Influence of flexoelectricity on the spin cycloid in (110)-oriented $\mathrm{BiFe}{\mathrm{O}}_{3}$ films

Influence of flexoelectricity on the spin cycloid in (110)-oriented $BiFe O_{3}$ films

D. Sando, F. Appert, S. R. Burns, Q. Zhang, Y. Gallais, A. Sacuto, M. Cazayous, V. Garcia, S. Fusil, C. Carrétéro, J. M. Le Breton, A. Barthélémy, M. Bibes, J. Juraszek, and V. Nagarajan

Phys. Rev. Materials 3, 104404 – Published 9 October 2019

Abstract

The influence of film orientation, strain relaxation, and flexoelectric fields on the stability of the spin cycloid in (110)-oriented $BiFe O_{3}$ epitaxial films grown on $LaAl O_{3}$ substrates is investigated. By means of advanced x-ray-diffraction techniques, we show that thinner films have very large strain gradients which give rise to high flexoelectric fields. Using low-energy Raman spectroscopy and conversion electron Mössbauer spectroscopy (CEMS) we show that films up to 53 nm thick possess collinear antiferromagnetic order, with no cycloidal modulation. This suppression of the cycloid is proposed to be from strain and strain-gradient-induced flexoelectric fields. On the other hand, films thicker than 90 nm show a complex spin texture consistent with two separate cycloids, likely with different propagation directions. Interestingly, CEMS analysis suggests that the two cycloids have the same spin rotation plane. The multiple cycloids are suggested to arise from different ferroelastic domains (in turn influenced by twinning in the substrate) with different strain relaxation behaviors. These results offer insight into the factors that influence cycloid stability in the less common (110) film orientation and have implications for future magnonic devices.

Received 5 June 2019
Revised 29 August 2019

DOI:https://doi.org/10.1103/PhysRevMaterials.3.104404

Physics Subject Headings (PhySH)

Epitaxial strain Flexoelectricity Spin texture

Multiferroics

Mössbauer spectroscopy Raman spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

D. Sando ^1,2,*, F. Appert³, S. R. Burns¹, Q. Zhang¹, Y. Gallais⁴, A. Sacuto⁴, M. Cazayous⁴, V. Garcia⁵, S. Fusil⁵, C. Carrétéro⁵, J. M. Le Breton³, A. Barthélémy⁵, M. Bibes⁵, J. Juraszek³, and V. Nagarajan¹

¹School of Materials Science and Engineering, UNSW Sydney, High Street, Kensington, 2052, Australia
²Mark Wainwright Analytical Centre, UNSW Sydney, High Street, Kensington, 2052, Australia
³Normandie Univ., UNIROUEN, INSA Rouen, CNRS, GPM, 76000 Rouen, France
⁴Laboratoire Matériaux et Phénomènes Quantiques (UMR 7162 CNRS), Université Paris Diderot-Paris 7, 75205 Paris Cedex 13, France
⁵Unité Mixte de Physique, CNRS, Thales, Univ. Paris-Sud, Université Paris-Saclay, 91767 Palaiseau, France

^*daniel.sando@unsw.edu.au

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Vol. 3, Iss. 10 — October 2019

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Figure 1
(a) High-angle $2 θ − ω$ scans for BFO//LAO (110) films 19–144 nm in thickness. Multiple phases are identified (see text). Thickness dependence of (b) the out-of-plane lattice parameter and (c) phase fraction of the different phases. (d) Average strain $ɛ_{H}$ for the $BF O_{a}$ phase.
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Figure 2
Williamson-Hall plot analysis for strain gradients. (a) Williamson-Hall plot along the three Cartesian directions. (b) Predicted lattice constant (solid lines) according to Eq. (2). The average strain in each direction is shown as a dashed line. Data points are the average lattice parameter for the 19-nm-thick film. (c) Inhomogeneous strain in three directions as a function of thickness. (d) estimated flexoelectric field as a function of thickness (the dotted line is a guide to the eye).
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Figure 3
Low-energy Raman spectroscopy for BFO//LAO (110) films of various thicknesses. (a) The 53-nm film shows a single peak for each configuration, consistent with $G$ -type AFM order (i.e., no cycloid); (b) 93-nm film shows a cycloid with period $\sim 72 nm$ ; (c), (d) the 126- and 144-nm films show a complex spectrum suggesting the coexistence of two cycloids.
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Figure 4
(a) Geometry of the measurement with the gamma ray incident along $\vec{k} 1$ , that is, along the $[\bar{1} \bar{1} 0]$ direction. (b) Normal incidence spectrum fit with a cycloid with $(\bar{1} 10)$ cycloid plane. (c) Sketch of the spin structure consisting of cycloid with $(\bar{1} 10)$ cycloid plane and additional colinear phase inside the sample plane. (d) Adding a collinear component improves the fit considerably. (e) Spectra and fits for the full set of samples.
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Figure 5
Mössbauer spectroscopy in inclined geometry. (a) Geometry of the first tilted experiment where the γ ray is incident along the $[0 \bar{1} 0]$ direction, i.e., tilted 45° to the $(1 \bar{1} 0)$ plane. (b) Geometry of the second tilted experiment where the γ ray is incident at an angle 45° from the [110] direction in the $(1 \bar{1} 0)$ plane. (c) Mössbauer spectra for the first tilted experiment for the five films. Note that for the thickest film, the spectrum resembles the standard type-1 cycloid, while for the thinnest film, the spectrum is consistent with spins orthogonal to the γ-ray direction (see text). (d) Spectra for second tilted geometry show minimal dependence on thickness. The thickest film shows a spectrum very similar to that observed in normal incidence, while the thinnest film shows a symmetric spectrum consistent with spins tilted $\sim 45^{\circ}$ from the γ-ray direction (see text). (e) Geometry of the tilted Mössbauer experiments and the relevant angles. (f) Angles β for the collinear AFM phase, obtained from the fits of the data shown in (c), (d). For a pseudocollinear phase with spins aligned collinear along [001], the expected values of these angles are shown as dashed lines.
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Figure 6
(a) Dependence on thickness of (i) homogeneous strain $ɛ_{H}$ , (ii) flexoelectric field $E_{flexo}$ , (iii) fraction of $BF O_{b}$ phase, and (iv) fraction of pseudocollinear phase. Regions where the cycloid is stable are shown in orange, while blue denotes noncycloidal (pseudocollinear) states. (b) Dependence of collinear phase fraction on the phase fraction of $BF O_{b}$ phase, showing a monotonic trend. Note that extrapolation to 0% of $BF O_{b}$ suggests that the cycloidal phase has a prominent anharmonicity (see text).
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Physical Review Materials

Influence of flexoelectricity on the spin cycloid in (110)-oriented BiFeO3 films

D. Sando, F. Appert, S. R. Burns, Q. Zhang, Y. Gallais, A. Sacuto, M. Cazayous, V. Garcia, S. Fusil, C. Carrétéro, J. M. Le Breton, A. Barthélémy, M. Bibes, J. Juraszek, and V. Nagarajan

Phys. Rev. Materials 3, 104404 – Published 9 October 2019

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Influence of flexoelectricity on the spin cycloid in (110)-oriented $BiFe O_{3}$ films