information 4). We note that the damping-like contribution of the SOT, given by τ⃗ = ajm⃗ × (p⃗ × m⃗ ), where τ⃗ is the STT, aj is the damping like spin torque parameter, m⃗ is the normalized magnetization, and p⃗ is the spin polarization, vanishes when the magnetization rotates toward the spin polarization direction.27 Thus, the magnetization cannot be driven past the hard axis orientation, and consequently, there is no magnetization reversal regardless of current polarity applied to the W(O) layer (Figure 2b). While these simulations are performed in the zero-temperature limit, thermal fluctuations at finite temperature may drive reversal of

the magnetization, as the energy barrier for the magnetization to rotate toward the ± x direction is suppressed when the magnetization is along the hard axis direction. However, such a reversal mechanism is stochastic and not useful for technological applications. The role of thermal fluctuations in the switching process for Dxy and Dxx devices is thus complementary. For the Dxy device, thermal fluctuations are responsible for initiating switching dynamics, but as the cone angle for the magnetization precession builds up for reversal, SOT increases in magnitude driving the reversal process. In the Dxx device, SOT initiates the switching process, but thermal fluctuations set up an initial bias point for the ensuing magnetization reversal to occur after the application of current to the W(O) layer. Based on this understanding, we postulated that deterministic switching in the Dxx configuration can occur if there is an internal magnetic field to seed a reversal process when the magnetization is brought toward an intermediate hard axis state by SOT. Thus, fast switching may take place without the need for thermal fluctuations at either the beginning or intermediate points of the switching trajectories. To test this hypothesis, we C

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Figure 3. (a,b) SEM images of the Dxx− and Dxx+ devices patterned in the form of right trapezoids. (c,d) Remnant-state magnetization is shown as calculated from micromagnetic simulations for Dxx− and Dxx+ devices, respectively. (e,f) Measured RH loops for the Dxx− and Dxx+ devices, respectively, with the inset symbol showing the reference layer and free-layer magnetization orientation. (g,h) Measured RI loops for the loops for the Dxx− and Dxx+ devices, respectively with the inset symbol showing the reference-layer and free-layer magnetization orientation (i,j) Truth table summarizing conditions for switching and not switching for the Dxx− and Dxx+ devices, respectively.

performed micromagnetic simulations of a magnetic nanoelement that has the shape of a right trapezoid (Figure 2d) and that is subjected to the same current pulses as in Figure 2c. Micromagnetic simulations show that the magnetization rotation toward the in-plane hard axis direction under SOT is greater in the wider section of the trapezoid, while the magnetization in the narrow section of the trapezoid favors pointing tangent to the nanoelement boundary (Figure 2d, 500 ps time frame). This can be understood because the shape anisotropy energy density is greater in the narrower section of the trapezoid. Depending upon the polarity of the current pulse, the magnetization at the trapezoid tip has a component either along the initial magnetization direction or opposite to it (Figure 2d compares the magnetization at 500 ps for ± Ix). The preferred moment orientation is determined by the internal effective magnetic fields of the nanoelement and originates predominately from the magnetostatic and exchange interactions. This can also be observed in the nanoelement remnant state, in which the magnetization of the sloped edge of the

trapezoid is correlated to the magnetization state of the rectangular region.28,29 Magnetization reversal can occur through growth of the domain starting from the top left corner upon removal of the current pulse. If the magnetization has a component along the same direction as the initial state in the trapezoid tip, then switching does not occur. Similar arguments apply to the case in which the magnetization starts from the −x orientation, wherein reversal only occurs with a negative current (Figure 2e). Furthermore, in the case of a right trapezoid, in which the left leg has a positive slope, the currents required for switching to the ±x configurations become ±Ix. The switching current magnitude is equivalent for switching to the ±x states under this mechanism. Thus, deterministic switching with controlled switching current polarity can be achieved in the Dxx device without an external magnetic field through engineering of the sample geometry so that the internal magnetic field can initiate the reversal process. Indeed, even the presence of small lithographic defects that routinely occur due to line edge roughness, affect the micromagnetic D

