<figure><img src="image_1.png" /></figure>

HAL
open science

A spin-orbit-torque memristive device

Shuai Zhang, Shijiang Luo, Nuo Xu, Qiming Zou, Min Song, Jijun Yun, Qiang Luo, Zhe Guo, Ruofan Li, Weicheng Tian, et al.

► To cite this version:

Shuai Zhang, Shijiang Luo, Nuo Xu, Qiming Zou, Min Song, et al. A spin-orbit-torque memristive device. Advanced Electronic Materials, 2019, 5 (4), pp.1800782. 10.1002/aelm.201800782. hal-04964917

HAL Id: hal-04964917

https://hal.science/hal-04964917v1

Submitted on 25 Feb 2025

**HAL** is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_2.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
A Spin-Orbit-Torque Memristor

Shuai Zhang¹, Shijiang Luo¹, Nuo Xu², Qiming Zou³, Min Song⁴, Jijun Yun⁵, Qiang Luo¹, Zhe Guo¹, Ruofan Li¹, Weicheng Tian¹, Xin Li¹, Hengan Zhou⁶, Huiming Chen¹, Yue Zhang¹, Xiaofei Yang¹, Wanjun Jiang⁶, Ka Shen⁷, Jeongmin Hong¹, Zhe Yuan⁷, Li Xi⁵, Ke Xia⁷, Sayeef Salahuddin², Bernard Dieny⁸, Long You¹,⁹*

1. School of Optical and Electronic Information, Huazhong University of Science and Technology, Wuhan 430074, China

2. Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA-94720, USA

3. Department of Electrical and Computer Engineering, University of Nebraska-Lincoln, Lincoln, NE 68588-0511, USA

4. Faculty of Physics and Electronic Science, Hubei University, Wuhan 430062, China

5. Key Laboratory for Magnetism and Magnetic Materials of Ministry of Education, Lanzhou University, Lanzhou 730000, China

6. Department of Physics, Tsinghua University, Beijing 100084, China

7. The Center for Advanced Quantum Studies and Department of Physics, Beijing Normal University, 100875 Beijing, China

8. Univ. Grenoble Alpes, CEA, CNRS, Grenoble INP, INAC-Spintec, 38000 Grenoble, France

9. Wuhan National Lab for Optoelectronics, Huazhong University of Science and Technology, Wuhan 430074, China

* Email: lyou@hust.edu.cn
Memristors, or memory resistors, demonstrated by solid-state devices with continuously tunable resistance [1-6], have emerged as a new paradigm for self-adaptive networks that require synapse-like functions (artificial neurons, for example). Spin-based memristors offer advantages over other types of memristors because of their significant endurance (over $10^{12}$ cycles) and high energy efficiency [7, 8]. Yet it remains a challenge to build dense and functional spintronic memristors with structures and materials that are compatible with existing ferromagnetic devices [9]. Here, we demonstrate a memristive device based upon Ta /CoFeB /MgO heterostructures, which are commonly used in out-of-plane magnetized magnetic tunnel junctions (MTJ) for random access memory (MRAM) [10]. To achieve the memristive function, a domain wall (DW) is driven back and forth in a continuous manner in the CoFeB layer by applying in-plane positive or negative current pulses along the Ta layer, utilizing the spin-orbit torque (SOT) that the current exerts on the CoFeB magnetization [11-16]. Hence, the magnetization and consequently the anomalous Hall effect (AHE) resistance is modulated in an analog manner, being controlled by the pulsed current characteristics including amplitude, duration, and repetition number. The quasi-continuous AHE resistance variation is explained by the SOT-induced DW creep motion. These results pave the way for developing SOT-based energy-efficient neuromorphic systems.
Spintronic memristors are resistive switching devices in which the resistance can be varied in an analogue and non-volatile manner between a minimum and a maximum resistance depending on the charge that have traversed the device. They can be based on tunnel magnetoresistance (TMR) or anomalous Hall effect (AHE) resistance [7]. So far, a few studies have experimentally reported spintronic memristors based on DW manipulation, through spin transfer torque [8, 9]. However, only a few discrete resistance states were observed in these experiments, due to the fact that DW can only be pinned at a few locations. Only very recently, Fukami et al [15] demonstrated analog memristive behavior in a PtMn/[Co/Ni] antiferromagnetic (AFM)/FM bi-layer system by performing R-I sweeps. The memristive switching mechanism in this system was theoretically considered to be predominantly governed by domain nucleation instead of DW propagation, though comprehensive understanding of the mechanism was not clear. According to the experiments and explanation in Ref.[15], the resistance of these devices may remain constant when repetitive current pulses with a fixed amplitude and duration are applied. Such behavior is not desirable for the realization of synaptic plasticity since the memristor resistance should be changeable in an analog manner by the number of applied pulses [4, 5].

