Large magnetoelectric coupling in multiferroic oxide heterostructures assembled via epitaxial lift-off

Epitaxial films may be released from growth substrates and transferred to structurally and chemically incompatible substrates, but epitaxial films of transition metal perovskite oxides have not been transferred to electroactive substrates for voltage control of their myriad functional properties. Here we demonstrate good strain transmission at the incoherent interface between a strain-released film of epitaxially grown ferromagnetic La0.7Sr0.3MnO3 and an electroactive substrate of ferroelectric 0.68Pb(Mg1/3Nb2/3)O3-0.32PbTiO3 in a different crystallographic orientation. Our strain-mediated magnetoelectric coupling compares well with respect to epitaxial heterostructures, where the epitaxy responsible for strong coupling can degrade film magnetization via strain and dislocations. Moreover, the electrical switching of magnetic anisotropy is repeatable and non-volatile. High-resolution magnetic vector maps reveal that micromagnetic behaviour is governed by electrically controlled strain and cracks in the film. Our demonstration should inspire others to control the physical/chemical properties in strain-released epitaxial oxide films by using electroactive substrates to impart strain via non-epitaxial interfaces. Key properties of transition metal perovskite oxides are degraded after epitaxial growth on ferroelectric substrates due to lattice-mismatch strain. Here, the authors use epitaxial lift-off and transfer to overcome this problem and demonstrate electric field control of a bulk-like magnetization.

T ransition metal perovskite oxides display a wide range of functional properties that are mediated by strongly correlated electrons, and thus sensitive to lattice deformations 1,2 . One may therefore strain-tune epitaxial films of these materials according to the choice of single-crystal oxide substrate, e.g. in order to induce structural phase transitions 3 , modify charge conduction mechanisms 4,5 , enhance ferroic order 6,7 and control chemical reactivity 8,9 . Alternatively, an epitaxial film of any such material can be electrically strained both continuously and discontinuously by a ferroelectric substrate 10 . The continuous response is the well known (converse) piezoelectric effect. The discontinuous response arises due to ferroelectric domain switching, which can sometimes be accompanied by a phase transition [11][12][13] . Here we will use the term electroactive to collectively describe the continuous and discontinuous responses, thus deviating from the common practice of describing electrically driven strain from ferroelectric substrates purely as piezoelectric. Although electrically driven strain has been widely employed in multiferroic heterostructures for data-storage applications [14][15][16] based on the electrical control of magnetism [17][18][19] , it could be used more generally to control the various physical and chemical properties and phenomena that arise in transition metal perovskite oxides, as demonstrated for electrical resistivity 20 , metal-insulator transitions 21 and photoconductivity 22 .
Unfortunately, the key properties of transition metal perovskite oxides are degraded following epitaxial growth on ferroelectric substrates, as seen for ferromagnetic films with reduced Curie temperatures and suppressed magnetizations 17,18,23 . This degradation is a consequence of the >3% lattice-parameter mismatch that causes films to experience both strain and dislocations 17,18,[24][25][26] , even if epitaxial buffer layers are present 27 . Moreover, the orientation and magnitude of the voltage-driven in-plane strain 11 is necessarily constrained by the crystallographic orientation required for the epitaxy. Here we solve the mismatch problem, break the orientational constraint and achieve good strain-mediated magnetoelectric coupling by employing epitaxial lift-off 28,29 in order to achieve a form of van der Waals integration 30 via an interfacial glue that formed serendipitously.
Epitaxial lift-off permits an epitaxial film to be transferred to an arbitrary surface after being separated from its growth substrate by chemically etching a sacrificial interlayer. Epitaxial liftoff has been hitherto employed to transfer films of III-V semiconductors 28,29,31,32 and transition metal perovskite oxides [33][34][35][36][37][38][39][40] to passive substrates. Transition metal perovskite oxide films have not been hitherto transferred to electroactive substrates, but one may anticipate viable strain coupling in light of the fact that film properties can be mechanically manipulated via mechanically formed interfaces, as seen for manganite films transferred to flexible substrates 41,42 , and two-dimensional structures transferred to electroactive substrates 43 .
