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PHYSICAL REVIEW APPLIED 0, XXXXXX (2019) 1 Disentangling Highly Asymmetric Magnetoelectric Effects in Engineered 2 Multiferroic Heterostructures Q2 3 Enric Menéndez,1,* Veronica Sireus,1 Alberto Quintana,2 Ignasi Fina,3 Blai Casals,3 Rafael Cichelero,3 4 Mikko Kataja,3 Massimiliano Stengel,3,4 Gervasi Herranz,3 Gustau Catalán,4,5 Maria Dolors Baró,1 5 Santiago Suriñach,1 and Jordi Sort1,4 1 Departament de Física, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Cerdanyola del Vallès, Spain 6 2 Department of Physics, Georgetown University, Washington DC, 20057, USA 7 3 8 Institut de Ciència de Materials de Barcelona (ICMAB-CSIC), Campus UAB, Bellaterra, E-08193 Barcelona, 9 Spain 4 10 Institució Catalana de Recerca i Estudis Avançats (ICREA), Pg. Lluís Companys 23, E-08010 Barcelona, Spain 5 11 Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST, Campus UAB, Bellaterra, 12 E-08193 Barcelona, Spain 13 (Received 6 April 2019; revised manuscript received 30 May 2019; published XX XX 2019) 14 One of the main strategies to control magnetism by voltage is the use of magnetostrictive piezoelec- 15 tric hybrid materials, such as ferromagnetic-ferroelectric heterostructures. When such heterostructures are Q3 16 subjected to an electric field, piezostrain-mediated effects, electronic charging, and voltage-driven oxygen 17 migration (magnetoionics) may simultaneously occur, making the interpretation of the magnetoelectric 18 effects not straightforward and often leading to misconceptions. Typically, the strain-mediated magneto- 19 electric response is symmetric with respect to the sign of the applied voltage because the induced strain 20 (and variations in the magnetization) depends on the square of the ferroelectric polarization. Conversely, 21 asymmetric responses can be obtained from electronic charging and voltage-driven oxygen migration. By 22 engineering a ferromagnetic-ferroelectric hybrid consisting of a magnetically soft 50-nm thick Fe75 Al25 23 (at. %) thin film on top of a 110-oriented Pb(Mg1/3 Nb2/3 )O3 -32PbTiO3 ferroelectric crystal, a highly Q4 24 asymmetric magnetoelectric response is obtained and the aforementioned magnetoelectric effects can 25 be disentangled. Specifically, the large thickness of the Fe1-x Alx layer allows dismissing any possible Q5 26 charge accumulation effect, whereas no evidence of magnetoionics is observed experimentally, as expected 27 from the high resistance to oxidation of Fe1-x Alx , leaving strain as the only mechanism to modulate the 28 asymmetric magnetoelectric response. The origin of this asymmetric strain-induced magnetoelectric effect 29 arises from the asymmetry of the polarization reversal in the particular crystallographic orientation of the 30 ferroelectric substrate. These results are important to optimize the performance of artificial multiferroic 31 heterostructures. 32 DOI: 10.1103/PhysRevApplied.0.XXXXXX 33 I. INTRODUCTION effect in magnetostrictive-piezoelectric hybrid materials 45 (artificial multiferroics), such as ferromagnetic (FM)- 46 34 Electric field control of magnetism has attracted much ferroelectric (FE) heterostructures, has resulted in one of 47 Q6 35 scientific and technological interest due to its energy the mechanisms with the largest possible voltage-driven 48 36 efficiency implications, envisaging ultralow power dissi- modulation of the magnetic properties. Magnetostrictive 49 37 pation magnetic storage and magnetoelectronic devices FMs in combination with FE materials with strong 50 38 [1–3]. From a technological viewpoint, a reproducible, piezoelectric properties are typically used [11–16]. Due 51 39 strong, and tunable magnetoelectric effect is required in to their high piezoelectric response, (1−x)·Pb(Mg1/3 52 40 a solid-state device configuration. So far, in contrast to Nb2/3 )O3 -x·PbTiO3 (PMN-x·PT) single crystals with com- 53 41 single-phase multiferroics (with intrinsic magnetoelectric positions in the region close to the morphotropic phase 54 42 coupling) [4–6] and direct field effects (charge-mediated boundary (i.e., x around 35 mol. %) are one of the most 55 43 mechanism) in ultrathin metals and nanoporous alloys employed ferroelectric materials [17–22] in these engi- 56 44 [7–10], the strain-mediated converse magnetoelectric neered FM-FE heterostructures [13–15,23–33]. 57 In general, when an artificial FM-FE heterostructure is 58 * subjected to an electric field, inverse magnetostriction in enricmenendez@gmail.com 59 2331-7019/19/0(0)/XXXXXX(11) XXXXXX-1 © 2019 American Physical Society ENRIC MENÉNDEZ et al. PHYS. REV. APPLIED 0, XXXXXX (2019) 60 the FM induced by the piezoelectric strain arising from the ON), resulting in a graded material including Co- to O- 115 61 FE, charge accumulation at the surface of the FM (typi- rich regions. A positive bias reverses the process oxidizing 116 62 cally only observed for thicknesses of a few nm) [7–10], Co back to Co3 O4 (ferromagnetism: OFF). Hence, full 117 63 and voltage-driven oxygen migration may simultaneously understanding of the asymmetric magnetoelectric effect 118 64 occur. This makes interpretation of the observed effects in this type of multiferroic heterostructures (comprising 119 65 not straightforward, leading to misinterpretations. More- PMN-PT) is lacking and deserves to be further studied in 120 66 over, when addressing the magnetoelectric response of a detail. 