In this paper, we report SOT-induced memristive behavior in Ta/CoFeB/MgO heterostructures. These structures are commonly used in interfacial PMA-based magnetic tunnel junctions (MTJs) which exhibit large tunnel magnetoresistance (TMR) and are implemented in commercial magnetic RAM (MRAM) products [10]. The electrical measurements show that the AHE resistance of our devices can be tuned continuously by current pulses. In addition, the magnetic domain structure was investigated by magneto-optic Kerr effect (MOKE) microscopy. These characterization confirmed that the observed continuous resistance change is associated with DW propagation in creep regime. The relative proportion of upward- and downward-polarized magnetic domains can be controlled at the nanometer scale [17], which enables extremely fine tuning of the electrical resistance in these magnetic memristors.
<figure><img src="image_3.png" /></figure>

<figure><img src="image_4.png" /></figure>

<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /><figcaption>**Figure 1** | SOT memristor based on Ta/CoFeB/MgO heterostructures. **a,** Device structure with schematic of the measurement set-up. **b,** Current-induced switching under a small constant magnetic field $H_x$ = ±50 Oe. **c,** $R_H$-I loops with varying maximum current magnitude, $I_{max}$, under $H_x$ = +50 Oe. **d,** Normalized resistance $r_H$ as a function of current pulses (0.1 ms pulse width) accompanied by the real-time MOKE images of Hall bars.</figcaption></figure>

Our deposited film stack comprises the following layers: thermally-oxidized Si substrate/Ta (10 nm)/CoFeB (1.2 nm)/MgO (1.6 nm)/Ta (20 nm) (see Methods). The stack is patterned into 50 × 400 µm² Hall bar structures. To evaluate the perpendicular component of the magnetization, the Hall resistance ($R_H$) due to the anomalous Hall effect (AHE) is measured. The structure of the stack and measurement setup are shown in Fig. 1a. The AHE loop ($R_H$ versus out-of-plane field $H_z$) confirms the strong PMA of the CoFeB magnet with a coercivity field, $H_c$, of 10 Oe and an anisotropy field, $H_k$, of 4000 Oe (see Supplementary Information S1). Next, we investigate the response of $R_H$ to the in-plane current ($I$) under a small in-plane field, $H_x$ = ±50 Oe, as shown in Fig. 1b. At $H_x$ = +50 Oe, the current generates hysteretic magnetic switching between upward ($M_↑, R_H > 0$) and downward ($M_↓, R_H < 0$) polarization states, and the positive current (along +x direction) favors $M_↑$ (blue curve). When the small constant field $H_x$
is reversed, the current-driven transitions are inverted, and positive current now favors
$M_↓$ (red curve). Such bipolar switching behavior is a signature of SOT generation at the
Ta/CoFeB interface due to spin Hall effect and at the CoFeB/MgO interface due to
Rashba effect [13, 14]. Furthermore, the reversal of the $R_H$ is not abrupt; rather it looks
like a continuous transition with numerous intermediate resistance values (from -0.1 Ω
to 0.15 Ω, here). If one varies the maximal magnitude of the current, $I_{max}$, from low (27
mA) to high (51 mA), a series of hysteretic loops are observed, as depicted in Fig. 1c,
indicating that the final resistance state can effectively be determined by the current
cycle protocol. At the maximum current magnitude used (50 mA), the device
temperature can increase up to 380 K (Supplementary Information S2). However, since
the direction of magnetization switching depends on the polarity of the current, it cannot
be attributed to Joule heating.

