Complex strain evolution of polar and magnetic order in multiferroic BiFeO3 thin films

Electric-field control of magnetism requires deterministic control of the magnetic order and understanding of the magnetoelectric coupling in multiferroics like BiFeO3 and EuTiO3. Despite this critical need, there are few studies on the strain evolution of magnetic order in BiFeO3 films. Here, in (110)-oriented BiFeO3 films, we reveal that while the polarization structure remains relatively unaffected, strain can continuously tune the orientation of the antiferromagnetic-spin axis across a wide angular space, resulting in an unexpected deviation of the classical perpendicular relationship between the antiferromagnetic axis and the polarization. Calculations suggest that this evolution arises from a competition between the Dzyaloshinskii–Moriya interaction and single-ion anisotropy wherein the former dominates at small strains and the two are comparable at large strains. Finally, strong coupling between the BiFeO3 and the ferromagnet Co0.9Fe0.1 exists such that the magnetic anisotropy of the ferromagnet can be effectively controlled by engineering the orientation of the antiferromagnetic-spin axis.


Supplementary Note 1. Structural characterization of BiFeO3 thin films using X-ray diffraction
At room temperature, bulk BiFeO3 possesses a rhombohedral perovskite structure with a pseudocubic lattice parameter of = 3.965 Å, = 89.4°. 1 SrTiO3 has an cubic structure with = 3.905 Å and GdScO3 is orthorhombic with 0 = 5.488 Å, 0 = 5.746 Å, and 0 = 7.934 Å. 2 The orthorhombic unit cell can be described with a pseudocubic space group, in which the

Supplementary Note 3. Temperature-dependent X-ray linear dichroism studies
Soft X-ray absorption spectroscopy (XAS)-based linear dichroism studies have been established as an excellent tool to investigate element-specific magnetic properties (e.g., spin orientation, Néel temperature, and magnetic domain structure) of antiferromagnetic materials.
XLD is the difference of the absorption of linearly-polarized light, measured at a particular photon energy (in this case corresponding to the Fe L2,3 absorption edges), with two orthogonal polarizations. XLD can typically arise from two different origins: magnetic linear dichroism and crystal-field linear dichroism. In the case of multiferroic BiFeO3, the dichroism could arise from both the antiferromagnetism and crystal-field effects due to spontaneous polarization and straininduced lattice distortion. 4,5 In rhombohedral BiFeO3, which has d 5 high spin ground state of Fe 3+ , the magnetic linear dichroism mainly shows as variations in peak intensity, 6,7 and the crystal-field effects raise to shifts in peak position. 7,8 A negligible peak shift (< 0.1 eV) between the Fe L3 spectra with two different polarization of the BiFeO3 heterostructures studied herein indicates a small contribution from the crystal-field mechanism (data for normal incidence, Fig. 1d and for grazing incidence, Supplementary Fig. 4a). The magnetic contribution can be further isolated by temperature-dependent XLD studies since the magnetic linear dichroism is expected to decrease when the sample is heated to near the Néel temperature and the magnitude of the magnetic dichroism scales with the average of the square of the magnetic order parameter. In BiFeO3, the crystal-field contribution should persist to well above the Néel temperature since its ferroelectric Curie temperature is well above its Néel temperature. Temperature-dependent XLD at the Fe L2,3 edges for the BiFeO3 films found that XLD near TN is much smaller than that at 300 K ( Supplementary Fig. 4b), especially for XLD at the L2 edge which essentially vanishes at 650 K ( Supplementary Fig. 5), indicating that the XLD in our BiFeO3 heterostructures is largely dominated by magnetic origin. 7,9 Reproducibility is demonstrated by the measurements at room temperature obtained before and after, respectively, heating up to 650 K, indicating that there is no film decomposition during heating.

Supplementary Note 4. Atomic multiplet calculations
We have measured the polarization dependent Fe-L2 XAS spectra of the (110)-oriented  Theo.

Supplementary Note 5. Scanning transmission electron microscopy studies
High-angle annular dark-field (HAADF) and bright field (BF) scanning transmission electron microscopy (STEM) studies were carried out to characterize the interface abruptness and Theo.

Exp.
Theo.     Technologies). The macroscopic hysteresis loop measurements reveal that the out-of-plane spontaneous polarization of the films grown is ~ 90 μC/cm 2 , close to the value in (110)-oriented films grown on SrRuO3/SrTiO3 in previous studies. 10 Again, confirming that the film's polarization is essentially pointing along the [111] and has not rotated dramatically.

Supplementary Note 7. Ab initio calculations
The ab initio calculations adopted a supercell with 2×2×2 cubic perovskite unit cells, The evolution of several physical properties of BiFeO3 as a function of misfit strain were then probed ( Supplementary Fig. 12). It can be seen that the supercell volume and FeO6 octahedral volume increase when the in-plane misfit is changed from compressive to zero, then to tensile strain, while the out-of-plane [110] axis length decreases during this process. The decreasing outof-plane axis is not able to cancel out the increasing in-plane axis, leading to the volume trend. with previous studies. 11,12 From zero strain to large compressive strain, we observe that there is a jump from -5% to -10% in the [11 ̅ 0] component. This indicates there might be a phase transition during this process. This said, we found that the structure maintains a Cc symmetry until ~-5% misfit compressive strain, but loses all symmetry by -10% misfit. Despite this, the overall atomic structure shows no remarkable difference as this strain value is increased and, in turn, this means that this symmetry change (loss) does not affect the trend of the electronic polarization P and the antiferromagnetic axis L, since their directions change very slightly from -5% to -10% misfit.