PHYSICAL REVIEW LETTERS VOL..XX, 000000 (XXXX)
1
2 Electric-Field Control of Spin-Orbit Torques in Perpendicularly Magnetized
3 W=CoFeB=MgO Films
4 Mariia Filianina ,1,2 Jan-Philipp Hanke ,1,3 Kyujoon Lee ,1 Dong-Soo Han,1,4 Samridh Jaiswal ,1,5
5 Adithya Rajan,1 Gerhard Jakob,1,2 Yuriy Mokrousov,1,3 and Mathias Kläui 1,2,*
6 1Institute of Physics, Johannes Gutenberg University, 55099 Mainz, Germany
7 2Graduate School of Excellence Material Science in Mainz, 55099 Mainz, Germany
8 3Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
9 4Center for Spintronics, Korea Institute for Science and Technology, 02792 Seoul, Republic of Korea
10 5Singulus Technology AG, 63796 Kahl am Main, Germany
11 (Received 13 January 2020; revised manuscript received 3 April 2020; accepted 29 April 2020)
12 1 Controlling magnetism by electric fields offers a highly attractive perspective for designing future
13 generations of energy-efficient information technologies. Here, we demonstrate that the magnitude of
14 current-induced spin-orbit torques in thin perpendicularly magnetized CoFeB films can be tuned and even
15 increased by electric-field generated piezoelectric strain. Using theoretical calculations, we uncover that the
16 subtle interplay of spin-orbit coupling, crystal symmetry, and orbital polarization is at the core of the
17 observed strain dependence of spin-orbit torques. Our results open a path to integrating two energy efficient
18 spin manipulation approaches, the electric-field-induced strain and the current-induced magnetization
19 switching, thereby enabling novel device concepts.
20 DOI:
21 Controlling efficiently the magnetization of nanoscale of in-plane thin films [15–18]. Moreover, as strain can be 51
22 devices is essential for many applications in spintronics, applied locally, it provides a playground to develop and 52
23 and is, thus, attracting significant attention in basic and realize complex switching concepts in simplified device 53
24 applied science. In recent years, current-induced switching architectures. 54
25 via spin-orbit torques (SOTs) [1] has emerged as one of While attempts were made to investigate the effect of 55
26 the most promising approaches to realize scalable magneto- strain on switching by spin torques [19–21], primarily the 56
27 resistive random-access memories (MRAM). The SOT- effect of strain on the anisotropy and the resulting impact 57
28 induced switching is realized in a ferromagnet-heavy metal on the switching was studied. Furthermore, these previous 58
29 (FM-HM) bilayers, where the existence of sizable damp- studies focused exclusively on systems with in-plane mag- 59
30 inglike Tjj ∝ m × ðy ×mÞ and fieldlike T⊥ ∝ m × y com- netic easy axis and experimental studies in perpendicularly 60
31 ponents of the SOT due to the flow of an electrical current magnetizedmultilayers are still elusive. However, in the light 61
32 along the x direction was theoretically and experimentally of the potential for technological applications, it is most 62
33 studied [2–9]. These torques originate from the spin Hall desirable to optimize all magnetic parameters including the 63
34 effect in the bulk of the HM material [10] and the inverse SOTs in ferromagnetic elements. In particular using systems 64
35 spin galvanic effect at the FM-HM interface [11]. with perpendicular magnetic anisotropy (PMA) is attractive 65
36 Itwas shown that the dampinglike torque termcan be large as increased thermal stability, higher packing densities, and 66
37 enough to switch the magnetization direction at low current improved scaling behavior are intrinsic to PMA materials as 67
38 densities down to 107–108 Acm−2 [6,12], which makes compared to their in-plane magnetized counterparts [22,23]. 68
39 them particularly attractive for device applications [13]. In this work, we demonstrate electrically induced strain 69
40 While sample parameters such as composition and layer control of SOTs in perpendicularly magnetizedW=CoFeB= 70
41 thickness of FM-HM heterostructures can be adjusted to MgO multilayers grown on a piezoelectric substrate. The 71
42 design the magnitude and the sign of SOTs, their “dynami- SOTs are evaluated by magnetotransport and second- 72