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Nano Letters state significantly enough in the Dxx configuration to affect its switching dynamics (Supporting Information 4). We also note that if the trapezoid is entirely symmetric about the x-axis, switching does not occur because the magnetization on the two edges of the nanoelement rotate in opposite directions (Supporting Information 4). Furthermore, our simulations show that the Dxx switching process based on this mechanism can be faster than the Dxy switching process, as characterized by a monotonic evolution of the spatial average of the magnetization of the nanoelement with respect to time (Supporting Information 3). The magnetization switches within one precession cycle and does not involve any vortex states. In contrast, the switching of Dxy devices at the same current density requires several precession cycles during the reversal process and involves many metastable vortex states (Supporting Information 5). Switching based on the scheme described above was experimentally investigated by examining devices in which the MTJ was patterned into right trapezoid shapes. Figure 3a,b illustrate scanning electron microscope (SEM) micrographs of two such devices that have been fabricated in which the MTJ is 150 and 100 nm long at the two bases and has a width of 75 nm. The MTJ stack is patterned into a trapezoidal shape down to the W(O) layer, using the same fabrication procedure as was used to fabricate the Dxy devices. We shall refer to these devices with negative and positive sloped left legs as Dxx− and Dxx+, with the last subscript letter representing the slope of the trapezoid’s left leg. Panels c and d of Figure 3 show the remnant state, as calculated by micromagnetic simulations, of the magnetization of these two devices, respectively. The RH loops of the Dxx− and Dxx+ devices, respectively, for a magnetic field applied, Hx, along the x direction, are shown in panels e and f of Figure 3. Both devices have nominally identical RH loops, which implies that the reference layer magnetization in both devices are oriented in the same direction. The magnetization direction of the free and reference layers are illustrated by the blue and red arrows inset in panels e and f of Figure 3. The current-induced switching for Dxx− and Dxx+ devices performed using 1 ms current pulses are shown in the RI loops in panels g and h of Figure 3, respectively. A magnetic field applied along the x direction was also applied to compensate for the dipole field from the reference layer for the current induced switching measurements. In the Dxx− device, positive (negative) current drives switching from AP → P (P → AP), respectively, while the opposite occurs in the Dxx+. The direction of magnetization that has been switched under a given current can be determined by comparing RH loops and RI loops for a device of a given geometry and are shown in the inset in panels g and f of Figure 3 for both devices. Because the reference layer magnetization orientation is fixed under the current pulse, the free-layer magnetization switched in different directions with the same current polarity for the Dxx+ and Dxx− devices. The switching observed experimentally in Figure 3e−h is indeed consistent with what is predicted by the micromagnetic simulations (Figure 2c−d). The truth tables (Figure 3i,j) summarize the basic switching operations for the Dxx− and Dxx+ devices. Deterministic switching of such devices as determined by their geometry can be potentially useful in building nonvolatile nanomagnetic logic circuits30−32 that require the switching of several nanomagnets in a complementary manner.30−32 Here, we show the operation of a nonvolatile inverter (NOT gate circuit) that can be built using Dxx+ and Dxx− devices that share

a common W(O) layer (Figure 4a). If both devices have their reference layer pointing in the same direction, the Dxx+ and

Figure 4. (a) Schematic of a nonvolatile inverter (NOT gate) circuit realized with mirror imaged Dxx− and Dxx+ devices connected in series and sharing a common W(O) layer. (b) Truth table describing nonvolatile inverter operation. (c) Experimental demonstration of an inverter operation based on the serial connection of a Dxx− and Dxx+ devices. The input voltage, resistance of both devices, and output voltage as a function of iteration number are plotted.

