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.


The interfacial layer between transferred LSMO and platinized PMN-PT
Cross-sectional scanning transmission electron microscopy (STEM) revealed the presence of a 10 nm-thick amorphous layer between the LSMO film and top electrode of the platinized PMN-PT substrate (Supplementary Figure 2a). This amorphous layer, which mediates the strain-mediated magnetoelectric effects that we observed, was found to be flat and uniform over several microns in our STEM lamella. The maximum thickness variation was 2 nm, and we may infer that contaminants did not self-assemble into large pockets 1 .
Elemental analysis revealed that the amorphous layer contained Si, O and accumulation of C at both interfaces (Supplementary Figure 2b). We attribute these residuals to the partial degradation of the PDMS membrane during the SrRuO3 etch (no residuals of Sr or Ru are apparent). Carbon may also be present near the Pt electrode due to adsorbed hydrocarbons, which typically become trapped between substrates and transferred two-dimensional crystals 2,3 .
Electron energy loss spectroscopy (EELS) images obtained at the Mn L3/L2 edges (not shown) did not identify a change of Mn oxidation state in the LSMO film near its interface with the amorphous layer. This implies a weak van der Waals-like bonding rather than chemical reaction, as suggested for LSMO transferred to Si substrates 4 . show EELS data for this area, namely images obtained at the as-specified carbon, oxygen and silicon edges (presented separately and together); and the K-edge intensity distribution for C and O (normalised counts do not indicate relative composition). Scale bars in (b) are 2 nm. All data for sample C.   The Curie temperature of LSMO was enhanced by the release of epitaxial growth strain, as determined after subsequent transfer to PMN-PT (Supplementary Figure 6). Figure 6. Curie temperature enhancement in LSMO following strain release. Temperature-dependent remanent magnetization for LSMO in LSMO/SRO//STO after growth (red) and in LSMO:PMN-PT after transfer (blue). Data were obtained on warming in zero magnetic field in a SQUID magnetometer, after having applied a saturating in-plane field of 400 Oe along an arbitrary direction at room temperature. The samples used here are similar to those described elsewhere in this paper, permitting qualitative comparison only.  • There was essentially a single broad peak after thermal depolarization.

Supplementary
• On applying and removing -10 kV cm -1 , there was a single 222pc reflection and a split 031pc reflection, implying the formation of O1,2 domains.
• On approaching the peak strain at 2.67 kV cm -1 , the single 222pc reflection observed after poling was replaced by a split peak, and the split 031pc reflection observed after poling was replaced by a single peak, implying the formation of R1,2 domains. The concomitant formation of minority R3,4 domains with in-plane polarizations 5 is evidenced by the creation and subsequent destruction of an additional 031pc reflection with low intensity.
• At higher fields, the switching current approached zero, the strain approached saturation, the O1,2 domains were re-established and the R phase was eliminated.
The two strain states that we achieved at electrical remanence 6 ( Fig. 2b in main paper) are therefore identified with the O and R phases in our major loop here as follows: • The A state obtained after removing a saturating field is identified with the O phase observed here after poling.
• The B state obtained after reaching the coercive field on a major loop and then removing the applied field is identified with the R phase observed here near the coercive field.
Note that states A and B were obtained after positive poling (    Supplementary Note 9

Creation of the A and B remanent states in LSMO:PMN-PT
The four-fold anisotropy in LSMO after transfer (Fig. 1e of the main paper, reproduced in Supplementary Figure 9a) was modified by 30 bipolar cycles that each comprised major or minor loops of the type used to measure macroscopic magnetoelectric effects (Fig. 3 of the main paper). The inclusion of minor loops permitted access to remanent states A and B, whose evolution is shown in Supplementary Figure 9b

Reproducibility of macroscopic magnetoelectric measurements
Major loops of Mx(E) for sample A (Fig. 3 in the main paper) and two similar samples are similar (Supplementary Figure 10).
Supplementary Figure 10 also shows that magnetoelectric effects are completely suppressed by a saturating magnetic field. This confirms our expectation 7 that there are no strain-driven changes in the magnitude of the local magnetic moment, consistent with the magnetic rotations that we observed (Fig. 5 in the main paper).

Supplementary Figure 10. Macroscopic magnetoelectric effects in LSMO:PMN-PT.
In-plane magnetization component Mx normalized by saturation magnetization Ms versus electric field E. The lower three plots were measured for Samples A-C in zero magnetic field H, after applying and removing H = 1 kOe along x. The uppermost plot was measured for Sample A with H = 1 kOe along x.

Influence of cracks on the magnetic domain structure
In three regions of the LSMO:PMN-PT sample, cracks (left panels in Supplementary   Figure 11) were found to coincide with a subset of magnetic domain perimeters (right panels in Supplementary Figure 11), suggesting that cracks are at least partially responsible for the coercivity enhancement in the transferred film.

Supplementary Figure 11. Correlation between cracks and magnetic domains in LSMO:PMN-PT. Photoemission electron microscopy (PEEM) images for three different areas of the sample, with contrast from (left) x-ray absorption spectroscopy (XAS) and (right)
x-ray magnetic circular dichroism (XMCD). Red arrow denotes the in-plane projection of the grazing-incidence x-ray beam. Data for Sample A.

Simulation of magnetoelectric effects
First, we will present a free energy density that describes the magnetoelectric effects in our transferred LSMO film, where the observed inhomogeneity is attributed to an invariant uniaxial stress anisotropy arising from the transfer. Then we will use this free energy density to simulate macroscopic and microscopic magnetoelectric effects, for comparison with our experimental observations.