43 cal” control in a given system on-demand by external harmonic methods under in-plane strain of different char- 73
44 means is of great fundamental and technological interest. acter and magnitudes. We find that the strain, as modulated 74
45 One of the energy-efficient tools for that is offered by the by the electric field applied across the piezoelectric sub- 75
46 use of electric-field-induced mechanical strain [14]. strate, leads to distinct responses of fieldlike and damp- 76
47 Avoiding the need for electrical currents and, thus, elimi- inglike torques, with a large change of the latter by a factor 77
48 nating the associated losses, strain is known to effectively of 2. Based on the electronic structure of realistic hetero- 78
49 tune magnetic properties such as magnetic anisotropy and, structures, we explain our experimental findings by theo- 79
50 consequently, the magnetic domain structure and dynamics retical ab initio calculations and reveal the microscopic 80
1 © 2020 American Physical Society
PHYSICAL REVIEW LETTERS VOL..XX, 000000 (XXXX)
(a) V we used the dc electric fields that allowed us to vary the strain 105
within the linear response regime [38], as this provides 106
reliable electrical control over the induced strain. 107
We also note that the Hall cross in Fig. 1(b) was 108
1]
[01 fabricated such that the arms were oriented along the 109Ta (3 nm)
MgO (2 nm)
[100] ½011̄ and ½100 directions of the PMN-PT(011) substrate, 110
z Co 2 0Fe 6 0B 2 0 (0.6 nm)W (5 nm)
x which correspond to the directions of tensile and com- 111
y substrate: PMN-PT(011) pressive strain, respectively, as set by the crystallographic 112
(b) structure of the substrate [38]. The experimental results of 113
100 the SOTs obtained in the configuration with the current 114
50 (x axis) flowing along the ½011̄ and ½100 directions will be 115
10 µm referred to as modified by tensile and compressive strain, 116
0
respectively, [Fig. 1(a)]. We present the estimation of the 117
-50
0 kV m-1 strain exerted on the Hall bar due to the electric field 118
-1 y
-100 400 kV m x applied between the bottom electrode and all top electrodes 119
-30 -20 -10 0 10 20 30 in the Supplemental Material [24]. We also note that in the 120
0 z (mT) configuration shown in Fig. 1(a) the Hall bar itself acts as a 121
top electrode, so that uniform strain can be expected. 122
F1:1 FIG. 1. (a) Schematic of the Hall-cross device fabricated on top First, we characterize the magnetic hysteresis of the 123
F1:2 of the PMN-PT(011) substrate and the electrical contacts to the system at zero dc electric field. Figure 1(b) shows the 124
F1:3 Hall bar as well as additional electrical contacts used for the anomalous Hall voltage sweep with the OOPmagnetic field 125
F1:4 application of the OOP electric field to generate strain. In this −1
F1:5 configuration the current flow (x axis) is along the ½ (μ H ) measured for W=CoFeB=MgO=Ta at 0 kVm 126011̄ direction 0 z
F1:6 of the PMN-PT substrate, thus, in the text it is referred to as (red line), demonstrating the easy-axis switching typical 127
F1:7 tensile strain configuration. For compressive strain, the current for W-based thin CoFeB stacks. [39,40] The OOP mag- 128
F1:8 flow (x axis) is along the ½100 direction. (b) 1ω Hall voltage netization loop, measured at 400 kVm−1 (black line), is 129
F1:9 hysteresis loop measured in the OOP direction at 0 (red), and overlaid on top of it and shows no sizable change due to the 130
F1:10 400 kVm−1 (black) applied to the PMN-PT substrate using a generated strain indicating that the system has always a 131
F1:11 current of 0.33 mA. The inset shows the optical microscope dominating PMA. This is further supported by the mea- 132
F1:12 image of the Hall-cross structure used for the spin torque surements probing the anisotropy changes induced by the 133
F1:13 measurements. strain presented in the Supplemental Material [24]. 134
The current-induced effective SOT fields were measured 135
81 origin of the observed strain effects on the magnetoelectric using 2ω Hall measurements [41,42], as the high harmonic 136
82 coupling and the spin-orbit torques. technique provides robust determination of relative changes 137
