Coherent Magnetoelastic Domains in Multiferroic ${\mathrm{BiFeO}}_3$ Films

The physical properties of epitaxial films can fundamentally differ from those of bulk single crystals even above the critical thickness. By a combination of nonresonant x-ray magnetic scattering, neutron diffraction and vector-mapped x-ray magnetic linear dichroism photoemission electron microscopy, we show that epitaxial (111)-${\text{BiFeO}}_3$ films support submicron antiferromagnetic domains, which are magnetoelastically coupled to a coherent crystallographic monoclinic twin structure. This unique texture, which is absent in bulk single crystals, should enable control of magnetism in ${\text{BiFeO}}_3$ film devices via epitaxial strain.

Figure 1

Monoclinic structure of ${\text{BiFeO}}_3$. (a) Side on (along $+{\mathbf{b}}_{\mathrm{h}}$ direction) and (b) top down (along $-{\mathbf{c}}_{\mathrm{h}}$ direction) projections of BFO crystal structure showing the relationship between the rhombohedral (black) and monoclinic (green) unit cells and their axes. The hexagonal and monoclinic settings are indicated by subscript $h$ and $m$, respectively. (c) Rocking curve scans of the $(006{)}_h$ reflection in the film (red) and crystal (blue), respectively. The peak intensities have been normalized to unity.

Figure 2

Magnetic diffraction reciprocal space maps. (a) Schematic of the monoclinic distortion model showing the undistorted (translucent) and distorted (opaque) diffraction patterns (see main text). (b)–(d) Reciprocal space maps about $(009{)}_h$ measured at room temperature by NXMS with linear, left circular, and right circular polarized light, respectively. The measured $(009{)}_h$ position is slightly off center due to the sphere-of-confusion error of the diffractometer. (e) Reciprocal space map about the $(003{)}_h$ measured by neutron diffraction at 10 K. The white circle in the lower left corner indicates the instrumental resolution. (f)–(h) Simulated NXMS reciprocal space maps about $(009{)}_h$ with linear, left circular, and right circular polarized light, respectively. The scale bar in the bottom right shows the magnitude of the propagation vector (all images on the same scale) and the reciprocal lattice directions (in the hexagonal setting) are indicated by the black arrows.

Figure 3

PEEM imaging of magnetic $\mathbf{k}$ domains in $(111)\text{-\hspace{0.17em}}{\text{BiFeO}}_3$ films. (a)–(c) PEEM images obtained using x-ray linear dichroism (XMLD) with the light areas corresponding to domains of ${\mathbf{k}}_1$, ${\mathbf{k}}_2$, and ${\mathbf{k}}_3$ propagation vectors, respectively. (d) Discrete vector map of the $\mathbf{k}$ domains obtained from (a)–(c), where the direction of the propagation vector is indicated by the colored arrows. The scale bar refers to (d).