Our implementation of epitaxial lift-off results in an epitaxially grown film of ferromagnetic La 0.7 Sr 0.3 MnO 3 (LSMO) transferred to an electroactive single-crystal substrate of 0.68Pb(Mg 1/3 Nb 2/3 )O 3 -0.32PbTiO 3 (PMN-PT). The LSMO film is grown on (001)-oriented SrTiO 3 (STO) via a sacrificial layer of SrRuO 3 (SRO), which is subsequently dissolved before transferring the LSMO film to the PMN-PT substrate. We choose STO as the growth substrate because of its small (~1%) lattice mismatch with both LSMO and SRO, and we choose SRO as the sacrificial layer because it can be selectively etched without damaging the LSMO film or STO substrate 44 . We choose the (001) pc orientation of LSMO in order to minimize the magnetocrystalline anisotropy barrier for in-plane rotations of magnetization 45 , and we choose the (011) pc orientation of PMN-PT in order to achieve two strain states at electrical remanence 46 (pc denotes pseudocubic).
Ferroelectric domain switching in our PMN-PT substrate is accompanied by a rhombohedral-orthorhombic phase transition, and the large resulting strain is effectively transmitted to the transferred LSMO film, whose magnetization is enhanced after epitaxial lift-off to a value that greatly exceeds the value for LSMO grown directly on PMN-PT 23 . Despite a layer of adsorbates at the interface, the magnetoelectric coupling coefficient is similar to values recorded for epitaxial heterostructures 17,18 , and a twofold magnetic anisotropy in the film can be electrically switched by 90°in a repeatable and non-volatile manner. Photoemission electron microscopy (PEEM) with contrast from X-ray magnetic circular dichroism (XMCD) is used to obtain magnetic vector maps that reveal unanticipated complexity, namely few-micron-sized magnetic domains whose boundaries are defined by cracks in the film, and electrically driven magnetic domain rotations through various angles. This complexity represents both a challenge and an opportunity in the development of laminated magnetoelectric memory devices.

Results
Sample fabrication and characterization. An elastomer membrane of polydimethylsiloxane (PDMS) was used to transfer a 45 nm-thick layer of LSMO from its STO (001) growth substrate to platinized PMN-PT (011) pc , after dissolving the intervening epitaxial layer of 30-nm-thick SRO with NaIO 4 (aq) (ref. 44 ) (Fig. 1a). The a || [100] pc and b || [010] pc axes of LSMO that lay parallel to the film edges were approximately aligned with the x || [100] pc and y || 01 1 ½ pc axes of PMN-PT that lay parallel to the edges of the slightly larger substrate (Supplementary Note 1). For simplicity, samples will be labelled LSMO:PMN-PT, without reference to the Pt electrodes that are considered as if they were an integral part of the PMN-PT substrate, and without reference to an amorphous interfacial layer that we observed in cross-sectional scanning transmission electron microscopy (STEM) (Fig. 1b). Chemical analysis revealed this interfacial layer of adsorbates to be primarily composed of SiO x and C (Supplementary Note 2), implying partial degradation of the PDMS membrane during the SRO etch. Two other polymers, which might have provided better mechanical support 47 , retained only small LSMO flakes after etching.
X-ray diffraction (XRD) measurements of our LSMO/SRO// STO (001) precursor confirmed that the LSMO layer experienced tensile in-plane epitaxial strain of~1% (red data, Fig. 1c) and a compressive out-of-plane strain of similar magnitude (Supplementary Note 3). The high quality of the LSMO film was confirmed by the presence of thickness fringes, and a narrow 002 pc rocking curve of full-width half-maximum 0.2°(red data, inset of Fig. 1c). Moreover, XRD reciprocal space maps around the STO 103 reflection confirmed a good match between the inplane lattice parameters of the LSMO, SRO and STO (Supplementary Note 3). XRD measurements of the LSMO film after it had been transferred to the platinized PMN-PT (011) pc substrate revealed that the epitaxial strain had been completely released (blue data, Fig. 1c), and that the full-width-half-maximum of the 002 pc rocking curve had increased to 1.7°(blue data, inset of Fig. 1c). This enhancement of texture is attributed to the faceted PMN-PT (011) pc surface that necessarily results from ferroelectric domains of low symmetry (Supplementary Note 4), and cracking in the LSMO film that arose at least in part while it was supported by the flexible PDMS membrane (Supplementary Note 5).