83 Figure 1(a) shows the schematic of the Hall-cross of the SOTs [1] (see Supplemental Material [24] for more 138
84 device employed for the measurements of the dampinglike details). 139
85 (DL) and the fieldlike (FL) effective SOT fields inW(5 nm)/ Figure 2 shows the representative in-plane field depend- 140
86 CoFeB(0.6 nm)/MgO(2 nm)/Ta(3 nm) multilayer fabricated encies of the first (V1ω) and the second (V2ω) harmonics of 141
87 on a ½PbðMg Nb O Þ -½PbTiO  ð011Þ (PMN-PT) the Hall voltage when an ac current with the current density 1420.33 0.66 3 0.68 3 0.32
88 substrate, employed to electrically generatemechanical strain of j ¼ 3.8 × 1010 A m−2c was applied to the current line. 143
89 [24]. An optical microscope image of the Hall-cross device The dc poling voltage was set to zero, thus, no strain was 144
90 used in the experiment is presented in the inset in Fig. 1(b) and imposed on the Hall cross. The longitudinal [Fig. 2(a)] and 145
91 more details are provided in the Supplemental Material [24]. the transverse [Fig. 2(b)] field sweeps exhibit the expected 146
92 Uniaxial in-plane strain was generated by applying an symmetries: for the longitudinal field, the slopes of V2ω 147
93 out-of-plane (OOP) dc electric field across the piezoelectric versus the field are the same for both magnetization 148
94 PMN-PT(011) substrate. Generally, the piezoelectric strain directions along þz (þMz) or −z (−Mz), whereas their 149
95 response to the applied electric field exhibits a hysteretic sign reverses for the transverse field sweep. 150
96 behavior [38]. However, electric fields that exceed the Using the procedure described in the Supplemental 151
97 material-specific coercive field pole the substrate and lead Material [24] we analyze the transverse (μ0ΔHT) and the 152
98 to a regime where the generated strain is characterized by longitudinal (μ0ΔHL) components of the SOT effective 153
99 a linear response. The linear regime is maintained until the field for both magnetization directions Mz and plot the 154
100 substrate is poled in the other direction by application of average of these field components as a function of the 155
101 the electric fields larger than the opposite coercive field [38]. applied current density jc in Fig. 2(c). The resulting linear 156
102 Therefore, before the first measurements, but after the dependencies are fitted such that the slopes μ0ΔHT=jc and 157
103 structuring process, we poled the PMN-PT substrate by μ0ΔHL=jc determine the FL, μ Heff0 FL, and the DL, μ eff0HDL, 158
104 applying an electric field ofþ400 kVm−1. In the following, SOT effective fields, respectively. Similarly, the effective 159
2
V (µV)
PHYSICAL REVIEW LETTERS VOL..XX, 000000 (XXXX)
125 + M - M (b) + M - M jc  [011] jc  [100](a) z z z z
120 -3.0 -2.0(a) (c)
115
110 600 -3.5 -2.5
500
500
-4.0 -3.0
-110 400 400
-115 -100 0 100 -100 0 100µ0 Hx (mT) µ 0 Hx (mT) -4.5 -3.5
-120
-125 -4.0
-50 0 50 -50 0 50 -5.0
2.5 (b) (d) 3.5µ0 Hx (mT) µ 0Hy (mT)
1.0 2.0
(c) 3.0
0.5
0.0 1.5 2.5
-0.5 µ0ΔH T
1.0 2.0
-1.0 µ0ΔH L
-1.5 0.5 1.5
-2.0 0 200 400 -200 0 200 400
Electric field, kV m-1 Electric field, kV m-1
-2.5
0 1 2 3 4 5 6 FIG. 3. (a) FL and (b) DL SOT effective fields as a function of F3:1
j (1010 A m-2) the electric field applied across the PMN-PT(011) for the current F3:2c
flowing along the tensile (½011̄) strain direction. (c) FL and F3:3
F2:1 FIG. 2. (a) V1ω and V2ω (inset) signals as a function of the in- (d) DL SOT effective fields as a function of the electric field F3:4
F2:2 plane field directed along the current flow. (b) V1ω and V2ω (inset) applied for the current flowing along the compressive (½100) F3:5
F2:3 signals as a function of the in-plane field directed transverse to the strain direction. The solid lines represent the linear fit of the data F3:6
F2:4 current flow. The data were measured at the current density of to guide the eye. F3:7
F2:5 3.8 × 1010 Am−2. Black and red symbols represent signals for
F2:6 the magnetization pointing alongþz and −z, respectively. (c) The constant to account for the effect of uniaxial strain. This 183
F2:7 longitudinal (μ0ΔHL) and the transverse (μ0ΔHT) components of strain can be quantified by the ratio δ ¼ ða0 − ajÞ=aj, 184