121 67 FM-FE heterostructure, not all the possible mechanisms In this work, we disentangle the magnetoelectric effects 122 68 are taken into account, resulting in another source of mis- of an engineered FM-FE heterostructure, which consists 123 69 understandings. Disentangling these diverse contributions of a magnetically soft and isotropic 50-nm thick Fe75 Al25 124 70 is thus crucial for gaining further insight into the control (at. %) thin film grown on top of a 110-oriented PMN- 125 71 of magnetism by voltage in FM-FE heterostructures and 32PT) ferroelectric crystal. The magnetoelectric properties 126 72 in the design and optimization of the next generation of are measured using vibrating sample magnetometry while 127 73 magnetic storage and magnetoelectric devices. applying out-of-plane electric fields and in-plane magnetic 128 74 In a first approximation, the electric-field modula- fields either along the [001] or [1–10] in-plane orthogo- 129 75 tion of magnetic properties via strain transfer in FM- nal directions of the substrate. Besides the low cost of Fe 130 76 FE heterostructures should be symmetric with respect to and Al, Fe1-x Alx alloys with large Fe contents are mag- 131 77 voltage polarity (i.e., butterflylike magnetization voltage netostrictive [42–44], highly resistant to oxidation [45], 132 78 control). Additionally, since the strain largely vanishes and exhibit soft ferromagnetism [12]. This makes Fe1-x Alx 133 79 after removal of the external electric field, the magnetic alloys a suitable candidate as FM in FM-FE hybrids. While 134 80 changes are generally volatile (i.e., not permanent) when the thickness of 50 nm disables any possible effect arising 135 81 the applied electric field is removed [15,30,31,34]. Fur- from charge accumulation, the high resistance to oxidation 136 82 thermore, the magnetostrictive coupling is a function of ensures minimized voltage-driven oxygen migration pro- 137 Q7 83 the square of magnetization (M ) and electric polarization cesses, leaving strain as the only mechanism to modulate 138 84 (P) and, therefore, in principle, the sign of M cannot the magnetoelectric response, which, in contrast to typical 139 85 be switched with P. However, strong asymmetries with strain-induced magnetoelectric effects, is asymmetric with 140 86 voltage have been observed in the magnetic properties respect to the sign of the applied voltage. Depending on the 141 87 of FM-PMN-PT heterostructures, eventually resulting in direction of the applied magnetic field with respect to the 142 88 a “looplike”-controlled magnetization, and therefore, in in-plane crystallographic directions of the FE crystal (i.e., 143 89 permanent changes (i.e., nonvolatile) [23–27]. Thus, if [001] and [1–10]), the degree of asymmetry of the strain- 144 90 the magnitude of P at +Vapplied is different from that induced magnetoelectric effects is different. Volatilelike 145 91 at −Vapplied , the magnitude of M can be changed with (i.e., “butterflylike” and thus less asymmetric) magneto- 146 92 voltage polarity. This asymmetric magnetoelectric effect electric effects are observed when applying the magnetic 147 93 is of potential interest for alternative types of energy- field along [001], whereas a permanentlike (i.e., “looplike” 148 94 efficient magnetic memories that would be solely con- and thus highly asymmetric) magnetoelectric response 149 95 trolled with electric voltage. Although the origin of this is distinguished along [1–10]. Anyhow, this asymmet- 150 96 effect is often attributed to particular ferroelectric domain ric strain-induced magnetoelectric effect arises from the 151 97 switching mechanisms of the FE, this nonvolatile behavior asymmetry of the polarization reversal in the ferroelectric 152 98 has also been linked to charge-mediated effects [28] or to substrate. [110]-oriented crystals are not isotropic in-plane 153 99 a coexistence of strain- and charge-mediated magnetoelec- (i.e., [001] and [1–10] orthogonal axes are not equivalent), 154 100 tric coupling (i.e., magnetoelectroelastic effects) due to the and hence, the out-of-plane switching asymmetry of elec- 155 101 polarity-dependent nature of direct-field effects [29–31]. tric polarization translates via the in-plane anisotropy into 156 102 Moreover, in contrast to piezostrain and direct field an in-plane switching asymmetry in these crystals. 157 103 effects, magnetoionics results not only in changes of extrin- 104 sic magnetic properties, such as coercivity or remanence, 105 but also in saturation magnetization (which can precisely II. EXPERIMENTAL DETAILS 158 106 sense the degree of oxidation). In most of these studies, 107 detailed investigations of eventual changes in the satura- 50-nm thick Fe75 Al25 (at. %) films are grown by cosput- 159 108 tion magnetization with applied voltage have been largely tering at room temperature on 110-oriented PMN-32PT 160 109 omitted, thus overlooking possible voltage-driven oxygen single crystals using an AJA International, Inc. magnetron 161 110 diffusion (magnetoionics) phenomena [35–41], which also sputtering system. Depositions are carried out at a rate of 162 111 depend on the electric polarity. As a clear example, Ref. around 0.6 Å/s. 163 112 [40] reports on the voltage-controlled ON-OFF room tem- The Fe75 Al25 films are grown on 0.5-mm thick and 164 113 perature ferromagnetism in paramagnetic Co3 O4 . A nega- 3 × 4 mm2 rectangular-shaped [110] PMN-PT substrates. 165 114 tive voltage partly reduces Co3 O4 to Co (ferromagnetism: The orthogonal in-plane directions of the substrates are 166 XXXXXX-2 DISENTANGLING HIGHLY ASYMMETRIC. . . PHYS. REV. APPLIED 0, XXXXXX (2019) Q1 167 determined by azimuthal XRD scans (not shown) lay- plane). A larger number of points are recorded close to the 222 168 ing the [001] and the [1–10] directions along the shortest ferroelectric coercive field since it is in this region where 223 169 and longest dimensions of the substrate, respectively. For the largest changes in strain are achieved. 224 170 simplicity, from now on, 0 and 90° will refer to the mag- 171 netoelectric measurements carried out while applying the III. RESULTS AND DISCUSSION 225 172 magnetic field along the [001] or [1–10] directions of the 173 substrate, respectively. Substituting Fe by Al significantly increases the mag- 226 174 SEM using secondary electrons in a FEI Magellan 400L netostriction in Fe1-x Alx alloys. However, this increase 227 175 microscope operated at 20 kV is used to structurally and shows a maximal behavior for Al contents around 19 at. 228 176 morphologically characterize the top surface of the sam- % [42]. At the same time, Al also plays a crucial role 229 177 ples. To investigate the inner parts of the as-grown sam- in enhancing the resistance to oxidation. The choice of 230 178 ples, a cross-section lamella is prepared by focused ion a Fe75 Al25 (at. %) composition is aimed at having an 231 Q8 179 beam and placed onto a Cu TEM grid. To characterize alloy that simultaneously exhibits large magnetostriction 232 180 the cross section from structural and compositional view- [42–44] and high resistance to oxidation [45]. Even though 233 181 points, TEM, energy dispersive X-ray (EDX) analysis, and lower Al contents down to 19 at. % would result in a 234 182 high-angle annular dark-field scanning transmission elec- larger magnetostriction, oxidation resistance would then be 235 183 tron microscopy (HAADF STEM) are performed using worsened due to the limited amount of Al. 236 184 a TECNAI F20 HRTEM/STEM microscope operated at By comparing the θ /2θ XRD measurement of the 237 185 200 kV. Further structural characterization is carried out PMN-32PT crystal and the Fe1-x Alx / PMN-32PT bilayer 238 Q9 186 by θ/2θ XRD, grazing incidence XRD (GIXRD) with an [Fig. 1(a)], it can be seen that there is only one peak cor- 239 187 incidence angle of 1°, and reciprocal space maps around responding to the Fe1-x Alx film, located at around 44.4°. 