To provide insight into the magnetization dynamics associated with the change in
resistance, magneto-optic Kerr effect (MOKE) microscopy was performed on the Hall
bars, as shown in Fig. 1d. To obtain a clearer observation, the Ta capping layer of the
device was thinned by etching. Starting from a saturated state $M_↓$ corresponding to the
normalized resistance value $r_H = -1$, the application of consecutive positive current
pulses nucleates a reversed domain at the left edge of the strip, followed by propagation
of the DW and the correlated continuous variation of the resistance. An almost saturated
state $M_↑$ ($r_H = +1$) is eventually reached as the in-plane current is large enough. These
MOKE images clearly indicate that the memristive behavior in our HM/FM bilayer
system originates from DW propagation. In addition, by applying the field at various
angles $\theta$ with respect to the normal to the sample and looking at the variation of the
switching field $H_{sw}$, it was found that the variation $H_{sw}(\theta)$ follows a 1/cos$\theta$ law which,
according to the Kondorsky model [18], suggests that DW motion dominates the
magnetization switching (see details in Supplementary Information S3).
<figure><img src="image_7.png" /><figcaption>**Figure 2** | Tuning $R_H$ using amplitude, polarity, duration and number of consecutive current pulses. a, Current modulation applied to the sample corresponding to a sequence of pulses 50 µs long of alternating polarity and increasing amplitude. b, Resistance modulation resulting from the sequence of pulses described in a. Current thresholds to observe resistance changes are found for both polarities ($I_{th} = \pm 46$ mA) and indicated by the yellow shaded areas. The inset in b shows a zoomed-in image of the change in resistance around the threshold region. c-f, Phase diagrams of $R_H$ as a function of the pulse width and pulse number for three pulse amplitudes $I = -70$ mA (c), $-80$ mA (d), $-90$ mA (e), and $+70$ mA (f) under an in-plane field $H_x = +50$ Oe.</figcaption></figure>

If a train of current pulses with alternating polarity is applied in conjunction with the collinear in-plane field (Fig.2a), a gradual resistance modulations can be observed, provided that the pulse amplitude exceeds the bipolar switching activation threshold, $I_{th}$, of the device (as illustrated in Fig. 2b). The resistance value starts at approximately 0 Ω, corresponding to a demagnetized state. Thus the $I_{th}$ required for current-driven DW motion by SOT is expected to be the same for both polarities ($I_{th} = \pm 46$ mA here). $R_H$ depends not only on the pulse-train amplitude but also on the pulse duration and number of repetitions. Figure 2c-f present the pulse duration/number phase diagrams for different pulse amplitudes. The results show that the resistance gradually decreases
(increases) with the number of consecutive pulses, which is caused by continuous
downward (upward) magnetic switching modulated by the pulses. Such a cumulative
effect further validates the memristive functionality of our device. We note that R<sub>H</sub>
varies more abruptly with a longer duration and/or higher amplitude of pulse (Fig. 2c-
e), which correlates with the DW motion depending on the pulse duration/amplitude.