F2:8 the SOT effective field plotted as a function of current density j . jc
At each value of current density, the averaged values of the SOT where aj and a
0
j denote the lattice constant along the jthF2:9 185
F2:10 effective field for þM and −M are shown. in-plane direction in the relaxed and distorted case, 186z z
respectively. As a consequence, any finite strain reduces 187
160 fields were extracted for different dc electric fields applied the original C4v crystal symmetry to C2v, see Fig. 4(a). 188
161 to the PMN-PT substrate to vary the magnitude of the We employ a Kubo formalism [43] to represent the SOT 189
162 generated strain. Ti ¼ τijEj acting on the magnetization as the linear 190
163 The electric-field dependent results are summarized in response to the applied electric field Ej, mediated by the 191
164 Fig. 3. We find that the FL torque does not change torkance τij. Owing to the mirror symmetries of the strained 192
165 significantly for both tensile and compressive strains as films with OOP magnetization, the torkances τxx and τyy 193
166 shown in Figs. 3(a) and 3(c). On the contrary, Fig. 3(b) characterize FL SOTs rooted in the electronic structure at 194
167 demonstrates that the tensile strain increases the DL torque the Fermi surface, whereas τxy and τyx correspond to DL 195
168 up to 2 times when 400 kVm−1 is applied, which corre- torques, to which also electrons of the Fermi sea contribute. 196
169 sponds to ca. 0.03% strain [24,38]. On the other hand, when In order to model additionally disorder and temperature 197
170 the current is flowing along the compressive strain direction, effects, we evaluate these response coefficients using a 198
171 the magnitude of the DL torque decreases with increasing constant broadening Γ ¼ 25 meV of the first-principles 199
172 strain. Thus, we find experimentally that the magnitude of energy bands [43]. In the following, δ refers to the strain 200
173 the DL torque increases (decreases) upon the application of along the orientation of the applied electric field, which 201
174 electrically induced tensile (compressive) strain. points into the x direction. 202
175 In order to understand the microscopic origin of the Based on our electronic-structure calculations, we obtain 203
176 experimentally observed strain dependence of FL and DL the δ dependence of the SOTs shown in Fig. 4(b), which 204
177 SOTs, we perform density functional theory calculations of reveals similar qualitative trends as found in the experi- 205
178 the electronic structure of Fe1−xCox=Wð001Þ, which con- ment. Since FL and DL SOTs originate from different 206
179 sists of a perpendicularly magnetized monolayer and non- electronic states, they generally follow distinct dependen- 207
180 magnetic underlayers (see Supplemental Material [24]). cies on structural details. Specifically, while the FL term τxx 208
181 As illustrated in Fig. 4(a), we expand or contract the crystal is hardly affected if δ is varied, we predict that the 209
182 structure while keeping the in-plane area of the unit cell magnitude of the DL torque τxy increases (decreases) 210
3
µ0ΔHT,L (mT) V (µV)
V (nV)
V (nV)
µ0 H DL (mT/ 10
11 A m-2) µ 11 -20 H FL(mT/ 10 A m )
PHYSICAL REVIEW LETTERS VOL..XX, 000000 (XXXX)
(a) (b) (c)
(d) (e)
F4:1 FIG. 4. (a) The uniaxial strain δ modifies the equilibrium crystal structure of the Fe0.7Co0.3=Wð001Þ film, and reduces the symmetry
F4:2 from C4v to C2v. (b) Dependence of FL (blue) and DL (red) torkances on strain along the direction of the electric field, where a constant
F4:3 broadening of the energy bands by 25 meV is used. (c) Microscopic contribution of all occupied bands to the DL SOT in relaxed and
F4:4 strained crystal structure. Gray lines indicate the Fermi surface. (d) As compared to the behavior without strain (gray), the density of dyz
F4:5 states in the magnetic layer changes for majority (red) and minority (blue) spin channels owing to tensile strain of δ ¼ 1%. The red and
F4:6 blue curves, showing the difference with respect to the unstrained case, are scaled by a factor of 10. (e) Momentum-space distribution of
F4:7 the dyz polarization of all occupied majority states in the magnetic layer of the relaxed and strained system.