240 188 (001) and (1–10) reflections of the PMN-32PT using Cu This is consistent with the (110) reflection of an Fe1−x Alx 241 189 Kα radiation in a Malvern-PANalytical X’pert Pro MRD phase with x ≈ 25 at. %, evidencing that the Fe1−x Alx 242 Q10 190 diffractometer. phase grows with a strong crystallographic texture. Nev- 243 191 The ferroelectric polarization versus applied voltage ertheless, the top view SEM image of the sample surface 244 192 (i.e., electric field) loop is collected by grounding one shown in Fig. 1(b) indicates that the sample is highly gran- 245 Q11 193 of the electrodes (silver paste) while biasing the other ular along the plane of the sample, showing a strong degree 246 194 (Fe-Al + silver paste) using the static hysteresis standard of in-plane polycrystallinity. Moreover, the (110) peak, 247 195 mode of the TFAnalyser2000 (Aixacct) with an integra- which appears in the GIXRD measurement, evidences that 248 196 tion time of 1 ms and a relaxation time of 1 s. With this the Fe1−x Alx layer (Fig. S1), despite being highly tex- 249 197 protocol, the displacive current flowing through the cir- tured, does not grow epitaxially. Figure 1(c) shows the 250 198 cuit (I ) is measured and the polarization is obtained from TEM image of a cross section along the [1–10] direction 251 Q12 199 the integrated current in time and normalized by the area of the heterostructure, evidencing that the Fe1−x Alx layer 252 200 (A): P = A Idt + C. The constant C is selected to obtain 1 is indeed around 50-nm thick. Moreover, the TEM images 253 201 a loop where the polarization values at maximum nega- show that an interfacial layer between the substrate and 254 202 tive and positive applied voltage are equal. The used sign the Fe1−x Alx layer of about 5 nm is formed. The compo- 255 203 convention is the standard, that is, the positive applied sition of the Fe1-x Alx layer is determined to be Fe75 Al25 256 204 voltage corresponds applying to the PMN-PT electric field (at. %) by TEM-EDX. As can be seen in the composi- 257 205 pointing toward the grounded electrode. tional analysis carried out by HAADF STEM (Fig. S2), the 258 206 The magnetic and magnetoelectric properties are mea- interfacial layer is rich in O and Al. HRTEM [Fig. 1(d)] 259 207 sured using a MicroSense (LOT-QuantumDesign) vibrat- reveals that this interface layer is partly crystalline. The 260 208 ing sample magnetometer (VSM), while the voltage is in FFT corresponding to the red rectangle in Fig. 1(d) results 261 Q14 209 situ applied out-of-plane using an Agilent B2902A power in two spots, which correspond to an interplanar distance 262 210 supply. A top electrode consisting of silver paint and the of 3.47 Å, which is compatible with the (012) planes of 263 211 Fe1-x Alx layer itself and a bottom silver paint electrode rhombohedral Al2 O3 (00-001-1243), in concordance with 264 212 are used to apply the electric field across the FM-FE het- the compositional mappings of Fig. S2. 265 213 erostructure. From an electric view point, the sample is The sample is sketched and the main crystallographic 266 214 out-of-plane poled using a silver paste bottom electrode, directions of the PMN-32PT crystal are represented in 267 215 which sticks the sample to a nonconducting VSM holder Fig. 2(a). Figure 2(b) shows the ferroelectric hysteresis 268 216 and a top electrode made of silver paste and the conducting loop measured in quasistatic conditions, whereas Fig. 2(c) 269 Q13 217 metallic Fe1-x Alx layer. is the square of the electric polarization represented in 270 218 The magnetoelectric characterization is carried out by Fig. 2(b) as a function of electric field. The latter is pro- 271 219 in-plane vibrating sample magnetometry while out-of- portional to the deformation that the PMN-PT undergoes 272 Q15 220 plane poling (i.e., the electric field is applied along the when subjected to an electric field due to its piezoelectric- 273 221 [110] direction, which is perpendicular to the sample ity [46]. Interestingly, (110)-cut PMN-x·PT single crystals 274 XXXXXX-3 ENRIC MENÉNDEZ et al. PHYS. REV. APPLIED 0, XXXXXX (2019) (a) (b) (c) (d) F1:1 FIG. 1. (a) θ/2θ x-ray diffraction patterns corresponding to a pristine (i.e., as-deposited) 50-nm thick Fe75 Al25 /110 PMN-PT sample F1:2 (black line) and a bare 110 PMN-PT substrate (red line). (b) Scanning electron microcopy image taken using secondary electrons of F1:3 the surface of a 50-nm thick Fe75 Al25 /110 PMN-PT sample. (c) TEM image of the cross section along [1–10] of a pristine 50-nm F1:4 thick Fe75 Al25 /110 PMN-PT sample. (d) High resolution TEM image of the interface layer formed between the Fe75 Al25 film and Q17 F1:5 the PMN-PT substrate. The inset shows the FFT of the area marked with a red rectangle. 275 in an out-of-plane poling configuration, do not only dis- in-plane magnetic field along [001] [i.e., 0° configura- 302 276 play anisotropic in-plane piezoelectric coefficients, which tion, Fig. 2(a)], whereas Fig. 4 shows the magnetoelec- 303 277 results in compressive and tensile stresses along [001] and tric measurements when the in-plane magnetic field is 304 278 [1–10] directions, respectively, but also a strong strain applied along [1–10] (i.e., 90° configuration). Specifically, 305 279 response when x is within the region of the morphotropic the samples are subjected to the following electric proto- 306 280 phase boundary (i.e., x is around 35 mol. %) [18,46–48]. col (see “Voltage protocol” in the Supplemental Material 307 281 Remarkably, the ferroelectric loop of Fig. 2(b) is not sym- [51]): First, hysteresis loops are recorded while follow- 308 282 metric. This could be ascribed to the interplay of the ing the ascending branch (A) of the ferroelectric