Giant reversible anisotropy changes at room temperature in a (La,Sr)MnO3/Pb(Mg,Nb,Ti)O3 magneto-electric heterostructure

In a model artificial multiferroic system consisting of a (011)-oriented ferroelectric Pb(Mg,Nb,Ti)O3 substrate intimately coupled to an epitaxial ferromagnetic (La,Sr)MnO3 film, electric field pulse sequences of less than 6 kV/cm induce large, reversible, and bistable remanent strains. The magnetic anisotropy symmetry reversibly switches from a highly anisotropic two-fold state to a more isotropic one, with concomitant changes in resistivity. Anisotropy changes at the scale of a single ferromagnetic domain were measured using X-ray microscopy, with electric-field dependent magnetic domain reversal showing that the energy barrier for magnetization reversal is drastically lowered. Free energy calculations confirm this barrier lowering by up to 70% due to the anisotropic strain changes generated by the substrate. Thus, we demonstrate that an electric field pulse can be used to ‘set’ and ‘reset’ the magnetic anisotropy orientation and resistive state in the film, as well as to lower the magnetization reversal barrier, showing a promising route towards electric-field manipulation of multifunctional nanostructures at room temperature.


A. X-ray diffraction characterization and dynamical tuning of transition temperatures
The poled PMN-PT substrate in this work can be indexed at room temperature to a monoclinic unit cell with a small deviation from orthorhombic (β~89.86° for a similar composition). 1  For an applied electric field along the [011] direction, we can examine the possible out-of-plane and in-plane lattice dimensions as a function of poling state and calculate how much change in epitaxial mismatch can be generated by rotation of the ferroelectric (FE) axis from partially out of plane to wholly in the (011) plane.
X-ray diffraction characterization of the LSMO/PMN-PT sample using a lab diffractometer (Bruker D8 Discover) was performed to evaluate the change in film and substrate lattice parameters as a function of applied electric field. Lattice parameters for the LSMO film determined from reciprocal space maps, and electric-field induced changes in unit cell dimensions are presented in Table S1. Differences between the changes in lattice parameter from X-ray diffraction results as compared to the macroscopic strain gauge results from Ref. 2 may be due to partial loss of strain transfer through strain gauge adhesive or similar effects. -1100 ppm -800 ppm Table S1 -Spatially averaged change in dimension along orthogonal directions of a PMN-PT substrate measured between the Pxy and Pz configurations in zero electric field as measured by a strain gauge (from Wu et al. 2 ) compared to the change in the same directions determined from X-ray diffraction reciprocal space maps for the LSMO/PMN-PT sample. Figure S1(a) illustrates the change in out of plane {220} peak intensity for the PMN-PT substrate, with the peaks indicated by vertical lines. Here we plot ω-2θ line scans as a function of substrate poling state as the ω-2θ scans clearly show the electric-field induced changes in relative peak intensity and thus changes to the FE domain populations. Figure S1 -(a) Out-of-plane X-ray diffraction ω-2θ scans near the {220} peaks for a PMN-PT substrate as a function of poling state, with vertical lines corresponding to spacings as specified in Table S2. (b) Schematic of a monoclinic cell with a body diagonal indicated by bold arrow and (c) 011 projection of the monoclinic cell.
In Table S2, we tabulate the {220} PMN-PT unit cell parameters found in reference 1, the corresponding 2θ angle, as well as epitaxial mismatch to a fully strained (011)-oriented LSMO. While one might expect all possible orientations present in a thermally randomized sample, we have determined from Figure S1 that the predominant in-plane orientations for the PMN-PT Pz and Pxy poling states after electric field cycling correspond to d202 and d220, respectively ( 202 / = 95% for Pz, ( 220 or 2 ̅ 02 )/ = 70% and 022 / = 5% for Pxy). The monoclinic orientation in the Pz poling state is straightforward to understandwith a large electric field along the out of plane [011] direction, all FE domains will rotate to align their FE axes with the electric field, and the out of plane [011] length will be large compared to the inplane [011 ̅ ] direction. For the Pxy poling state, the FE axis rotates to lie in the (011) Figure  S1(a) bolded, tabulating in-plane and out-of-plane dimensions as well as in-plane angle, δ. The corresponding diffraction angle from the out-of-plane spacing is also indicated. For comparison, the epitaxial mismatch between (011)-oriented LSMO and PMN-PT unit cells along the orthogonal in-plane directions is also tabulated.
The last two columns of Table S2 show the epitaxial misfit strain between a pseudocubic LSMO unit cell and monoclinic PMN-PT unit cell for each of the possible in-plane {011} planes, and the most significant change between d202 and d220 is along the [011 ̅ ] direction, whereas a change between d202 and 2 ̅ 02 is along the [100] direction. To first order, we expect an anisotropic strain change in the LSMO unit cell on any single PMN-PT FE domain transitioning from Pz to Pxy, with a large change in either the in-plane [011 ̅ ] or [100] direction of more than 2400 ppm and little change along the orthogonal in-plane direction. The experimentally derived changes in lattice parameter for the LSMO film presented in Table S2 suggest that the dominant switching route between Pz and Pxy poling states is from d202 to d220 due to the large change along the [011 ̅ ] direction and negligible change along the [100] direction.
However, this is a simplification of the mismatch between the rhombohedral LSMO unit cell and the PMN-PT in-plane dimensions. For instance, PMN-PT compositions near the morphotropic phase boundary undergo electric-field induced changes in symmetry (e.g. from rhombohedral to orthorhombic), as well as phase transitions due to stress or temperature near ambient conditions. 3,4 Furthermore, the rhombohedral LSMO unit cell forms a microtwin structure when templating on a cubic (110)-oriented SrTiO3 surface, 5 but a change in in-plane shear strain from the as-grown state on PMN-PT can be generated due to the change in in-plane angle δ (see Table S1) between the inequivalent [100] and the [011 ̅ ] directions. Thus, for the (011) LSMO film, we can expect both elongation type strain along the direction as well as a contribution from shear strain as a function of PMN-PT poling state. A series of PEEM-XMCD images as a function of in-plane azimuthal angle allows for the determination of both the magnitude and direction of the local sample magnetization. Figure S2 shows the in-plane magnetization direction for a sample poled in the Pz state after thermal demagnetization to 340 K and cooling to room temperature in zero magnetic field. PEEM-XMCD images were continuously acquired while heating and cooling to ensure the sample was heated at least 10 K above the point that all magnetic contrast was lost. Magnetic domains align both along the [100] and [011 ̅ ] directions to first order, but a more careful comparison of the color levels shows variation in neighboring domains of 10 degrees (e.g. pink vs red domains are mostly oriented along the [100] but are canted away from this direction by ±10°).

