Untilting BiFeO₃: The influence of substrate boundary conditions in ultra-thin BiFeO₃ on SrTiO₃

We report on the role of oxygen octahedral tilting in the monoclinic-to-tetragonal phase transition in ultra-thin BiFeO₃ films grown on (001) SrTiO₃ substrates. Reciprocal space maps clearly show the disappearance of the integer-order Bragg peak splitting associated with the monoclinic phase when the film thickness decreases below 20 unit cells. This monoclinic-to-tetragonal transition is accompanied by the evolution of the half-order diffraction peaks, which reflects untilting of the oxygen octahedra around the [110] axis, proving that the octahedral tilting is closely correlated with the transition. This structural change is thickness-dependent, and different from a strain-induced transition in the conventional sense.

As one of the few room temperature multiferroic materials (ferroelectric: T_C ∼ 1103 K, antiferromagnetic: T_N ∼ 643 K) and the only known one that is a stable phase, bismuth ferrite (BiFeO₃) has been studied extensively in recent years.^1–11 The bulk form of BiFeO₃ is known to have a rhombohedrally distorted quasi-cubic perovskite structure with an a⁻a⁻a⁻ (Glazer notation¹²) octahedral tilt pattern,¹³ exhibiting both anti-ferrodistortive displacements and a spontaneous polarization along the ⟨111⟩ pseudocubic axes. When epitaxial BiFeO₃ thin films are grown under compressive strain on (001)-oriented perovskite substrates, several studies^2,4,7–9 have reported that the polarization direction is tilted towards the [001] out-of-plane direction, while maintaining a significant in-plane component, depending on the amount of epitaxial strain from the substrate. This effect is accompanied by a significant enhancement of the spontaneous polarization and a series of phase transitions from rhombohedral (R) for small strains to R-like monoclinic (M_A) to T-like monoclinic (M_C) and to tetragonal (T) for larger strains, the latter two of which exhibit a giant c/a ratio.^7,8 Bismuth ferrite films (thickness >26 nm) grown on (001) SrTiO₃ (STO) substrates (−1.4% compressive strain) exhibit the R-like monoclinic structure (M_A) with a c/a ratio close to unity.^8,9,14

Previous studies^15–17 have shown that the effects of the perovskite heterointerfaces generally extend over only a few unit cells. In particular, ultra-thin BiFeO₃ films grown on (001) SrTiO₃ substrates with a SrRuO₃ buffer layer showed evidence for a transition to tetragonal symmetry.^11,18,19 Also, it has been reported that BiFeO₃ films grown on (001) SrTiO₃ can have a tetragonal structure with a giant c/a ratio, resulting from the higher strain induced by a Bi₂O₃ layer, which can be formed between the film and the substrate.^20,21

In this paper, we report on the thickness dependence of the BiFeO₃ thin film structure in the ultra-thin regime under moderate compressive strain from (001) SrTiO₃ substrates. We find that the transition from monoclinic to tetragonal is accompanied by a change in the octahedral tilt pattern which reflects the increase in symmetry. A correct determination and deeper understanding of the ultra-thin regime of the BiFeO₃ film structure is critical in the sense that the multiferroic and electronic properties depend strongly on the film heteroepitaxy. Most importantly, this is essential for many innovative applications of multiferroics such as low-power electronics and energy storage.¹⁰ 

The BiFeO₃ thin films were grown by reactive molecular-beam epitaxy (MBE) on SrTiO₃ (001) substrates (miscut < 0.1°) in an adsorption-controlled regime²² utilizing distilled ozone.²³ Synchrotron x-ray diffraction experiments were carried out at beamlines 13-BM-C, 33-ID-D, and 33-BM-C of the Advanced Photon Source. To identify the symmetry of the BiFeO₃ films, high-resolution three-dimensional reciprocal space maps (3D RSMs) were measured around high-order film Bragg peaks and half-integer order peaks which are sensitive to the anti-ferrodistortive octahedral tilting pattern. Using a PILATUS 100K area detector,^24,25 the intensity distribution around each peak was measured in a series of single scans along the L-direction as a set of two-dimensional reciprocal space slices. These were then used to reconstruct the 3D RSMs.²⁶ Note that all reciprocal space positions are given in units of the inverse substrate (SrTiO₃) lattice constants, and all RSMs are presented with the same color scale.