loop. The 309 283 following aspects: (i) electrode asymmetry (the bottom piezoelectric is always brought to ferroelectric saturation 310 284 electrode is made by silver paste, while the top elec- at −6 kV/cm before applying the indicated measurement 311 285 trode consists of the Fe1-x Alx layer and silver paste), voltage to achieve better control of the sample state. Then, 312 286 which might lead to asymmetric electric fields at the inter- the protocol is reversed (i.e., from positive to negative 313 287 faces with the sample; (ii) macroscopic defect gradients saturation) to apply electric fields corresponding to the 314 288 [49]; and (iii) difficulty to reach saturation of the elec- descending branch (D) of the ferroelectric loop. 315 289 tric polarization (i.e., unsaturated loop), meaning that the For the 0° configuration, although the behavior is asym- 316 290 initial polarity dominates thus, envisaging complex and metric, the dependences of both the remanence (i.e., 317 291 path-dependent ferroelectric reversal mechanisms [50]. squareness, mR /mS ) and the coercivity (HC ) with the 318 292 In the absence of an electric field, the sample shows an applied electric field along [001] show an important com- 319 293 isotropic in-plane magnetic behavior (Fig. S3) as expected ponent with a butterflylike shape [Figs. 3(b) and 3(c), 320 294 from the high degree of polycrystallinity in the plane of respectively], resembling the variation of strain with volt- 321 295 the sample [Fig. 1(b)]. This is very convenient to dis- age in a piezoelectric material [Fig. 2(c)]. This is consistent 322 296 entangle magnetoelectric effects since they may result in with the converse magnetoelectric effect being dominated 323 297 anisotropic changes of magnetic anisotropy as happens by strain coupling via inverse magnetostriction. In addi- 324 298 in other heterostructures, such as Co40 Fe40 B20 /PMN-PT tion to the strain contribution, the observed asymmetry 325 299 [15,24,25]. with electric field polarity could be a fingerprint of the 326 300 Figure 3 shows the VSM characterization as a coexistence of strain and charge effects through magne- 327 301 function of the applied voltage while applying the toelectroelastic effects [30], since strain is proportional 328 XXXXXX-4 DISENTANGLING HIGHLY ASYMMETRIC. . . PHYS. REV. APPLIED 0, XXXXXX (2019) Q1 (a) (a) (b) (b) (c) (c) F2:1 FIG. 2. (a) Schematic representation of the out-of-plane poling F2:2 applied to the samples. (b) Ferroelectric hysteresis loop (elec- FIG. 3. (a) Hysteresis loops recorded along in-plane direction F3:1 F2:3 tric polarization P vs applied electric field E) of an as-deposited [001] (0o configuration) by vibrating sample magnetometry at a F3:2 F2:4 50-nm thick Fe75 Al25 /110 PMN-PT sample. (c) Square of P given applied electric field applied out-of-plane. The piezoelec- F3:3 F2:5 (which is proportional to the piezoelectric strain) vs E. tric is always brought to ferroelectric saturation at −6 kV/cm F3:4 before registering the magnetic measurement. (b) and (c) depen- F3:5 dences of the magnetic moment at remanence normalized by the F3:6 329 to P 2 whereas direct field effects are a function of P. magnetic moment at saturation (mR /mS ) and coercivity (HC ) with F3:7 330 However, taking into account that the electric field in the applied electric field. Ascending (A) and descending (D) refer F3:8 331 metals (e.g., Fe1-x Alx ) is strongly screened at the sur- to the branches of the ferroelectric hysteresis loop as sketched in F3:9 332 face, resulting in no penetration beyond the Thomas-Fermi the inset of panel (b). F3:10 333 screening length (which is around 0.5 nm) [9,52], charge 334 effects due to the accumulation of electrostatic charges 335 at the surface are rather unlikely to be significant since the PMN-PT [i.e., nonsaturated (i.e., minor) ferroelectric 339 336 the Fe1-x Alx layers are 50-nm thick. Anyhow, this in- loop], envisaging that path-dependent mechanisms of 340 337 plane magnetic asymmetry could be linked to the non- electric polarization reversal could also be a source of 341 338 symmetric perpendicular-to-plane ferroelectric behavior of magnetic asymmetry. 342 XXXXXX-5 ENRIC MENÉNDEZ et al. PHYS. REV. APPLIED 0, XXXXXX (2019) (a) electric field is rather weak, that of the squareness (i.e., 348 mR /mS ) exhibits a looplike shape with an asymmetry with 349 respect to the electric polarity much more pronounced than 350 when magnetization is measured along the [001] direction. 351 Remarkably, from negative to positive electric fields, the 352 magnetic properties switch from an easy to a hard axis 353 behavior. As possible origins of this observation, elec- 354 tronic charging, oxygen migration, and strain-mediated 355 effects will be discussed in the following. 356 First, although the Fe1-x Alx film is exceedingly thick 357 to present significant charge-mediated effects, the effects 358 of charge accumulation might propagate within the spin- 359 (b) spin exchange correlation length, which extends several 360 nm toward the interior of the alloy [50]. To verify this pos- 361 sibility, a thinner Fe75 Al25 film (20-nm thick) is grown in 362 the same fashion with the aim to enhance eventual surface 363 charging effects. As can be seen in Fig. S4, the dependence 364 of the squareness (i.e., mR /mS ), along [1–10] (i.e., 90° con- 365 figuration), with the applied electric field also exhibit a 366 looplike dependence but the relative changes are, in fact, 367 less pronounced in this thinner sample. Specifically, for 368 the 50-nm thick sample, the maximum relative change in 369 remanence is around 61.4%, whereas, for the 20-nm thick 370 sample, the change is 53.6%, indicating that interfacial 371 charge effects (and also their propagation via the spin-spin 372 (c) correlation length) are ruled out as the main mechanism 373 governing this reorientation of the magnetic easy axis with 374 voltage. This sample also shows an Al2 O3 -based interfa- 375 cial layer of around 5 nm in thickness at the interface 376 with the PMN-PT. Regarding the role of these Al2 O3 -based 377 interfacial layers in possible charge-mediated effects, 50- 378 nm and 20-nm thick Fe75 Al25 layers are still too thick 379 to exhibit significant direct field effects. Effectively, since 380 Al2 O3 is also highly insulating, the interfacial layers add 381 up to the PMN-PT, resulting in a slightly thicker insulating 382 substrate. 