The release of epitaxial strain increased the LSMO saturation magnetization of 2.27 ± 0.03 μ B /Mn by 19% to 2.7 ± 0.1 μ B /Mn (Fig. 1d), which is roughly six times larger than the roomtemperature saturation magnetization of highly strained LSMO grown directly on PMN-PT (ref. 23 ). Similarly, the release of epitaxial strain led to an increase of Curie temperature (Supplementary Note 6), as expected 48 . The enhanced magnetism is a consequence of enhanced double exchange following the release of epitaxial strain 49 , and should not be attributed to the oxidizing effect of the NaIO 4 (aq) reagent on optimally doped films that are well annealed. The release of epitaxial strain also modified the biaxial magnetic anisotropy of the LSMO film (Fig. 1e). After growth, the in-plane LSMO <110> pc directions were magnetically easy due to magnetoelastic anisotropy arising from the biaxial in-plane strain imposed by the STO substrate 45,50,51 . After strain release and film transfer, the in-plane LSMO <100> pc directions were magnetically easy due to uniaxial magnetocrystalline anisotropy in each twin variant of the now twinned film 52 (Supplementary Note 7). Given that the transfer process reduces the magnitude of the easy-axis anisotropy (Fig. 1e), the increase of easy-axis coercivity ( Fig. 1d) is inferred to arise because of the observed cracks (Supplementary Note 5) and any accompanying microstructural defects.
Electrically driven strain in platinized PMN-PT. After thermally depolarizing PMN-PT in order to set zero strain, a bipolar cycle of electric field E produced orthogonal in-plane strains ε x and ε y that took opposite signs to each other at almost every field, and underwent sign reversal near the coercive field (solid butterfly curves, Fig. 2a). Given that the two butterfly curves would be interchanged and different in magnitude if they arose purely from ferroelectric domain switching in rhombohedral PMN-PT of nominally the same composition 46 , we infer that polarization reversal was instead associated with a phase transition [11][12][13] , as confirmed by measuring XRD reciprocal space maps while applying an electric field (Supplementary Note 8). Large fields promoted the orthorhombic (O) phase by aligning the polarization along an outof-plane <011> pc direction, whereas switching through the coercive field promoted rhombohedral (R) twins whose polarizations lay along the subset of <111> pc directions with an out-of-plane component. (A similar argument would hold if this latter phase were monoclinic 53 rather than rhombohedral.) A minor electrical loop (blue dots in Fig. 2a) permitted two strain states to be created in PMN-PT at electrical remanence 12,46 , with ε x = −0.16% in state A and ε x = + 0.02% Strain-mediated electrical control of macroscopic magnetization in LSMO:PMN-PT. The biaxial magnetic anisotropy that we observed after transfer (Fig. 1e) was rendered uniaxial at both A and B during the course of 30 bipolar electrical cycles (Supplementary Note 9). Subsequent bipolar cycles modified the x and y components of magnetization by~100% and~40% (solid butterfly curves, Fig. 3), respectively, and similar results were observed for two similar samples (Supplementary Note 10). The peak magnetoelectric coefficient α = µ 0 dM x /dE = 6.4 × 10 −8 s m −1 is similar to the value reported 18 for an LSMO film that benefited from good epitaxial coupling with a PMN-PT (001) substrate. The interconversion of remanent states A and B (blue dots in Fig. 3) rotated the single magnetic easy axis by 90° (Fig. 4), while the finite loop-squareness minimum in state B (Fig. 4d) may represent a vestige of the original fourfold anisotropy, or uniaxial regions trapped from state A.
