Twin wall distortions through structural investigation of epitaxial BiFeO3 thin films

Abstract

In this work, epitaxial (001) BiFeO3 thin films were deposited on SrTiO3 and TbScO3 single-crystal substrates and analyzed with high-resolution x-ray diffraction—reciprocal space mapping. A basic method was developed to extract structural details of the as-grown BiFeO3 film, including (i) epitaxial strain, (ii) ferroelastic domains, and (iii) lattice rotations. After demonstrating the method, extrinsic distortions at vertical twin walls were determined for specific BiFeO3 heterostructures. A relatively large distortion (0.20° ± 0.08°) was measured in a multidomain (12) and incoherent film, while a nearly intrinsic distortion (0.04° ± 0.03°) was measured in a two-domain coherent film. This work offers insights into the structure of multiferroic BiFeO3 thin films with a general approach that is appropriate for low symmetry epitaxial heterostructures.

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ACKNOWLEDGMENTS

We thank Dr. Dillon Fong at Argonne National Labs for reading of the manuscript and providing constructive comments. This work is supported by the Army Research Office under Grant No. W911NF-10-1-0362.

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Correspondence to Chang-Beom Eom.

APPENDIX

APPENDIX

The bulk real space structures of the BiFeO3 film and the substrates were described with individual sets of basis vectors in a single Cartesian coordinate system (see subcells in Fig. 1). After defining the heterostructure in real space, the basis vectors were transformed to reciprocal space using standard Gibb’s relations.31 The real space lattice corresponding to the substrates was fixed. In contrast, the real space lattice of the BiFeO3 film was matched to the data considering the following parameters: subcell definition (ap, bp, cp, αp, βp, and γp) and parameters associated with structural variants (R), specifically (r1, r2, r3, or r4) and lattice rotations (\(\hat k\), ω).

The substrate lattice (Fig. 1) transformation matrices were defined for SrTiO3 with a = 3.905 Å and TbScO3 with am = cm = \({{\sqrt {a_{\rm{o}}^2 + b_{\rm{o}}^2 } } \mathord{\left/ {\vphantom {{\sqrt {a_{\rm{o}}^2 + b_{\rm{o}}^2 } } 2}} \right. \kern-\nulldelimiterspace} 2}\) = 3.953 Å, bm = \({{c_{\rm{o}} } \mathord{\left/ {\vphantom {{c_{\rm{o}} } 2}} \right. \kern-\nulldelimiterspace} 2}\) = 3.957 Å, and βm = \(2\tan ^{ - 1} \left( {{{a_{\rm{o}} } \mathord{\left/ {\vphantom {{a_{\rm{o}} } {b_{\rm{o}} }}} \right. \kern-\nulldelimiterspace} {b_{\rm{o}} }}} \right)\) = 87.243°.123233

$${S^{{\rm{STO}}}} = \left[ {\matrix{ a & 0 & 0 \cr 0 & a & 0 \cr 0 & 0 & a \cr } } \right].$$
((1))
((2))

A transformation matrix was also used to define the BiFeO3 film subcell (F) although in contrast to the substrates, the lattice parameters ap, bp, cp, and intercell angles αp, βp, and γp were made flexible as to fit the experimental data (general triclinic structure).

((3))

where,

$${\gamma ^/} = {\pi \over 4} - {{{\gamma _{\rm{p}}}} \over 2},$$
$${F^{\left[ {1,3} \right]}} = {F^{\left[ {2,3} \right]}} = 0,$$

The expressions for F were geometrically derived assuming the subcell initially lies flat on the crystallographic growth surface (F[2,3] = F[1,3] = 0) and equally spaced from the [100] and [010] axes.

Four ferroelastic variations are in a rhombohedral system which quadruples the number of independent lattices that must be considered. These were accounted for using separate matrices, r1–4, where each may be visualized as a stretching of the subcell along the <111> diagonals (Fig. 1).28

((4))

Additionally, structural variants (R) were considered to account for the possibility of lattice rotations. This was accomplished considering the ferroelastic variants (r1–4) and a rotation matrix.31

((5))

Here ω is the magnitude of the rotation about a unit vector \(\hat k\) = [k1, k2, k3]. Here discussion was limited to ωf and ωd, which are notations used in the text to describe lattice rotation of the entire film due to miscut and individual ferroelastic domains due to twin walls, respectively.

At this point, transformation of all the individual real space lattices of the film and substrate to reciprocal space (H K L) was performed using the standard Gibb’s relations generating respective reciprocal lattices in the same coordinate system (Fig. 1).31

To compare with the measured 2D RSM data, the nearest scattering vector GHKL of each reciprocal lattice was projected onto the exact plane measured in reciprocal space. The projected GProj was calculated with,

$${G_{{\rm<Prefix>oj</Prefix>}}} = P{\left( {{P^/}P} \right)^{ - 1}}{P^/}{G_{HKL}},$$
((6))

where P defines the measured plane in reciprocal space (P/ is the transpose). For {002} and {103} reflections,

((7))

and for {113} reflections,

((8))

A full list of reflections used in this study is given in Table II with the position equivalent bulk Bragg reflections. The Bragg reflections for single-crystal substrates were used for calibration.

TABLE II.
figureTab2

Position select equivalent Bragg reflections for bulk unit cell and sub-cell

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Folkman, C.M., Baek, SH. & Eom, CB. Twin wall distortions through structural investigation of epitaxial BiFeO3 thin films. Journal of Materials Research 26, 2844–2853 (2011). https://doi.org/10.1557/jmr.2011.327

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Keywords

  • Crystallographic structure
  • Epitaxy
  • Ferroelectric