383 After discarding charge effects, we focus on possi- 384 ble voltage-driven oxygen migration (i.e., magnetoionics) 385 phenomena since this magnetoelectric mechanism is polar- 386 ity dependent and it could result in strong permanent 387 F4:1 FIG. 4. (a) Hysteresis loops recorded along in-plane direction (nonvolatile) changes [35–38,40,41]. As can be seen in 388 F4:2 [1–10] (90o configuration) by vibrating sample magnetometry at F4:3 a given applied electric field out-of-plane. The piezoelectric is Fig. 5, the magnetic moment at saturation remains vir- 389 F4:4 always brought to ferroelectric saturation at −6 kV/cm before tually constant during the voltage protocol (changes are 390 F4:5 registering the magnetic measurement. (b) and (c) dependences lower than 2% and the maximum change is related to an 391 F4:6 of the magnetic moment at remanence normalized by the mag- increase in magnetic moment), indicating that no oxida- 392 F4:7 netic moment at saturation (mR /mS ) and coercivity (HC ) with the tion occurs during voltage actuation. This in agreement 393 F4:8 applied electric field. Ascending (A) and descending (D) refer to with the structural characterization, which evidences the 394 F4:9 the branches of the ferroelectric hysteresis loop as sketched in formation of an interfacial layer based on Al2 O3 , which 395 F4:10 the inset of panel (b). acts as a barrier for oxygen migration, isolating and pro- 396 tecting the system from further oxidation. The θ/2θ XRD 397 343 A quite different dependence of the magnetoelectric measurement of a sample subjected to a full voltage proto- 398 344 coupling to the polarity of the electric field is observed col shows no traces of phases other than Fe1-x Alx , further 399 345 when the magnetization is measured along the [1–10] confirming the protective character of the Al2 O3 -based 400 346 direction (i.e., 90° configuration). In this case, while the interface layer (Fig. S5) and the resistance of Fe1-x Alx to 401 347 dependence of the magnetic coercivity on the applied oxidation. 402 XXXXXX-6 DISENTANGLING HIGHLY ASYMMETRIC. . . PHYS. REV. APPLIED 0, XXXXXX (2019) Q1 (a) (b) F5:1 FIG. 5. (a) and (b) dependences of the magnetic moment at saturation with the applied electric field when the magnetic field is F5:2 applied along the [001] (0o configuration) or [1–10] (90o configuration) directions, respectively. 403 Taking into account the asymmetry in the measured ferroelastic switching (consecutive 71° + 109° switching). 439 404 ferroelectric hysteresis loop of the PMN-PT [Fig. 2(b)] In crystals oriented with [001] out of the plane (and thus 440 405 and ruling out voltage-driven electronic charging and oxy- parallel to the electric field), this occurs isotropically: all 441 406 gen migration effects, the magnetoelectric behavior of the in-plane switching directions are energetically equivalent, 442 407 sample seems to be solely governed by strain-mediated thus all ferroelastic switching events are equally probable 443 408 effects (i.e., by the ferroelectric and/or piezoelectric nature and happen in the same proportion. In contrast, [110]- 444 409 of the PMN-PT). Thus, the strong in-plane magnetoelec- oriented crystals are not isotropic in-plane (i.e., [001] and 445 410 tric asymmetry along in-plane [001] and [1–10] axes in [1–10] orthogonal axes are not equivalent), and hence, the 446 411 our [110]-oriented crystals might be related to the spe- out-of-plane switching asymmetry of electric polarization 447 412 cific symmetry related ferroelectric response of our [110]- [Figs. 2(b) and 2(c)] translates, via the in-plane anisotropy, 448 413 oriented PMN-PT crystals as compared to the more usual into an in-plane switching asymmetry in these crystals. 449 414 [100]-oriented substrates. PMN-PT compositions around In order to investigate the ferroelectric reversal of the 450 415 the morphotropic phase boundary exhibit a complex phase PMN-PT, we perform in-plane reciprocal space mappings 451 416 diagram [19]. Specifically, poling along [110] results in around the (001) and (1–10) x-ray diffraction reflections 452 417 [111] and [11−1] as statistically equivalent spontaneous of a PMN-PT substrate in pristine conditions (i.e., 0 V in 453 418 polarization directions [21]. Moreover, considering a pseu- Fig. 6) and at 0 V after applying −6 kV/cm (i.e., rema- 454 419 docubic cell for [110] PMN-PT, [111] fully falls in the nence from −6 kV/cm in Fig. 6). The (001) and (1–10) 455 420 plane determined by [110] and [001] (Fig. S6). Ferro- XRD reflections of [110] PMN-PT correspond to the in- 456 421 electric reversal in this material can take place via nucle- plane orthogonal [001] and [1–10] directions, respectively. 457 422 ation and domain wall movements of 71°, 109°, and This allows us to investigate the influence of the electric 458 Q16 423 180° domain walls [53–56]. In (Bi, Fe)O3 , which is a field on the interplanar distances d001 and d1–10 and thus 459 424 model multiferroic with a rather similar crystalline struc- on the electric field-induced deformation along the short- 460 425 ture, the domain wall energy γ follows the sequence: est and longest dimensions of the sample. To estimate these 461 426 γ 109° < γ 180° < γ 71° [54]. Specifically, on top of single interplanar distances, the maximum intensity of the peaks 462 427 180° switching, there are consecutive 71° + 109° switch- is considered. Prior to the voltage application, the inter- 463 428 ing events. Domain walls of 180° and 71° imply a polar- planar distances are d001 = 4.02385 Å (qx  = 0.24852 Å−1 ) 464 429 ization reversal, which takes place in the same plane (i.e., and d1–10 = 2.84725 Å (qy  = 0.35122 Å−1 ). Upon voltage 465 430 the plane where [111] lies), resulting in minimized in- actuation at negative ferroelectric remanence, d001 = 466 431 plane distortions along [1–10]. Conversely, 109° domain 4.02375 Å (qx  = 0.24852 Å−1 ) and d1–10 = 2.84275 Å 467 432 walls lead to a 90° twist of the polarization (the polariza- (qy  = 0.35177 Å−1 ). In absolute values, along [001], the 468 433 tion rotates out of the plane of the domain wall), giving interplanar distance remains almost unaltered (0.0025% 469 434 rise to significant in-plane distortions along [1–10]. To of change), whereas along [1–10], there is a permanent 470 435 some extent, 109° domain walls resemble ferromagnetic change of around 0.16% of the initial value. Interest- 471 436 Bloch domain walls [55]. In other words, particularly when ingly, it is along this direction where the magnetic prop- 472 437 loops are unsaturated, a path-dependent polarization rever- erties exhibit a pronounced nonvolatile behavior (looplike 473 438 sal, on top of 180° switching events, is enabled through dependence). In contrast to the 71° and 180° domains, 474 XXXXXX-7 ENRIC MENÉNDEZ et al. PHYS. REV. APPLIED 0, XXXXXX (2019) (a) (b) (c) (d) F6:1 FIG. 6. (a) and (b) in-plane reciprocal space mappings around the (001) and (1–10) planes of a pristine substrate (i.e., 0 kV/cm), F6:2 respectively. (c) and (d) in-plane reciprocal space mappings around the (001) and (1–10) planes of a PMN-PT substrate at negative F6:3 ferroelectric remanence (measured at 0 kV/cm after being subjected to −6 kV/cm), respectively. 