211 linearly with respect to tensile (compressive) strain. For strain-induced change of the density of dyz states in the 236
212 instance, expanding the lattice by 1% along the electric- magnetic layer as compared to the case with fourfold 237
213 field direction drastically enhances the DL torkance by rotational symmetry. While the density of minority-spin 238
214 about 35%. To elucidate this remarkable behavior, we states at the Fermi level is hardly affected by tensile strain, 239
215 compare in Fig. 4(c) the momentum-space distribution of the majority-spin states are redistributed rather strongly. 240
216 the microscopic contributions to the DL SOT for relaxed As revealed by the momentum-resolved orbital polarization 241
217 and strained films. In contrast to the occupied states around in Fig. 4(e), microscopically, this effect stems from 242
218 theM point that are barely important, electronic states near pronounced δ-driven variations of the dyz polarization 243
219 the high-symmetry points Γ, X, and Y constitute the major around the X point, which correlates with the presented 244
220 source of the DL torkance. In particular, tensile strain changes of the DL torkance, Fig. 4(c). 245
221 promotes strong negative contributions around X and Y As the system considered in this work has a relatively 246
222 [see Fig. 4(c)], leading to an overall increase in the strong PMA, the static magnetic properties of the CoFeB 247
223 magnitude of τyx as depicted in Fig. 4(b). film as visible from the hysteresis loop [Fig. 1(b)] did not 248
224 To further associate our findings with the underlying show any significant change with the applied strain. Prior 249
225 electronic structure, we turn to the orbital polarization of work has focused on systems where the dominating effect 250
226 the states in the magnetic layer, the physics of which is of the strain was a change of the anisotropy [19–21], 251
227 dominated by d electrons. Whereas the behavior of dxy, but here we have strong PMA and probe the change of the 252
228 dx2−y2 , and dz2 is independent of the sign of the applied SOTs as the main factor. The sizable change in the torques 253
229 strain δ, the states of dyz and dzx character transform found can be explained by our theoretical calculations. 254
230 manifestly differently with respect to tensile or compressive Using our microscopic insights obtained from the 255
231 strain. Remarkably, the latter orbitals also mediate the electronic structure calculations, we uncovered that the 256
232 hybridization with the heavy-metal substrate, which distinct nature of the experimentally observed trends for 257
233 implies that their dependence on structural details offers FL and DL torques roots in unique changes of the orbital 258
234 additional microscopic insights into the SOTs in the studied polarization of the electronic states due to distortions of 259
235 thin films. As an example, we consider in Fig. 4(d) the the lattice. Beyond revealing the key role of hybridized 260
4
PHYSICAL REVIEW LETTERS VOL..XX, 000000 (XXXX)
261 states at the FM-HM interface, our results suggest a clear The work was financially supported by the Deutsche 316
262 scheme for generally engineering spin-orbit phenomena. Forschungsgemeinschaft (DFG, German Research 317
263 Utilizing the complex interplay of spin and orbital magnet- Foundation) in particular by Grant No. KL1811/18 318
264 ism, spin-orbit coupling, and symmetry, we can tailor the (318612841) and the Graduate School of Excellence 319
265 magnitude of SOTs in multilayer devices by designing the “Materials Science in Mainz” (DFG/GSC266). Y. M. 320
266 orbital polarization of the states near the Fermi energy by acknowledges support by the DFG through the Priority 321
267 strain. Programme SPP 2137, and additional support was provided 322
268 Importantly, our work opens up a route for shaping by the Collaborative Research Center SFB/TRR173 323
269 fundamental spin-orbitronic concepts into competitive (Projects No. A01—290396061/TRR173, A11—268565 324
270 technologies by dynamically tuning the SOTs in perpen- 370/TRR173 and B02—290319996/TRR173). A. R., G. J., 325
271 dicularly magnetized multilayer systems by means of and M. K. acknowledge funding from the European 326
272 electrically controlled strain. For example, as the strain Union’s Framework Programme for Research and 327
273 can be generated locally and imposed on selected parts of Innovation Horizon 2020 (2014-2020) under the Marie 328
274 the switching area, one can tune the current density such Skłodowska-Curie Grant Agreement No. 860060 (ITN 329
275 that the DL torque is large enough to switch the magneti- MagnEFi). D.-S. H. acknowledges funding from the 330
276 zation direction in these parts, while it is too small to switch Korea Institute of Science and Technology (KIST) institu- 331
277 the unstrained parts. In this case it would be possible to tional program (No. 2E30600) and the National Research 332
278 switch only selected parts of the area in one run with the Council of Science & Technology (NST) grant (No. CAP- 333
279 given current density. The selected parts can then be altered 16-01-KIST) funded by the Korea government (Ministry of 334
280 on demand by utilizing a different configuration of the Science and ICT). J. H. and Y. M. also gratefully acknowl- 335
281 electric fields, which allows for an additional level of edge the Jülich Supercomputing Centre and RWTH 336
282 control. Thus, by designing particular strain patterns of the Aachen University for providing computational resources 337
283 switching area by electric fields, an energy efficient under project jiff40. 338
284 multilevel memory cell capability can be realized, which
285 is practically important, e.g., for the emerging field of 341
286 neuromorphic computing [44]. *Klaeui@uni-mainz.de 34309342
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