Free energy density
The inhomogeneity that we observed in our XMCD-PEEM vector maps (Fig. 5 in the main paper) evidences different types of region in our transferred LSMO film. We will arbitrarily consider there to be nine types of region, and we will neglect exchange coupling between adjacent regions. The free energy density F for the LSMO film may then be written as: where Fi denotes the total free energy density for all distributed regions of the i th type, where the local magnetization in regions of the i th type adopts direction i, where the magnitude of the local magnetization is equal to the saturation magnetization Ms = 425 emu cm -3 of the transferred LSMO film (blue data, Fig. 1d in the main paper), and where E denotes the electric field applied across the PMN-PT substrate. The function Fi(i,E) is given by: where each term on the right is described below. Positive angles (i, α, β and φ i ) imply anticlockwise rotations with respect to the x direction in PMN-PT as viewed from the LSMO film.

Magnetocrystalline anisotropy
The term -K c sin 2 ( i -α) cos 2 ( i -α) is common to all nine types of region in the LSMO film, and describes the four-fold magnetocrystalline anisotropy (ref. 45 in the main paper), for which α = 40 is one of the hard directions (Fig. 1e in the main paper). The anisotropy constant Kc = HaMs/2= 3.5 kJ m -3 was estimated from the values of anisotropy field Ha = 165 Oe and saturation magnetization Ms = 425 emu cm -3 that we measured for the transferred LSMO film (blue data, Fig. 1d in the main paper). Supplementary Figure 12a shows a polar plot of the magnetocrystalline anisotropy density for the LSMO film.

Piezostress anisotropy
The term -K s (ε eff (E)) cos 2 ( i -β) is common to all nine types of region in the LSMO film, and describes the uniaxial stress anisotropy due to piezoelectric strain from the substrate. For this term, β = 0 is the hard direction for the negative value of anisotropy constant K s (ε eff (E)) in state A, and β = 90 is the hard direction for the positive value of anisotropy constant K s (ε eff (E)) in state B. The anisotropy constant K s (ε eff (E))= 3 2 λE Y ε eff (E) changes sign due to electrically driven changes in the effective strain 8 by the LSMO film, where: • x(E) and y(E) are the electric-field dependent strains transmitted by the PMN-PT substrate (Fig. 2a in the main paper); • strain-transfer coefficient = 40% was found to be reasonable by comparing our results for Mx(E) and My(E) (Supplementary Figure 13) with our macroscopic measurements ( Fig. 3 in the main paper); • the LSMO Poisson's ratio ν = 0.33 was calculated from the strain in our epitaxial LSMO film prior to transfer (the XRD data in Fig. 1c in the main paper implies an out-of-plane pseudocubic lattice parameter of 3.841 Å, the SrTiO3 substrate implies an in-plane pseudocubic lattice parameter of 3.905 Å, and the bulk lattice parameter of LSMO was taken to be 9 3.873 Å); • we assume ε z = 0; • LSMO magnetostriction 10 λ = 3  10 -5 ; • LSMO Young's modulus 11 EY = 100 GPa.
Supplementary Figure 12b shows a polar plot of the electrically controlled stress anisotropy density for the LSMO film.

Constant stress anisotropy
The term -K u cos 2 ( i -φ i ) describes a uniaxial stress anisotropy, which we assume to arise in the i th type of region due to stress arising from the transfer of the LSMO film (we set Ku = Kc).
The nine types of region are characterized by nine equally separated directions φ i = πi 9 . Each of these directions describes an easy axis for -K u cos 2 ( i -φ i ) , and collectively the nine directions average to zero (consistent with our macroscopic measurements of strain and magnetic anisotropy). Supplementary Figure 12c shows polar plots of the constant stress anisotropy for each type of region. The free energy density F i ( i ,E) for each type of region is shown in Supplementary Figure 12d for state A, and in Supplementary Figure 12e for state B.
The free energy density F(E) for the LSMO film displays a two-fold anisotropy (Fig. 12f), with the easy axis along y (state A) or x (state B), as observed experimentally (Fig. 4 in the main paper).

Simulation of macroscopic magnetoelectric effects
The free energy density F(E) for the LSMO film was used to simulate plots of Mx(E) and My(E) at magnetic remanence, for comparison with our macroscopic magnetoelectric measurements ( Fig. 3 in the main paper).
To account for the initial application and removal of the saturating magnetic field along the measurement axis, we added the magnetostatic energy density -MsHcos(i -) to the free energy density Fi(i,E) for each type of region. Here, H = 1000 Oe denotes the magnitude of the saturating field that we used in our experiments, γ denotes the measurement direction

Simulation of microscopic magnetoelectric effects
The free energy density F(E) for the LSMO film was used to simulate electrically driven magnetic domain rotations in zero-magnetic field, for comparison with our corresponding microscopic observations based on XMCD-PEEM vector maps (Fig. 5a-f in the main paper).
To identify the demagnetized starting state at E = 0, we set the initial directions of magnetization in each type of region at random, with the constraint that all nine directions be equally spaced in angle. We then minimised Fi(i,E) for each type of region, in order to obtain nine values of i that no longer averaged exactly to zero.
After thus obtaining the nine values of i that describe the demagnetized starting state at E = 0, we used the following three steps to identify the electrically driven angular changes i between states A and B (Supplementary Table 2, Supplementary Figure 14). First, we used our experimentally obtained plots of x(E) and y(E) (Fig. 2a in the main paper) to obtain εeff(E).
Second, at every tenth experimental value of E, we used εeff(E) to minimize Fi(i,E) for each type of region and thus obtain nine magnetization directions i. Third, we identified the nine values of i for states A and B in the electrical cycle.
The resulting values of i reproduce key features of our experimental observations because they are widely distributed in magnitude (from a few degrees up to 62), and because some rotation angles calculated here (Regions of type 7, 9 and 3, Supplementary Table 2) are similar to those observed experimentally (Regions 1-3, Fig. 5f in the main paper).