<figure><img src="image_8.png" /><figcaption>**Figure 3** | Resistance tuning obtained by programming consecutive pulse sequences (duration in 150 µs) under H<sub>x</sub> = + 50 Oe. **a**, Current-pulse sequence applied to the sample characterized by sequences of positive pulses of fixed number alternating with sequences of negative pulses of increasing number. **b**, AHE resistance responses to the current excitation of **a**. **c**, Current-pulse sequence applied to the sample characterized by sequences of positive pulses of increasing number alternating with sequences of negative pulses of fixed number. **d**, AHE resistance responses to the current excitation of **c**. The magnetization was initially saturated in the downward state by a reset pulse of -90 mA. The pulse amplitudes are +70 mA and -70 mA for positive and negative values, respectively. **a**, **b** illustrate the long-term depression effects, while **c**, **d** illustrate the long-term potentiation effects.</figcaption></figure>
In particular, the resistance variation induced by programming consecutive pulses
sequences can be utilized to imitate “long-term potentiation and depression” (LTPD)
synaptic behaviors [4, 5]. This is illustrated in Fig.3. We first saturate the magnetization
in the *M*↓ state by a reset pulse (–90 mA). Next, we apply positive pulses with a fixed
amplitude (+70 mA) and number of pulses (20) and subsequently negative pulses with
a constant amplitude (–70 mA) but an increasing number of pulses (from 10 to 20, 40
and 80), as shown in Fig. 3a. The response of *R*<sub>H</sub> to these consecutive pulses sequences
(see Fig. 3b) indicates that positive pulses with the same properties (such as amplitude,
duration and number) can reproducibly determine the same resistance state (0.1 Ω),
whereas the change in number of negative pulses enables different resistance levels.
Similarly, *R*<sub>H</sub> gradually increases when the number of positive pulses varies (from 10
to 20, 40, and 80 successively, see Fig. 3c, d). As a result, the behavior of the resistance
variation shown in Fig. 3a, b illustrates the long-term depression effects, while the trend
in Fig. 3c, d illustrates the long-term potentiation effects. The synaptic plasticity (LTPD)
further demonstrates that our memristive device can be used in self-adaptive networks
with synaptic functionality.
<figure><img src="image_9.png" /><figcaption>**Figure 4** | **Resistance and magnetization switching dynamics.** a-d, Dependence of the resistive state (**a**, **b**) and the corresponding magnetization dynamics (**c**, **d**) on the cumulative pulse time (**t**) for down-to-up (**a**, **c**) and up-to-down (**b**, **d**) switching. A small in-plane field of +50 Oe is applied. **e**, Schematic of the magnetic moment orientation near the DW with right-handed chirality. The black dashed frame represents the region where AHE resistance is measured. The tilted DW is equalized to a straight line (green dotted line). **f**, DW velocity, **v**, versus current density **J**. **g**, Scaling plot of log **v** versus J⁻⁰.²⁵.</figcaption></figure>

In memristive devices, a common approach to continuously modulating the
resistance is to apply consecutive identical pulses [4-6]. Figure 4a-d show the evolution
of $r_H$ and the corresponding magnetization dynamics as a function of cumulative pulse
time ($t$). Under positive pulses, the initial state is gradually set to $r_H = -1$, while under
negative pulses, it gradually reaches $r_H = +1$. Three key stages emerge during the
evolution of the magnetization switching. As depicted in Fig. 4a (b), segment B–C (B’–
C’) represents the memristive stage, where $r_H$ gradually increases (decreases) with the
pulse time due to DW motion in the AHE detection region. When the DWs have not yet
reached or have already left the detection region, $r_H$ remains constant, as shown in A-B
and C-D in Fig. 4a (A'-B' and C'-D' in Fig. 4b).

The MOKE images further reveal that these DWs are actually right-handed chiral Néel walls stabilized by Dzyaloshinskii-Moriya interaction (DMI) [19, 20] since the observed direction of the DW motion is always the same as that of the current flow (see Fig. 4c, d and Fig. S5 in Supplementary Information). The DMI effective field ($H_{DMI}$) in our system is estimated to be approximately 100 Oe (see Supplementary Information S5). The schematic in Fig. 4e describes the magnetization reversal by DW propagation (the case in Fig. 4c). The orientation of the SOT effective field ($H_{eff,z}$) acting on the Néel walls is aligned with the magnetization of one of the adjacent domains [21]. Therefore, the DW can move along the current flow direction until the whole CoFeB magnetization has been switched. We can conclude that the memristive switching behavior in the Ta/CoFeB/MgO structure is induced by SOT-driven Néel-type DW motion. In addition, the DMI leads to a tilting of the DWs during their motion [22]. The vertical component of the Oersted field is found to have opposite polarity at the two long edges of the device (see details in Supplementary Information S6) and might also contribute to the observed tilting.