475 the electric polarization reversal through the 109° domains ruling out voltage-driven O migration as an operative 498 476 takes place via a 90° twist when reversing the electric field, magnetoelectric mechanism. Conversely, both the rema- 499 477 which results in additional stress-induced anisotropy along nence (i.e., mR /mS ) and the coercivity (HC ) exhibit a strong 500 478 [1–10], thus explaining the strong asymmetry with volt- dependence on the applied voltage (amplitude and sign). In 501 479 age polarity of the magnetic properties in this direction and perfect crystals with symmetric electrodes such asymme- 502 480 their nonvolatility upon removing the electric voltage. As try should not exist. However, crystals are never perfectly 503 481 can also be seen in Fig. 6, electric field actuation results symmetric [49], and the ferroelectric hysteresis measure- 504 482 in sharpened peaks. This could be ascribed to a decrease ments (Fig. 2) show that the positive and negative polar- 505 483 in mosaicity in the plane of the sample due to the under- ities are nonequivalent in our substrates. Likewise, along 506 484 gone deformation. Concerning the role of the Al2 O3 -based [001], mR /mS and HC show a slightly asymmetric butter- 507 485 interfacial layers in these piezostrain-mediated effects, the flylike dependence, while along [1–10], mR /mS exhibits 508 486 strain transfer from PMN-PT to the Fe75 Al25 layer should a clear looplike behavior, evidencing strong nonvolatile 509 487 not be significantly weakened by the Al2 O3 -based interfa- properties. Asymmetry can sometimes be attributed to 510 488 cial layer because, as can be seen in Fig. 1(d), this layer is interfacial charging effects. However, electrostatic charge 511 489 very thin and it grows rather epitaxially with the PMN-PT. effects are mostly significant when dealing with ultrathin 512 films and a thinner Fe1-x Alx sample grown in the same 513 fashion as a thicker one exhibits reduced permanent effects, 514 490 IV. CONCLUSIONS so interfacial charging is ruled out as the explanation. 515 491 The magnetoelectric behavior of 50-nm thick Fe75 Al25 Thus, the combination of macroscopic crystal asymme- 516 492 (at. %) films grown onto [110] PMN-32PT substrates try plus strain is left as the most plausible mechanism 517 493 is investigated in detail by performing in-plane vibrat- to modulate the magnetoelectric response of the investi- 518 494 ing sample magnetometry along the [001] and [1–10] gated system. Indeed, detailed structural characterization 519 495 directions of the PMN-PT while applying an exter- by reciprocal space mappings around the (001) and (1–10) 520 496 nal out-of-plane electric field. The magnetic moment x-ray diffraction reflections of a PMN-PT substrate reveal 521 497 at saturation remains virtually unaltered with voltage, that the application of an electric field results in permanent 522 XXXXXX-8 DISENTANGLING HIGHLY ASYMMETRIC. . . PHYS. REV. APPLIED 0, XXXXXX (2019) Q1 523 strains only in the [1–10] direction. This explains the [4] W. Eerenstein, N. D. Mathur, and J. F. Scott, Multi- 574 524 strong nonvolatility of the magnetic properties, which is ferroic and magnetoelectric materials, Nature 442, 759 575 525 linked to ferroelastic switching (consecutive 71° + 109° (2006). 576 526 switching) rather than single 180° switching events. 109° [5] G. Catalan and J. F. Scott, Physics and applications of 577 Bismuth ferrite, Adv. Mater. 21, 2463 (2009). 578 527 domain switching implies a 90° twist of the polariza- [6] N. Izyumskaya, Y. Aliyov, and H. Morkoç, Oxides, oxides, 579 528 tion when reversing polarity, thus causing a stress-induced and more oxides: high-( oxides, ferroelectrics, ferromagnet- 580 529 magnetic anisotropy along [1–10], explaining the dissim- ics, and multiferroics, Crit. Rev. Solid State Mater. Sci. 34, 581 530 ilar magnetic behavior with voltage polarity along the 89 (2009). 582 531 direction, which shows irreversible and permanent strain [7] M. Weisheit, S. Fähler, A. Marty, Y. Souche, C. Poinsignon, 583 532 upon removing the electric voltage. Our results reveal that, and D. Givord, Electric field-induced modification of 584 533 in order to properly understand magnetoelectric mecha- magnetism in thin-film ferromagnets, Science 315, 349 585 534 nisms in artificial FM-FE heterostructures, it is neces- (2007). 586 535 sary to clearly assess the intrinsic polarization reversal of [8] C.-G. Duan, J. P. Velev, R. F. Sabirianov, Z. Zhu, J. Chu, 587 536 the ferroelectric material, especially when using PMN-PT S. S. Jaswal, and E. Y. Tsymbal, Surface magnetoelectric 588 effect in ferromagnetic metal films, Phys. Rev. Lett. 101, 589 537 or other complex ferroelectric materials in these artifi- 137201 (2008). 590 538 cial multiferroic materials. Finally, even though the sign [9] I. V. Ovchinnikov and K. L. Wang, Theory of electric-field- 591 539 of magnetization cannot be switched with electric polar- controlled surface ferromagnetic transition in metals, Phys. 592 540 ization, the magnitude of magnetization can be changed Rev. B 79, 020402(R) (2009). 593 541 with voltage polarity (i.e., different magnitudes of electric [10] A. Quintana, J. Zhang, E. Isarain-Chávez, E. Menén- 594 542 polarization between plus and minus Vapplied ), implying dez, R. Cuadrado, R. Robles, M. D. Baró, M. Guer- 595 543 that strain-mediated effects could eventually be used for rero, S. Pané, B. J. Nelson, C. M. Müller, P. Ordejón, J. 596 544 memory purposes. Nogués, E. Pellicer, and J. Sort, Voltage-induced coerciv- 597 ity reduction in nanoporous alloy films: a boost toward 598 energy-efficient magnetic actuation, Adv. Funct. Mater. 