Strain-mediated electrical control of microscopic magnetization in LSMO:PMN-PT. The local magnetization of the thermally demagnetized film was imaged using PEEM with contrast   from XMCD. The resulting vector maps of the in-plane magnetization direction ϕ revealed that the electrically remanent A and B states were magnetically inhomogeneous within a 20 μm field of view (Fig. 5a, b); and that switching from A to B rotated the net magnetization in our limited field of view towards the x-axis (Fig. 5c, d), consistent with our macroscopic measurements of magnetic anisotropy (Fig. 4c, d). The magnetization was reasonably homogeneous within few-micron-sized domains whose boundaries coincided partly with cracks (Supplementary Note 11), and the electrically driven magnetic rotations in 1.3 μmdiameter regions (1-3 in Fig. 5a, b, e) ranged from large (64°in region 1) to medium (−36°in region 2) to small (16°in region 3) (Fig. 5f). Although the clockwise and anticlockwise nature of these rotations could be explained in terms of the ambipolar shear strains associated with rhombohedral ferroelectric domain switching 54 , the very different rotation magnitudes imply the presence of an additional factor. By assuming this additional factor to be a spatially varying uniaxial magnetic anisotropy, due to spatially varying stress associated with the formation of the observed cracks (Supplementary Note 5), a magnetic free energy model was able to approximately reproduce both the local and macroscopic magnetoelectric effects (Supplementary Note 12).

Discussion
Our macroscopic magnetic measurements yield two key results. First, growth using a well-matched substrate, followed by strain release via epitaxial lift-off 28,29 , resulted in an LSMO film magnetization that is greatly enhanced with respect to the value for an LSMO film that contained strain and dislocations following direct growth on PMN-PT 23 . Second, our strain-mediated magnetoelectric coupling is just as effective as strain-mediated coupling across an epitaxial interface 17,18 in spite of the incoherent bonding between our magnetostrictive film and electroactive substrate. Our structurally contiguous micron-sized regions were separated by cracks that could be avoided if one were to transfer micron-size patterned structures, or modify the procedure and transfer millimetre-sized crack-free films 36 . However, the presence of cracks was instructive because the resulting micromechanical boundary conditions likely served to influence the magnetic rotations of our micron-size magnetic domains. Close control of these boundary conditions via lithographic patterning would permit a transferred ferromagnetic film to function as the electrically controlled free layer of a magnetic tunnel junction for data-storage applications [14][15][16] , and the free choice of in-plane misorientation angle would permit the realization of schemes for electrically driven magnetization reversal [55][56][57] . As we have shown, the magnetization would not suffer from the epitaxial suppression that compromises oxide device performance 58 . More generally, the physical and chemical properties of any epitaxially grown film could be electrically controlled via strain after transfer to an electroactive substrate, with no constraints on relative crystallographic orientation, and no epitaxial strain to suppress film functional properties. Separately, it would be interesting to investigate strain-mediated coupling while varying the thickness and composition of the interfacial glue that formed here serendipitously. It would also be interesting to better support the LSMO film during transfer in order to avoid the observed cracks. Ultimately, electroactive substrates themselves could be replaced by electroactive films that have been released in order to avoid substrate clamping 59 . Our work therefore opens the way for multifunctional heterostructures to be assembled from epitaxial oxides via mechanical separation and stacking, just as two-dimensional and other materials may be combined using similar methods of van der Waals integration 30 . These multifunctional heterostructures could then be transferred to silicon host structures in the wider-ranging quest for CMOS compatibility.  , e] at electrically remanent states A (purple lobes) and B (orange lobes), with pixel colours and angular changes marked on the periphery. Straight green and red arrows denote the in-plane projections of the grazing-incidence X-ray beam that were used to obtain the vector maps in a, b. All data were obtained for sample A following macroscopic magnetoelectric measurements and subsequent thermal demagnetization. All data were obtained at room temperature. Source data are provided as a Source Data file.
NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-020-16942-x ARTICLE NATURE COMMUNICATIONS | (2020) 11:3190 | https://doi.org/10.1038/s41467-020-16942-x | www.nature.com/naturecommunications PT substrate (edges along x || [100] pc and y || 01 1 ½ pc ) by 5°(samples A, B) and 20°(sample C). All experimental data were obtained using sample A or its precursor components, with the following exceptions: measurements of strain and electrical polarization were obtained using PMN-PT from the same master substrate that we used for sample A; atomic force microscopy (AFM) data were obtained using sample B; STEM data were obtained using sample C; the Curie temperature measurements in Supplementary Fig. 6 were obtained using similar samples; and the macroscopic magnetoelectric data in Supplementary Fig. 10 were obtained using samples A-C.
Epitaxial growth of LSMO/SRO bilayers. Epitaxial LSMO (45 nm)/SRO (30 nm) bilayers were grown by pulsed laser deposition (KrF excimer laser, 248 nm, 1 Hz) on STO (001) substrates (5 mm × 5 mm × 1 mm) that had been annealed in flowing oxygen for 90 min at 950°C. The SRO was grown in 10 Pa O 2 at 600°C (1200 pulses, 1.5 J cm −2 ). The LSMO was grown in 15 Pa O 2 at 760°C (1800 pulses, 2 J cm −2 ). After growth, the LSMO/SRO//STO stacks underwent in situ annealing in 50 kPa O 2 for 1 h at 700°C. Using X-ray reflectivity measurements, the growth rates for single layers of SRO and LSMO were both found to be~0.025 nm per pulse. Transfer of LSMO. PDMS stamps were cut to 5 mm × 5 mm × 1.5 mm from a commercial specimen (Gelfilm from Gelpak), and each was brought into conformal contact with a given LSMO/SRO//STO stack by heating in air at 70°C for 10 min (conformal contact was verified by the change in optical reflectance on elimination of the air gap). After floating the resulting PDMS/LSMO/SRO//STO stacks in NaIO 4 (aq) (0.4 M) for several hours, the SRO layers dissolved to release bilayers of PDMS/LSMO, which were washed with deionized water, and dried with N 2 gas. Using tweezers, each PDMS/LSMO bilayer was subsequently transferred to a platinized PMN-PT substrate, which had been previously cleaned using acetone and isopropanol, and recently cleaned by annealing in air at 120°C for 10 min. After transfer, the entire stack was annealed in air (at 100°C for 10 min) to promote adhesion at the newly formed interface. After cooling to 70°C and peeling off the PDMS stamp with tweezers, interfacial adhesion was further improved by annealing in air at 150°C for 10 min.
X-ray diffraction. We acquired 2θ-ω scans and rocking curves for LSMO with a Panalytical Empyrean diffractometer (Cu-Kα 1 , 1.540598 Å), using a hybrid twobounce primary monochromator on the incident beam, and a two-bounce analyser crystal before the proportional point detector. Reciprocal space maps of PMN-PT were acquired with the same incident beam optics and a PIXcel 3D positionsensitive detector, using the frame-based 1D mode with a step time of 10 s.
We used Sample A and its epitaxial precursor to obtain 2θ-ω scans and rocking curves before applying an electric field (Fig. 1c). For the transferred LSMO film in Sample A, offset angle ω was obtained by averaging the rocking-curve-peak-values for azimuthal angles of φ = 0°and φ = 180°. Our electric-field-dependent XRD data were also obtained using sample A, after acquiring a subset of the magnetoelectric data and then repeating the last anneal of the fabrication process (10 min in air at 150°C) in order to depolarize the substrate. We first obtained reciprocal space maps of PMN-PT at successively larger positive fields after negative poling ( Supplementary Fig. 5d, e), before acquiring reciprocal space maps for remanent states A and B (Fig. 2b-d). We then obtained 2θ-ω scans of LSMO for remanent states A and B (Supplementary Fig. 6).
Atomic force microscopy. Atomic force microscopy (AFM) images were obtained in tapping mode using a Veeco Digital Instruments Dimension D3100 microscope.