Dxx− switch to opposite resistance states under the application of the same polarity current. Following the convention that the reference layer magnetization points toward the −x direction, the Dxx+ device will have a higher resistance compared to the Dxx− device for a positive current. Likewise, upon the application of the reverse current polarity pulse, the Dxx− device will have a higher resistance compared to the Dxx+ device. One can thus think of the Dxx+ and Dxx− device as sort of complementary devices similar to transistors in CMOS technology. The connection of both devices in series thus functions as a nonvolatile inverter, as the logical output will remain once the Dxx+ and Dxx− devices have been switched to their respective states. The truth table in Figure 4b summarizes the inverter operation. The operation of such an inverter circuit up to 20 cycles is demonstrated (Figure 4c). Pulses of 2.5 V and 1 ms long are used in this demonstration, but extending these studies to nanosecond-long switching is anticipated. The generalization of this type of logic to build AND and OR gates is thus straightforward and borrows the concepts from CMOS logic. The advantage in this circuit compared to CMOS is that it is nonvolatile and has no static power dissipation. While complementary switching of two MTJs can also be E

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(4) Liu, L.; Pai, C.-F.; Li, Y.; Tseng, H. W.; Ralph, D. C.; Buhrman, R. A. Spin-Torque Switching with the Giant Spin Hall Effect of Tantalum. Science (Washington, DC, U. S.) 2012, 336 (6081), 555− 558. (5) Lee, S. W.; Lee, K. J. Emerging Three-Terminal Magnetic Memory Devices. Proc. IEEE 2016, 104, 1831−1843. (6) Pai, C. F.; Liu, L.; Li, Y.; Tseng, H. W.; Ralph, D. C.; Buhrman, R. A. Spin Transfer Torque Devices Utilizing the Giant Spin Hall Effect of Tungsten. Appl. Phys. Lett. 2012, 101 (12), 122404. (7) Emori, S.; Bauer, U.; Ahn, S.-M.; Martinez, E.; Beach, G. S. D. Current-Driven Dynamics of Chiral Ferromagnetic Domain Walls. Nat. Mater. 2013, 12 (7), 611−616. (8) Ryu, K.-S.; Thomas, L.; Yang, S.-H.; Parkin, S. Chiral Spin Torque at Magnetic Domain Walls. Nat. Nanotechnol. 2013, 8 (7), 527−533. (9) Fukami, S.; Yamanouchi, M.; Koyama, T.; Ueda, K.; Yoshimura, Y.; Kim, K. J.; Chiba, D.; Honjo, H.; Sakimura, N.; Nebashi, R.; Kato, Y.; Tsuji, Y.; Morioka, A.; Kinoshita, K.; Miura, S.; Suzuki, T.; Tanigawa, H.; Ikeda, S.; Sugibayashi, T.; Kasai, N.; Ono, T.; Ohno, H. High-Speed and Reliable Domain Wall Motion Device: Material Design for Embedded Memory and Logic Application. Digest of Technical Papers - Symposium on VLSI Technology 2012, 61−62. (10) Parkin, S. S. P.; Hayashi, M.; Thomas, L. Magnetic Domain-Wall Racetrack Memory. Science (Washington, DC, U. S.) 2008, 320 (5873), 190−194. (11) Liu, L.; Lee, O. J.; Gudmundsen, T. J.; Ralph, D. C.; Buhrman, R. A. Current-Induced Switching of Perpendicularly Magnetized Magnetic Layers Using Spin Torque from the Spin Hall Effect. Phys. Rev. Lett. 2012, 109 (9), 96602. (12) Yamanouchi, M.; Chen, L.; Kim, J.; Hayashi, M.; Sato, H.; Fukami, S.; Ikeda, S.; Matsukura, F.; Ohno, H. Three Terminal Magnetic Tunnel Junction Utilizing the Spin Hall Effect of IridiumDoped Copper. Appl. Phys. Lett. 2013, 102 (21), 212408. (13) Lee, O. J.; Liu, L. Q.; Pai, C. F.; Li, Y.; Tseng, H. W.; Gowtham, P. G.; Park, J. P.; Ralph, D. C.; Buhrman, R. A. Central Role of Domain Wall Depinning for Perpendicular Magnetization Switching Driven by Spin Torque from the Spin Hall Effect. Phys. Rev. B: Condens. Matter Mater. Phys. 2014, 89 (2), 24418. (14) Kent, A. D.; Worledge, D. C. A New Spin on Magnetic Memories. Nat. Nanotechnol. 2015, 10 (3), 187−191. (15) Cubukcu, M.; Boulle, O.; Drouard, M.; Garello, K.; Onur Avci, C.; Mihai Miron, I.; Langer, J.; Ocker, B.; Gambardella, P.; Gaudin, G. Spin-Orbit Torque Magnetization Switching of a Three-Terminal Perpendicular Magnetic Tunnel Junction. Appl. Phys. Lett. 2014, 104 (4), 42406. (16) Garello, K.; Avci, C. O.; Miron, I. M.; Baumgartner, M.; Ghosh, A.; Auffret, S.; Boulle, O.; Gaudin, G.; Gambardella, P. Ultrafast Magnetization Switching by Spin-Orbit Torques. Appl. Phys. Lett. 2014, 105 (21), 212402. (17) Aradhya, S. V.; Rowlands, G. E.; Oh, J.; Ralph, D. C.; Buhrman, R. A. Nanosecond-Timescale Low Energy Switching of In-Plane Magnetic Tunnel Junctions through Dynamic Oersted-Field-Assisted Spin Hall Effect. Nano Lett. 2016, 16 (10), 5987−5992. (18) Fukami, S.; Anekawa, T.; Zhang, C.; Ohno, H. A Spin−orbit Torque Switching Scheme with Collinear Magnetic Easy Axis and Current Configuration. Nat. Nanotechnol. 2016, 11 (7), 621−625. (19) Min, T.; Chen, Q.; Beach, R.; Jan, G.; Horng, C.; Kula, W.; Torng, T.; Tong, R.; Zhong, T.; Tang, D.; Wang, P.; Chen, M. M.; Sun, J. Z.; Debrosse, J. K.; Worledge, D. C.; Maffitt, T. M.; Gallagher, W. J. A Study of Write Margin of Spin Torque Transfer Magnetic Random Access Memory Technology. IEEE Trans. Magn. 2010, 46, 2322−2327. (20) Mellnik, A. R.; Lee, J. S.; Richardella, A.; Grab, J. L.; Mintun, P. J.; Fischer, M. H.; Vaezi, A.; Manchon, A.; Kim, E.-A.; Samarth, N.; Ralph, D. C. Spin-Transfer Torque Generated by a Topological Insulator. Nature 2014, 511 (7510), 449−451. (21) Fan, Y.; Upadhyaya, P.; Kou, X.; Lang, M.; Takei, S.; Wang, Z.; Tang, J.; He, L.; Chang, L.-T.; Montazeri, M.; Yu, G.; Jiang, W.; Nie, T.; Schwartz, R. N.; Tserkovnyak, Y.; Wang, K. L. Magnetization