27, 599 545 ACKNOWLEDGMENTS 1701904 (2017). 600 [11] Y. Wang, J. Hu, Y. Lin, and C.-W. Nan, Multiferroic mag- 601 546 Financial support by the European Research Coun- netoelectric composite nanostructures, NPG Asia Mater. 2, 602 547 cil (SPIN-PORICS 2014-Consolidator Grant, Agree- 61 (2010). 603 548 ment No. 648454), the Spanish Government (Grants [12] Y. Wei, C. Gao, Z. Chen, S. Xi, W. Shao, P. Zhang, G. 604 549 No. MAT2017-86357-C3-1-R, No. MAT2017-85232-R Chen, and J. Li, Four-state memory based on a giant and 605 550 (AEI/FEDER,UE), and No. MAT2015-73839-JIN, and non-volatile converse magnetoelectric effect in FeAl/PIN- 606 PMN-PT structure, Sci. Rep. 6, 30002 (2016). 607 551 associated FEDER), the Generalitat de Catalunya (Grants [13] M. Liu, O. Obi, J. Lou, Y. Chen, Z. Cai, S. Stoute, M. 608 552 No. 2017-SGR-292 and No. 2017 301 SGR1377) and Espanol, M. Lew, X. Situ, K. S. Ziemer, V. G. Harris, and 609 553 the European Union’s Horizon 2020 research and inno- N. X. Sun, Giant electric field tuning of magnetic prop- 610 554 vation programme under the Marie Skłodowska-Curie erties in multiferroic ferrite/ferroelectric heterostructures, 611 555 Grant No. 665919 is acknowledged. I. F. acknowledges Adv. Mater. 19, 1826 (2009). 612 556 his “Ramón y Cajal” Grant No. RYC-2017-22531. The [14] T. Wu, A. Bur, K. Wong, P. Zhao, C. S. Lynch, 613 557 ICN2 is funded by the CERCA programme/Generalitat de P. K. Amiri, K. L. Wang, and G. P. Carman, Giant 614 558 Catalunya. ICN2 and ICMAB also acknowledge financial electric-field-induced reversible and permanent mag- 615 559 support from the Spanish Ministry of Economy, Com- netization reorientation on magnetoelectric Ni/(011) 616 [Pb(Mg1/3 Nb2/3 )O3](1−x) −[PbTiO3 ]x heterostructure, Appl. 617 560 petitiveness and Universities through the “Severo Ochoa” Phys. Lett. 98, 012504 (2011). 618 561 Programme for Centres of Excellence in R&D (Grants No. [15] S. Zhang, Y. Zhao, X. Xiao, Y. Wu, S. Rizwan, L. 619 562 SEV-2017-0706 and No. SEV-2015-0496, respectively). Yang, P. Li, J. Wang, M. Zhu, H. Zhang, X. Jin, and 620 X. Han, Giant electrical modulation of magnetization 621 in Co40 Fe40 B20 /Pb(Mg1/3 Nb2/3 )0.7 Ti0.3 O3 heterostructure, 622 Sci. Rep. 4, 3727 (2014). 623 563 [1] C. Song, B. Cui, F. Li, X. Zhou, and F. Pan, Recent progress [16] T. H. E. Lahtinen, K. J. A. Franke, and S. van 624 564 in voltage control of magnetism: materials, mechanisms, Dijken, Electric-field control of magnetic domain wall 625 565 and performance, Prog. Mater. Sci. 87, 33 (2017). motion and local magnetization reversal, Sci. Rep. 2, 258 626 566 [2] J.-M. Hu, Z. Li, L.-Q. Chen, and C.-W. Nan, High- (2012). 627 567 density magnetoresistive random access memory operating [17] S. W. Choi, T. R. Shrout, S. J. Jang, and A. S. 628 568 at ultralow voltage at room temperature, Nat. Commun. 2, Bhalla, Dielectric and pyroelectric properties in the 629 569 553 (2011). Pb(Mg1/3 Nb2/3 )O3 -PbTiO3 system, Phys. Rev B 100, 29 630 570 [3] Y. Shiota, T. Nozaki, F. Bonell, S. Murakami, T. Shinjo, and (1989). 631 571 Y. Suzuki, Induction of coherent magnetization switching [18] S.-E. Park and T. R. Shrout, Ultrahigh strain and piezoelec- 632 572 in a few atomic layers of FeCo using voltage pulses, Nat. tric behavior in relaxor based ferroelectric single crystals, 633 573 Mater. 11, 39 (2012). J. Appl. Phys. 82, 1804 (1997). 634 XXXXXX-9 ENRIC MENÉNDEZ et al. PHYS. REV. APPLIED 0, XXXXXX (2019) 635 [19] B. Noheda, D. E. Cox, G. Shirane, J. Gao, and [32] I. Fina, A. Quintana, X. Martí, F. Sánchez, M. Foerster, L. 695 636 Z.-G. Ye, Phase diagram of the ferroelectric relaxor Aballe, J. Sort, and J. Fontcuberta, Reversible and magneti- 696 637 (1−x)·Pb(Mg1/3 Nb2/3 )O3 -x·PbTiO3 , Phys. Rev. B 66, cally unassisted voltage-driven switching of magnetization 697 638 054104 (2002). in FeRh/PMN-PT, Appl. Phys. Lett. 113, 152901 (2018). 698 639 [20] T. Wu, P. Zhao, M. Bao, A. Bur, J. L. Hockel, K. Wong, [33] I. Fina, A. Quintana, J. Padilla-Pantoja, X. Marti, F. Macia, 699 640 K. P. Mohanchandra, C. S. Lynch, and G. P. Carman, F. Sanchez, M. Foerster, L. Aballe, J. Fontcuberta, and 700 641 Domain engineered switchable strain states in ferroelec- J. Sort, Electric-field-adjustable time-dependent magneto- 701 642 tric (011) [Pb(Mg1/3Nb2/3)O3](1−x) -[PbTiO3]x (PMN- electric response in martensitic FeRh alloy, ACS Appl. 702 643 PT, x ≈ 0.32) single crystals, J. Appl. Phys. 109, 124101 Mater. Interfaces 9, 15577 (2017). 703 644 (2011). [34] L. Shu, Z. Li, J. Ma, Y. Gao, L. Gu, Y. Shen, Y. Lin, and 704 645 [21] G. Sébald, L. Lebrun, and D. Guyomar, Stability of mor- C. W. Nan, Thickness-Dependent voltage-modulated mag- 705 646 photropic <110> oriented 0.65PMN-0.35PT single crys- netism in multiferroic heterostructures, Appl. Phys. Lett. 706 647 tals, Phys. Rev B 51, 1491 (2004). 100, 022405 (2012). 707 648 [22] P. Kumar, C. Prakash, and T. C. Goel, Dielectric and elec- [35] U. Bauer, L. Yao, A. J. Tan, P. Agrawal, S. Emori, H. 708 649 trostrictive properties of PMNT near MPB, Sci. Technol. L. Tuller, S. van Dijken, and G. S. D. Beach, Magneto- 709 650 Adv. Mater. 8, 463 (2007). ionic control of interfacial magnetism, Nat. Mater. 14, 174 710 651 [23] T. Wu, A. Bur, K. Wong, P. Zhao, C. S. Lynch, P. K. (2015). 711 652 Amiri, K. L. Wang, and G. P. Carman, Electrical control [36] D. A. Gilbert, A. J. Grutter, E. Arenholz, K. Liu, B. J. 712 653 of reversible and permanent magnetization reorientation Kirby, J. A. Borchers, and B. B. Maranville, Structural and 713 654 for magnetoelectric memory devices, Appl. Phys. Lett. 98, magnetic depth profiles of magneto-ionic heterostructures 714 655 262504 (2011). beyond the interface limit, Nat. Commun. 7, 12264 (2016). 715 656 [24] S. Zhang, et al., Electric-Field Control of Nonvolatile [37] L. Zhang, S. Zeng, X. Yin, T. C. Asmara, P. Yang, K. 716 657 Magnetization in Co40 Fe40 B20 /Pb(Mg1/3 Nb2/3 )0.7 Ti0.3 O3 Han, Y. Cao, W. Zhou, D. Wan, C. S. Tang, A. Rusydi, 717 658 Structure at Room Temperature, Phys. Rev. Lett. 108, Ariando, and T. Venkatesan, The mechanism of electrolyte 718 659 137203 (2012). gating on high-TC cuprates: the role of oxygen migration 719 660 [25] P. Li, Y. Zhao, S. Zhang, A. Chen, D. Li, J. Ma, Y. and electrostatics, ACS Nano 11, 9950 (2017). 