In Figs. 1(a)–1(c), we show (HH)L slices through the 3D-RSMs around the 335 peaks for three different film thicknesses. We observe that the signal from the 50 unit cell (UC) thick film [Fig. 1(a)] is split into three distinct peaks: a bright one at the center, and two weaker peaks above and below the center peak. This splitting pattern corresponds to the well-known M_A monoclinic structure in the presence of four domains that tilt in different directions, reported for BiFeO₃ films on SrTiO₃ with thicknesses greater than 26 nm.^7,8 For the 20 UC film [Fig. 1(b)], however, the splitting is less pronounced, while for 10 UC [Fig. 1(c)], only a single peak is observed (although it is broadened in the out-of-plane direction due to the finite thickness of the film). HL maps around 405 peaks show the same behavior [Figs. 1(d)–1(f)] with a doubly split diffraction feature transforming into a single peak. These findings prove that there is a structural phase transition as the film thickness decreases.

This disappearance of the peak splitting for the 10 UC film can be explained either by formation of a single-domain monoclinic film structure, or, alternatively, by a transition to a tetragonal film unit cell. We can distinguish between these two possibilities by carefully investigating the symmetry of selected Bragg peaks in the 3D RSM. The single-domain monoclinic structure would result in a tilted film peak pattern with respect to the substrate lattice, while the tetragonal case should yield a perfectly fourfold symmetric diffraction pattern. To check the symmetry, the RSMs of four-fold symmetrically-equivalent positions for each peak were measured. Figures 2(a)–2(h) shows the equivalent RSMs for two families of Bragg peaks, 335 and 405, of the 10 UC film. All peaks evidently appear at the same L position, proving that the film structure is tetragonal rather than single-domain monoclinic.

In addition to the disappearance of the peak splitting, a narrowing of the peak width in the in-plane direction can be observed during the transition. The 50 UC monoclinic film peaks [Figs. 1(a) and 1(d)] have an in-plane peak width of approximately 0.01 reciprocal lattice units (r.l.u.), which corresponds to a lateral domain size of roughly 100 unit cells. The 10 UC film peaks [Figs. 1(c) and 1(f)], however, are much narrower (almost 1/10 of those of 50 UC film), with their widths being limited mostly by the instrumental resolution rather than the structural coherence length. This indicates that the 10 UC film is coherent with the substrate over significant distances (>400 nm) and does not form structural domains.

Definitive support for this transition from monoclinic to tetragonal symmetry comes from the measurements of half-integer order peaks associated with the oxygen octahedral tilt pattern in the BiFeO₃ film. For the previously reported monoclinic M_A structure in the BiFeO₃/SrTiO₃ system, an a⁻a⁻b⁰ octahedral tilt pattern is expected,⁸ which produces half-integer order peaks at all reciprocal space positions with strictly half-integer H, K, and L values, except where H=K=L. For the tetragonal symmetry, however, half-integer peaks at H=K positions are also expected to be missing.¹² Figure 3 shows the

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$32$ peaks for the three film thicknesses. The H=K [

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$32$⁠: Figures 3(a)–3(c)] peaks are becoming broader and weaker as the film thickness decreases. In contrast, the H≠K peaks [

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$32$⁠: Figs. 3(d)–3(f)] are narrowing with a concurrent reduction of the peak splitting, and the width of the 10 UC film peak becomes comparable to those of integer-order peaks (Fig. 2). Comparing the intensities, the

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$32$ peak is brighter than the one at

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$32$ for the 50 UC film, but for 10 UC, the

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$32$ peak is more intense. The extinction of the H=K peak [Fig. 3(c)] means that the octahedral rotation is primarily along the c axis and definitely identifies the octahedra tilt pattern as a⁰a⁰c⁻, which corresponds to tetragonal symmetry.