Moreover, we find that the extracted velocity ($v$) of DW motion in this work is slow compared to that (10-100 m/s) in previous reports [23]. For example, the velocity shown in Fig. 4c, d is estimated to be approximately 0.1 m/s (see Supplementary Information S7). Due to this low velocity, the continuous variation of $R_H$ and the memristive behavior can clearly be observed instead of abrupt bipolar switching. To investigate this further, we study the behavior of $v$ as a function of the current density ($J$) under an in-plane field of 50 Oe (see details in Supplementary Information S7), as shown in Fig. 4f. The observed nonlinear dependence of $v$ on $J$ may result from the motion in the creep regime [24] and follows the universal Arrhenius scaling relation [25]:

$$ \log(v) \propto J^{-\mu} \quad (1) $$

where $\mu$ is the creep exponent, found to be ~ 0.25 for field-driven creep both in Pt/Co/Pt and Ta/CoFeB/MgO systems [24, 26-28], but the value is currently unclear in the case of SOT-induced creep. Here, SOT can be treated as an effective field as mentioned
above, so we assume that $\mu = 0.25$. Fig. 4g shows the plot of log-scale $v$ as a function of $J^{-0.25}$. The good correlation between them confirms that the DW motion is well described by equation (1) and the creep model.

The comparison of the electrical measurements with the MOKE images (Fig. 4a-d) shows that the resistance varies systematically with the relative fraction of the upward domains, $s$. This trend can be well reproduced using a simple model that considers $r_H$ to vary linearly with $s$. During resistance modulation dynamics, $s$ varies from 0 (1) at the onset of switching to 1 (0) for down-to-up (up-to-down) reversal in the detection region. Following the assumptions above, one can write

$$r_H = 2s - 1, 0 \le s \le 1. \quad (2)$$

The evolution of $s$ is roughly proportional to $t$ and $v$ and can be expressed as

$$s = v \times (t - t_0) / L, t \ge t_0 \quad (3)$$

for down-to-up switching and as

$$s = 1 - v \times (t - t_0) / L, t \ge t_0 \quad (4)$$

for up-to-down switching, where $L$ is the length of the detection region (see Fig. 4e) and $t_0$ is the intrinsic propagation time when the DW reaches the detection region.

Thus equations (1)–(4) impose a strict framework for resistance response as a function of external electrical excitation. In other words, $R_H$ can be a function of $I$ and $t$ ($R_H = R(I, t)$) for our devices to imitate a memristor. For practical applications, our Ta/CoFeB/MgO heterostructures can be implemented as the free-layer stack in MTJs, in which a larger OFF/ON ratio will be obtained. Moving from the AHE measurement to practical application in MTJs, the evolution of $s$ (the relative fraction of the upward domains) will result in an immediate response in the TMR variation without an intrinsic propagation time, i.e., $t_0 = 0$ in equations (3) and (4). To further optimize the device structure, one of the approach to realize field-free SOT switching of PMA materials could be used for our SOT memristors, namely either by introducing a lateral structural asymmetry [29], or engineering a tilted anisotropy [30] or using interlayer exchange coupling [31].

In conclusion, we have reported memristive behavior in a Ta/CoFeB/MgO
multilayered structure, which is commonly used in spin transfer torque magnetic
random access memory. The resistance can be effectively tuned by current pulses,
whose amplitude, polarity, duration, and number can be varied. We established a
connection between the memristive behavior and SOT-induced magnetization
dynamics by deriving an understanding of the underlying mesoscopic switching
mechanisms. Slowly-propagating DWs generate a creep in the detection area of the
device, which yields a broad range of intermediate resistive states in the AHE
measurements. The Ta/CoFeB/MgO memristor device offers a practical structure that
relies on mature magnetic-material technology. As such, it could pave the way towards
the integration of high-density, energy-efficient components for non-volatile storage
and neuromorphic computing applications.
## Methods

**Sample preparation.** A thin-film stack of Ta (10 nm)/CoFeB (1.2 nm)/MgO (1 nm)/Ta (20 nm) was sputter-deposited on a thermally-oxidized Si substrate at room temperature. Vibrating sample magnetometer was used to characterize the magnetic properties of the thin-film stack and ensure that it exhibited perpendicular magnetic anisotropy (Supplementary Information S1). Hall bars were fabricated by photolithography and argon-ion milling. A Ta (10 nm)/Pt (100 nm) bilayer was capped on pads as electrodes by photolithography and lift-off techniques. The width and length of the channel in the Hall devices were 50 and 400 µm respectively; those of the Hall probes were 5 and 100 µm, respectively.

