Strain-Mediated Giant Magnetoelectric Coupling in a Crystalline Multiferroic Heterostructure

Multiferroic heterostructures based on the strain-mediated mechanism present ultralow heat dissipation and large magnetoelectric coupling coefficient, two conditions that require endless improvement for the design of fast nonvolatile random access memories with reduced power consumption. This work shows that a structure consisting of a [Pb(Mg1/3Nb2/3)O3]0.7-[PbTiO3]0.3 (001) substrate on which a crystalline FeGa(001)/MgO(001) bilayer is deposited exhibits a giant magnetoelectric coupling coefficient of order 15 × 10–6 s m–1 at room temperature. That result is a 2-fold increment over the previous highest value. The spatial orientation of the magnetization vector in the epitaxial FeGa film is switched 90° with the application of electric field. The symmetry of the magnetic anisotropy is studied by the angular dependence of the remanent magnetization, demonstrating that poling the sample generates a switchable uniaxial magnetoelastic anisotropy in the film that overcomes the native low 4-fold magnetocrystalline anisotropy energy. Magnetic force microscopy shows that the switch of the easy axis activates the displacement of domain walls and the domain structures remain stable after that point. This result highlights the interest in single-crystalline structures including materials with large magnetoelastic coupling and small magnetocrystalline anisotropy for low-energy-consuming spintronic applications.

a FEI Helios NanoLab 600 DualBeam focused ion beam instrument using Ga ions.
The MFM and TEM images were managed with Gwyddion 1 a free data visualization and analysis software.
Reflection high energy electron diffraction (RHEED) is used to monitor the growth process in situ. Figure S1a-f shows images taken on the PMN-PT(001) crystal, the MgO buffer layer, and the FeGa film. Prior to the growth of the film, the PMN-PT(001) crystal was kept at 800 o C to obtain a clean surface. The patterns displayed in Figure S1a plane with a 4-fold symmetry. Also, the ratio d1/d2 (with d1 and d2 the distances between RHEED streaks defined in Figure S1c,d) is about 1.4, the predicted value for a square lattice.
Obtaining the FeGa alloy is achieved by deposition of Fe and Ga atoms by co-evaporation using an e-beam gun and a high temperature cell at 1120 o C, respectively, with a growth rate around 0.7 nm/min and the substrate at 150 o C. 2 The RHEED images taken on the film ( Figure S1e,f)   S-5 The sample was characterized ex situ by aberration-corrected scanning transmission electron microscopy in combination with electron energy-loss spectroscopy (STEM-EELS) and atomic force microscopy (AFM). Figure S2a shows a representative high-angle annular darkfield (HAADF) image of the structure along the [100] zone axis of the PMN-PT substrate. The intensity of the signal scales with the atomic number of the element and the substrate presents the brighter dots due to Pb columns. Above, the MgO layer appears as black stripe due to the presence of light atoms, the next layer corresponds to the FeGa block, with the Mo capping layer at the top position. Figure

VSM and MOKE loops
From the VSM measurements, see Figure 1a in branches of the cycle. 8 The resulting symmetrized loops are shown in Figure S4. This film shows nonvolatile effects, and S K (E) is doubled-valued for the four regions studied. The overall jump of the magnetization in the polycrystalline film (around 10%) is much smaller than that observed in the crystalline film (larger than 60%, see Figure S4). Obtaining the Kerr rotation loops vs φ introduces uncertainty due to the location of the laser spot during the rotation of the sample. The spot laser is not aligned with the rotation axis and a continuous readjustment of the beam is required to avoid wandering over the nonhomogenous FE substrate. We have opted to modify the angular position of the magnetic field by the use of a quadrupole magnet, 9 because the rotation of the magnet is not possible as indicated in the ROTMOKE method. 10 The sketch of this configuration is shown in Figure   S6a.
The magnetic field µ 0 H x is contained in the plane of incidence of the light and µ 0 H y is along the transverse direction. Thus, θ K and the transverse Kerr effect T K signal are obtained by using a laser light with the p polarization. The magnetization component parallel to H is calculated as m x cos φ + m y sin φ, as can be deduced for the sketch in Figure S6a. To compare the θ K and T K signals, it is assumed that at the maximum applied field, θ K and T K correspond to the saturation values of the magnetization. The resulting coefficients are used S-11 as calibration factor for all the cycles carried out as a function of H x /H y with the maximum applied field given by µ 0 √ H 2 x + H 2 y = 100 mT. Figure S6b shows normalized Kerr signals for µ 0 H x = 100 mT, µ 0 H y = 0 mT, and µ 0 H x = 0 mT, µ 0 H y = 100 mT, for the 0-and 0+ states of the FE structure. These measurements were used to obtain the calibration values.
The influence of quadratic Kerr effects on the remanence value is eliminated by the average of the values at zero field for increasing and decreasing field sweeps. 8 Figure 4a in the main text shows the resulting S K (φ) curves with a clear uniaxial shape and the switching between easy and hard directions for the 0-and 0+ states.
S-12 Step 1: application of H = -3 mT, in such a way that H is antiparallel to M.

S-13
Step 2: application of an electric pulse to switch the EA (blue MH loop) into HA (yellow MH loop) in Fig. S7. In this example with negative bias.
Step 3: application of an electric pulse to switch back the HA and EA. In this case with positive bias. Due to the presence of H, M and H become parallel to each other at this step.
Step 4: H is dropped out.
Step 5: M is at the remanence value.
We consider that the magnetization is confined in the plane so α z = 0, α x = cos ϕ, α y = sin ϕ. Thus the terms that maintain a dependence with ϕ correspond to those present in Equation S1. S-15