C. XMCD images as a function of magnetic field for Pxy poling state
In the same sample location as Figure 4, the sample was poled into the Pxy state from the Pzstate and XMCD asymmetry images were taken during a magnetic field pulse sequence from negative to positive saturation along [100]. The magnetization strongly aligns with the <100> directions in contrast to the Pz state, and the field of view reverses through nucleation of a 180° reversal followed by domain wall motion. A 1 x 1 µm region was integrated as a function of magnetic field pulse and plotted as red circles in Figure 4 of the main text.  Figure S4 is a phase diagram of in-plane tensile strain for the (110)-oriented LSMO film with the experimentally determined normal strain values for the Pxy and Pz states indicated as points. For this map, we minimize the free energy from magnetocrystalline and magnetoelastic terms to find stable magnetization angles in the sample plane: with as direction cosines of the magnetization with respect to the orthogonal in-plane directions of the (011)-oriented film, 6 and the magnetoelastic energy term taken from Gao et al for a magnetostrictive film on a (011)-oriented substrate. 7 We first assume negligible in-plane shear strains, compliance tensor components as detailed in the methods section, and an isotropic magnetostriction constant of = −1 * 10 −5 at 300 K. [8][9][10] Examination of anisotropic and bulk magnetostriction constants for LSMO single crystals show that anisotropic effects are negligible within 30 K of the Curie temperature, whereas bulk magnetostriction increases significantly in magnitude near the Curie temperature. 11 The boundaries are generated from the second derivative of the free energy density. The slopes of the phase boundaries are proportional to unity, thus a large anisotropic strain in either direction can induce a strongly uniaxial magnetic easy axis, but nearly isotropic strain allows for the magnetocrystalline anisotropy to dominate and the magnetic easy axis has a fourfold symmetry. Figure S4 -Magnetic easy axis phase diagram as a function of in-plane strain along the two inequivalent crystallographic directions.

E. Supplementary Movie 1
Supplementary Movie 1 is a series of PEEM XMCD asymmetry images of a 30 micron field of view area used to generate the plot in Figure 5 (a). There are small changes in magnetic domain configuration as the electric field across the PMN-PT substrate is changed from -6.25 kV/cm to 1 kV/cm, but the largest rotation of magnetization occurs at approximately 1 kV/cm and 2.2 kV/cm as detailed in the main textthese changes correspond to the ferroelectric domain rotation from Pz-to Pxy and Pxy to Pz+, respectively. Piezoelectric-induced motion of the field of view or sample surface voltage fluctuations during image acquisition results in incomplete subtraction of topographical features when calculating XMCD asymmetry images, resulting in small black/white spots in some frames.

F. Surface roughness of LSMO/PMN-PT sample
The topography of the LSMO/PMN-PT sample was investigated after X-PEEM measurements through tapping mode atomic force microscopy (Veeco Multimode). A typical 3 micron x 3 micron region is shown in Figure S5, with surface roughness values below 1nm, similar to that found for PMN-PT substrate surfaces. 12 Figure S5 -Atomic force microscope image of the LSMO/PMN-PT sample, with the entire image having an RMS surface roughness of 0.65 nm, and region inside the red box having an RMS roughness of 0.45 nm.