720 661 Liu, D. T. Pierce, J. Unguris, H.-G. Piao, H. Zhang, M. [38] Q. Zhang, X. He, J. Shi, N. Lu, H. Li, Q. Yu, Z. Zhang, 721 662 Zhu, X. Zhang, X. Han, M. Pan, and C.-W. Nan, Spa- L.-Q. Chen, B. Morris, Q. Xu, P. Yu, L. Gu, K. Jin, and C.- 722 663 tially resolved ferroelectric domain-switching-controlled W. Nan, Atomic-resolution imaging of electrically induced 723 664 magnetism in Co40 Fe40 B20 /Pb(Mg1/3 Nb2/3 )0.7 Ti0.3 O3 mul- oxygen vacancy migration and phase transformation in 724 665 tiferroic heterostructure, ACS Appl. Mater. Interfaces 9, SrCoO2.5−σ , Nat. Commun. 8, 104 (2017). 725 666 2642 (2017). [39] A. Quintana, E. Menéndez, E. Isarain-Chávez, J. Fornell, 726 667 [26] X. Han, Y. Li, X. Guo, Z. Wang, Y. Zuo, L. Xi, and D. Xue, P. Solsona, F. Fauth, M. D. Baró, J. Nogués, E. Pel- 727 668 Large electric tunable remanent magnetization and in-plane licer, and J. Sort, Tunable magnetism in nanoporous CuNi 728 669 anisotropy field in (110) PMN-0.32PT/Cu/Fe65 Co35 mul- alloys by reversible voltage-driven element-selective redox 729 670 tiferroic heterostructures, Mater. Res. Express 1, 026103 processes, Small 4, 1704396 (2018). 730 671 (2014). [40] A. Quintana, E. Menéndez, M. O. Liedke, M. Butterling, 731 672 [27] L. Yang, Y. Zhao, S. Zhang, P. Li, Y. Gao, Y. Yang, H. A. Wagner, V. Sireus, P. Torruella, S. Estradé, F. Peiró, J. 732 673 Huang, P. Miao, Y. Liu, A. Chen, C. W. Nan, and C. Gao, Dendooven, C. Detavernier, P. D. Murray, D. A. Gilbert, K. 733 674 Bipolar loop-like non-volatile strain in the (001)-oriented Liu, E. Pellicer, J. Nogués, and J. Sort, Voltage-controlled 734 675 Pb(Mg1/3 Nb2/3 )O3 -PbTiO3 single crystals, Sci. Rep. 4, ON−OFF ferromagnetism at room temperature in a single 735 676 4591 (2014). metal oxide film, ACS Nano 12, 10291 (2018). 736 677 [28] C. Zhang, F. Wang, C. Dong, C. Gao, C. Jia, C. Jiang, [41] C. Bi, Y. Liu, T. Newhouse-Illige, M. Xu, M. Rosales, J. 737 678 and D. Xue, Electric field mediated non-volatile tuning W. Freeland, O. Mryasov, S. Zhang, S. G. E. te Velthuis, 738 679 magnetism at the single-crystalline Fe/Pb(Mg1/3 Nb2/3 )0.7 and W. G. Wang, Reversible Control of Co Magnetism by 739 680 Ti0.3 O3 interface, Nanoscale 7, 4187 (2015). Voltage-Induced Oxidation, Phys. Rev. Lett. 113, 267202 740 681 [29] Y. T. Yang, J. Li, X. L. Peng, B. Hong, X. Q. Wang, H. L. (2014). 741 682 Ge, D. H. Wang, and Y. W. Du, Surface-effect enhanced [42] N. Mehmood, R. S. Turtelli, R. Grössinger, and M. 742 683 magneto-electric coupling in FePt/PMN-PT multiferroic Kriegisch, Magnetostriction of polycrystalline Fe100−x Alx 743 684 heterostructures, AIP Adv. 7, 055833 (2017). (x=15, 19, 25), J. Alloys Compd. 322, 212504 (2010). 744 685 [30] J. Heider, M. Fechner, R. V. Chopdekar, C. Piamonteze, J. [43] R. Grössinger, R. S. Turtelli, and N. Mehmood, Materi- 745 686 Dreiser, C. A. Jenkins, E. Arenholz, S. Rusponi, H. Brune, als with high magnetostriction, IOP Conf. Ser.: Mater. Sci. 746 687 N. A. Spaldin, and F. Nolting, Magnetoelectroelastic con- Eng. 60, 012002 (2014). 747 688 trol of magnetism in an artificial multiferroic, Phys. Rev B [44] Y. Wei, G. Yang, H. Yang, and S. Xi, Selective control of 748 689 94, 014401 (2016). magnetism in FeAl/PIN-PMN-PT using an electric field, 749 690 [31] J. J. Yang, Y. G. Zhao, H. F. Tian, L. B. Luo, H. Y. Appl. Phys. Lett. 114, 082404 (2019). 750 691 Zhang, Y. J. He, and H. S. Luo, Electric field manipu- [45] J. H. Westbrook and R. L. Fleischer, Intermetallic Com- 751 692 lation of magnetization at room temperature in multifer- pounds, Structural applications of intermetallic com- 752 693 roic CoFe2 O4 /Pb(Mg1/3 Nb2/3 )0.7 Ti0.3 O3 heterostructures, pounds, (John Wiley & Sons, New York, 2000), 2nd ed., 753 694 Appl. Phys. Lett. 94, 212504 (2009). Vol. 3. 754 XXXXXX-10 DISENTANGLING HIGHLY ASYMMETRIC. . . PHYS. REV. APPLIED 0, XXXXXX (2019) Q1 755 [46] P. Weaver and M. G. Cain, Chapter: Temperature depen- [52] M. Zhernenkov, M. R. Fitzsimmons, J. Chlistunoff, J. 778 756 dence of ferroelectric and piezoelectric properties of PZT Majewski, I. Tudosa, and E. E. Fullerton, Electric-field 779 757 ceramics, in Characterisation of ferroelectric bulk materi- modification of magnetism in a thin CoPd film, Phys. Rev. 780 758 als and thin films, edited by M. G. Cain (Springer, 2014). B 82, 024420 (2010). 781 759 Series in Measurement Science and Technology, Vol. 2. [53] T. Zhao, A. Scholl, F. Zavaliche, K. Lee, M. Barry, A. 782 760 [47] H. Ouchi, K. Nagano, and S. Hayakawa, Materials with Doran, M. P. Cruz, Y. H. Chu, C. Ederer, N. A. Spaldin, R. 783 761 high Magnetostriction, J. Am. Ceram. Soc. 48, 630 (1965). R. Das, D. M. Kim, S. H. Baek, C. B. Eom, and R. Ramesh, 784 762 [48] H. Ouchi, Piezoelectric properties and phase relations of Electrical control of antiferromagnetic domains in multifer- 785 763 Pb(Mg1/3 Nb2/3 )O3 -PbTiO3 -PbZrO3 ceramics with Barium roic BiFeO3 films at room temperature, Nat. Mater. 5, 823 786 764 or Strontium substitutions, J. Am. Ceram. Soc. 51, 169 (2006). 787 765 (1968). [54] Y. Wang, C. Nelson, A. Melville, B. Winchester, S. 788 766 [49] A. Biancoli, C. M. Fancher, J. L. Jones, and D. Damjanovic, Shang, Z.-K. Liu, D. G. Schlom, X. Pan, and L.- 789 767 Breaking of macroscopic centric symmetry in paraelec- Q. Chen, BiFeO3 domain wall energies and struc- 790 768 tric phases of ferroelectric materials and implications for tures: a combined experimental and density func- 791 769 Flexoelectricity, Nat. Mater. 14, 224 (2015). tional theory + U study, Phys. Rev. B 110, 267601 792 770 [50] M. Foerster, I. Fina, S. Finizio, B. Casals, A. Mandziak, (2013). 793 771 F. Fauth, and L. Aballe, Disclosing odd symmetry, strain [55] P. Marton, I. Rychetsky, and J. Hlinka, Domain walls of fer- 794 772 driven magnetic response of Co on Pt/PMN-PT (0 1 1), J. roelectric BaTiO3 within the Ginzburg-Landau-Devonshire 795 773 Phys.: Condens. Matter. 31, 084003 (2019). phenomenological model, Phys. Rev. B 81, 144125 796 774 [51] See Supplemental Material at http://link.aps.org/supple (2010). 797 775 mental/10.1103/PhysRevApplied.0.XXXXXX for further [56] Z. Gareeva, O. Diéguez, J. Íñiguez, and A. K. Zvezdin, 798 776 structural, compositional, magnetic and magnetoelectric Complex domain walls in BiFeO3 , Phys. Rev. B 91, 799 777 characterization. 060404(R) (2015). 800 XXXXXX-11