Electron microscopy. Cross-sectional transmission electron microscopy (TEM) specimens were prepared via an in situ lift-out procedure in a dual-beam instrument (FEI Nova 600i) that incorporated a focused ion beam microscope and scanning electron microscope in the same chamber. Both 5 and 2 kV ions were used to polish the TEM lamella to a thickness of 50 nm, and remove side damage. High-resolution scanning transmission electron microscopy (STEM) was performed using a probe-side aberration-corrected FEI Titan G2, operated at 80-200 kV with a high-brightness field-emission gun (X-FEG). Bright-field STEM imaging was performed using a probe convergence angle of 21 mrad and a probe current of ∼90 pA. In bright-field images, identification of each atomic layer was achieved by elemental analysis using energy dispersive X-ray (EDX) and electron energy loss spectroscopy (EELS). EDX images were obtained using a Super-X four silicon drift EDX detector system with a total-collection solid angle of 0.7 sr. EELS images were obtained using a Gatan Imaging Filter (GIF) Quantum ER system, with an entrance aperture of 5 mm. The lamella was oriented by using the Kikuchi bands to direct the electron beam down the 01 1 ½ pc zone axis of PMN-PT.
Strain measurements. Platinized PMN-PT (derived from the master substrate used for sample A) was cleaned like sample A, using acetone and isopropanol, and then annealed in air at 150°C for 30 min in order to mimic the final depolarizing heat treatment experienced by sample A. A biaxial strain gauge (KFG-1-120-D16-16 L1M3S, Kyowa) was affixed using glue (CC-33A strain gauge cement, Kyowa) to the top electrode, with measurement axes along x and y. The initial values of resistance were used to identify zero strain along the two measurement directions. Strain-field data were obtained while applying bipolar triangular voltages at 0.01 Hz in the range ±10 kV cm −1 .
Macroscopic magnetization measurements. These were performed using a Princeton Measurements Corporation vibrating sample magnetometer, with electrical access to the sample as shown in ref. 17 . All data are presented after subtracting the diamagnetic contribution of substrate, and using optical microscopy to estimate film areas.
Magnetic vector maps. After completing all macroscopic magnetoelectric measurements, we obtained raw images of sample A after thermal demagnetization. The electrically remanent states A and B were interconverted in situ using a 300 V power supply that was connected via feedthroughs in the sample holder. Data were obtained on beamline I06 at Diamond Light Source, where we used an Elmitec SPELEEM-III microscope to map secondary-electron emission arising from circularly polarized X-rays that were incident on the sample surface at a grazing angle of 16°. The probe depth was ∼7 nm, and the lateral resolution in our 20 μm-diameter field of view was typically ∼50 nm (corresponding to pixels that represent~20 nm).
Raw images were acquired during 1 s exposure times with right (R) and left (L) circularly polarized light, both on the Mn L 3 resonance at 645.5 eV, and off this resonance at 642 eV. The pixels in a raw XMCD-PEEM image describe the XMCD asymmetry (I R − I L )/(I R + I L ), which represents the projection of the local surface magnetization on the incident-beam direction. Here, I R=L ¼ ðI R=L on À I R=L off Þ=I R=L off denotes the relative intensity for secondary-electron emission due to X-ray absorption on ðI R=L on Þ and off ðI R=L off Þ the Mn L 3 resonance (the comparison between intensities obtained on and off resonance avoids the influence of any inhomogeneous illumination).
We averaged 40 raw XMCD-PEEM images to obtain a single XMCD-PEEM image for each of two orthogonal sample orientations. These two images were combined in order to yield vector maps of in-plane magnetization, which are not necessarily perfectly circular after correcting for drift and distortion via an affine transformation that was based on topographical images of X-ray absorption for each sample orientation. Each of these topographical images was obtained by averaging all raw images that had been obtained on resonance with left-and rightpolarized light.
XAS images. X-ray absorption spectroscopy images are presented alongside XMCD-PEEM images (Supplementary Note 11) by plotting (I R + I L ) and (I R − I L )/(I R + I L ), respectively.

Data availability
The source data underlying Figs. 1c-e, 2a, 3, 4a-d and 5c-f are provided in a Source Data file. All other relevant data are available from all corresponding authors on request. Source data are provided with this paper.