**Electrical measurements.** For the anomalous Hall resistance ($R_H$) measurement, a constant 0.1-mA-bias read current ($I_R$) was applied using a DC current source (Keithley Model 6221), and the Hall voltage ($V_R$) was measured using a nanovoltmeter (Keithley Model 2182A) in the usual way. The same current source was used to apply current pulses ($I$) for the current-induced switching and the phase-diagram measurements. A unipolar current pulse with a duration of 0.5 s was used for the current-induced switching in Fig. 1b, c. In particular, in Fig. 1c, we first set the FM into a demagnetization state ($R_H \sim 0$ Ω) excited by a DC current (60 mA) in the absence of a magnetic field and then increased the maximum magnitude of the current cycles (from 27 mA to 51 mA). In the switching phase-diagram measurements, the pulse width was varied from 50 to 500 µs in increments of 10 µs. Before each measurement, the magnet was initialized to a saturated state $M_\uparrow$ (Fig. 2c-e) or $M_\downarrow$ (Fig. 2f). The initial intermediate state corresponding to $R_H \sim 0$ Ω in Fig. 2b was also excited by a DC current (60 mA) in the absence of a magnetic field.

**Magneto-optic Kerr effect imaging.** A Magneto-optic Kerr effect (MOKE) microscope was used to magnetically image the Hall bars. To observe contrast, first the magnet was saturated in the -z or +z direction, and an image was taken. This served as
a reference image. Next, a current pulse with a width of 0.1 ms under an in-plane field was applied, and another image was taken. Finally, the two images were aligned, and the first reference image was subtracted from the second image to generate the final MOKE image, which was used in this work.
References

1. Chua, L. O. Memristor-the missing circuit element. *IEEE Trans. Circuit Theory* **18**, 507-519 (1971).

2. Strukov, D.B., Snider, G.S., Stewart, D.R. & Williams, R.S. The missing memristor found. *Nature* **453**, 80-83 (2008).

3. Yang, J. J. *et al*. Memristive switching mechanism for metal/oxide/metal nanodevices. *Nat. Nanotechnol.* **3**, 429-433 (2008).

4. Jo, S.H., Chang, T., Bhadviya, B.B., Mazumder, P. & Lu, W. Nanoscale memristor device as synapse in neuromorphic systems. *Nano Lett.* **10**, 1297-1301 (2010).

5. Chang, T. *et al*. Synaptic behaviors and modeling of a metal oxide memristive device. *Appl. Phys. A* **102**, 857-863 (2011).

6. Chanthbouala, A. *et al*. A ferroelectric memristor. *Nat. Mater.* **11**, 860-864 (2012).

7. Wang, X., Chen, Y., Xi, H., Li, H. & Dimitrov, D. Spintronic memristor through spin-torque-induced magnetization motion. *IEEE Electron Device Lett.* **30**, 294-297 (2009).

8. Chanthbouala, A. *et al*. Vertical-current-induced domain-wall motion in MgO-based magnetic tunnel junctions with low current densities. *Nat. Phys.* **7**, 626-630 (2011).

9. Lequeux, S. *et al*. A magnetic synapse: multilevel spin-torque memristor with perpendicular anisotropy. *Sci. Rep.* **6**, 31510 (2016).

10. Ikeda, S. *et al*. A perpendicular-anisotropy CoFeB-MgO magnetic tunnel junction. *Nat. Mater.* **9**, 721-724 (2010).

11. Dyakonov, M. I. & Perel, V. I. Current-induced spin orientation of electrons in semiconductors. *Phys. Lett. A* **35**, 459-460 (1971).

12. Hirsch, J. E. Spin hall effect. *Phys. Rev. Lett.* **83**, 1834 (1999).

13. Miron, I. M. *et al*. Perpendicular switching of a single ferromagnetic layer induced by in-plane current injection. *Nature* **476**, 189-193 (2011).
14. Liu, L. Q. et al. Spin torque switching with the giant spin Hall effect of tantalum. *Science* **336**, 555–558 (2012).