achieved in standard two terminal MTJ devices, as well as by using Oersted magnetic fields, our scheme is considerably simpler to implement dense logic circuits. One may also use this scheme to control the state of nanomagnetic elements in nanomagnetic logic schemes, which require magnetic nanoelements to be coupled by their dipole fields and in close proximity.32,33 Moreover, improvements in the TMR and spin torque efficiency of the spin orbit material will increase the performance characteristics of the logic device presented here. In conclusion, we confirm very large θSH = −0.5 in W(O) through current-induced switching measurements of threeterminal devices in the Dxy configuration. We also demonstrate a field-free SOT switching scheme in the Dxx configuration by controlling the micromagnetic state of the magnetic nanoelement. Lastly, we demonstrate how this scheme may potentially be useful for high-speed memory applications and logic applications, as illustrated by the operation of a nonvolatile inverter circuit.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.7b05247. Information on the characterization of the magnetic free layer used for our devices as well as micromagnetic simulations for Dxy and Dxx devices. Figures showing VSM measurement, the determination of effective magnetization, current pulse and average magnetization time evolution, magnetization configurations, final-state magnetization maps, magnetization configurations, polarity current pulse, and circuit design. (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Stuart S. P. Parkin: 0000-0003-4702-6139 Author Contributions ∥

J.Z. and C.G. contributed equally to the work.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank K. P. Roche for fruitful discussions. The work of J.Z. was partially supported through the China Scholarship Council. Y.J. is thankful for the support from the National Basic Research Program of China (no. 2015CB921502) and the NSFC (no. 51731003).

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REFERENCES

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