15. Fukami, S., Zhang, C., DuttaGupta, S., Kurenkov, A. & Ohno, H. Magnetization switching by spin-orbit torque in an antiferromagnet-ferromagnet bilayer system. *Nat. Mater.* **15**, 535–541 (2016).

16. Cai, K. et al. Electric field control of deterministic current-induced magnetization switching in a hybrid ferromagnetic/ferroelectric structure. *Nat. Mater.* **16**, 712–716 (2017).

17. Baumgartner, M. et al. Spatially and time-resolved magnetization dynamics driven by spin-orbit torques. *Nat. Nanotechnol.* **12**, 980–986 (2017).

18. Kondorsky, E. On hysteresis in ferromagnetics. *Journal of Physics-USSR* **2**, 161 (1940).

19. Emori, S., Bauer, U., Ahn, S. M., Martinez, E. & Beach, G. S. Current-driven dynamics of chiral ferromagnetic domain walls. *Nat. Mater.* **12**, 611–616 (2013).

20. Yu, G. et al. Magnetization switching through spin-Hall-effect-induced chiral domain wall propagation. *Phys. Rev. B* **89**, 104421 (2014).

21. Lee, O. J. et al. Central role of domain wall depinning for perpendicular magnetization switching driven by spin torque from the spin Hall effect. *Phys. Rev. B* **89**, 024418 (2014).

22. Boulle, O. et al. Domain wall tilting in the presence of the Dzyaloshinskii-Moriya interaction in out-of-plane magnetized magnetic nanotracks. *Phys. Rev. Lett.* **111**, 217203 (2013).

23. Parkin, S. S. P., Hayashi, M. & Thomas, L. Magnetic domain-wall racetrack memory. *Science* **320**, 190–194 (2008).

24. Lemerle, S. et al. Domain wall creep in an ising ultrathin magnetic film. *Phys. Rev. Lett.* **80**, 849–852 (1998).

25. Chauve, P., Giamarchi, T. & Le Doussal, P. Creep and creep in disordered media. *Phys. Rev. B* **62**, 6241–6267 (2000).

26. San Emeterio Alvarez, L. et al. Spin-transfer-torque-assisted domain-wall creep in a Co/Pt
multilayer wire. *Phys. Rev. Lett.* **104**, 137205 (2010).

27. Lee, J.-C. et al. Universality classes for magnetic domain wall motion. *Phys. Rev. Lett.* **107**, 067201 (2011).

28. DuttaGupta, S. et al. Adiabatic spin-transfer-torque-induced domain wall creep in a magnetic metal. *Nat. Phys.* **12**, 333-336 (2016).

29. Yu, G. et al. Switching of perpendicular magnetization by spin-orbit torques in the absence of external magnetic fields. *Nat. Nanotech.* **9**, 548-554 (2014).

30. You, L. et al. Switching of perpendicularly polarized nanomagnets with spin orbit torque without an external magnetic field by engineering a tilted anisotropy. *Proc. Natl Acad. Sci. USA* **112**, 10310-10315 (2015).

31. Lau, Y.-C., Betto, D., Rode, K., Coey, J. M. D. & Stamenov, P. Spin-orbit torque switching without an external field using interlayer exchange coupling. *Nat. Nanotechnol.* **11**, 758-762 (2016).

## Acknowledgements

### Author contributions

L. Y. conceived the experiments. Q. L., S. Z., Z. G. and H. C. fabricated the samples. S. Z. performed the electrical characterization of the samples and developed the control instrumentation and software. S. Z., J. Y., R. L., L. X., H. Z. and W. J. performed the MOKE measurements. W. T. simulated the Oersted field by Comsol simulations. Z. Y., K. X., K. S., Y. Z., X. Y., Q. Z. and X. L. provided the theoretical support. L. Y., S. Z., S. L., M. S., J. H., S. S., and B. D. analyzed the data. L. Y., S. L., N. X. and S. Z. wrote the manuscript. All authors discussed the data and contributed to the manuscript.