It is important to note that the octahedral tilting selection rule¹² assumes rigid octahedra, which may not be the case for the 20 UC film where different symmetries can coexist and a gradual change of octahedral tilting is expected. Moreover, in addition to pure rotations, distortions of the oxygen octahedra may also affect the half-order peak intensities. These can be the cause of the broad and faint intensities near the

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$32$ position of the ultra-thin film [Fig. 3(c)], where one would expect perfect extinction according to the selection rule. A precise determination of the atomic coordinates associated with this tilt pattern is therefore not possible without taking these distortions into account. Nevertheless, the clear suppression of the H=K peak in ultra-thin films indicates that the rotations about the [110] axis are quenched, and the symmetry of the film structure is increased from monoclinic to tetragonal.

From the positions of each split diffraction peak, the lattice parameters of the film unit cell can be obtained. Table I shows the calculated lattice parameters and unit cell volumes of the 10 UC and 50 UC thick films. For the 20 UC film, the RSMs show evidence for both monoclinic (split peaks with broad in-plane widths) and ultra-thin tetragonal (one peak with narrow in-plane width and broad out-of-plane width) symmetry [Figs. 1(b) and 1(e)], indicating that these two phases coexist at this thickness. Since the monoclinic and tetragonal peak splitting patterns overlap each other, an accurate determination of the peak position was not possible for the 20 UC film. In the 50 UC film [Figs. 1(a) and 1(d)], evidence for the presence of a tetragonal phase can no longer be clearly observed, because the broad peaks originating from the M_A monoclinic structure completely dominate the intensity in the RSM. Thus, it remains unclear if a thin layer with tetragonal symmetry continues to exist at the interface or whether the entire film transitions to the monoclinic structure.

Specular diffraction 00L scans have been performed for the ultra-thin film, in order to check for the presence of Bi₂O₃ layers. Pronounced peaks are expected near L = 1.45 and L = 2.15 if such layers exist.²¹ As can be seen in Fig. 4, there are no peaks at these L positions. This excludes the possibility of having unknown crystalline layers being responsible for higher symmetry of the film by introducing additional strain on the film. Therefore, the tetragonal phase observed in the ultra-thin BiFeO₃ originates purely from the epitaxy between the film and the substrate.

In contrast to the previously reported M_A-M_C-T phase transition of thicker BiFeO₃ films as a function of strain or temperature,^8,27 we observed a direct transition from the monoclinic M_A phase to a tetragonal phase as a function of film thickness. This tetragonal phase in ultra-thin films is subject to only moderate strains (−1.4%) from the substrate, and does not exhibit the giant c/a ratio present in the tetragonal M_C and T phases induced by high compressive strain (< −4%). Moreover, as can be seen in Table I, there is no substantial difference between the unit cell volumes of the 50 UC film and the 10 UC film (Note that the volume of the M_A unit cell is doubled with respect to the tetragonal unit cell). Considering the fact that the usual strain-driven monoclinic to tetragonal phase transition involves a significant change in unit cell volume,^4,8 this also supports that our observations are not a conventional strain effect.

These findings suggest that a mechanism other than strain is involved in the phase transition in the ultra-thin regime. Our results favor an alternate explanation where the cubic (001) SrTiO₃ substrate with 4-fold in-plane symmetry provides a strong constraint in the octahedral tilting pattern in the BiFeO₃ film through corner-connectivity. We note here that several experimental and theoretical studies on the perovskite/perovskite interface have reported that the corner-connectivity between the BO₆ octahedra of the substrate and the film at the interface allows the octahedral tilt pattern of the substrate to propagate a few unit cells into the film, thereby determining the symmetry of the film structure.^15–17 For the BiFeO₃/SrTiO₃ system, this boundary condition for the corner-connectivity between SrTiO₃ (no octahedral tilting) and BiFeO₃ may suppress the octahedral tilting about the [110] direction in BiFeO₃, resulting in the tetragonal structure for ultra-thin films. Moreover, the absence of the octahedral tilting about in-plane axes also indicates that the film has a structure highly coherent with the substrate, explaining the narrow in-plane widths of the 10 UC film Bragg peaks.

In conclusion, the structural symmetry of ultra-thin BiFeO₃ films on (001) SrTiO₃ substrates was determined from 3D RSM measurements. The evolution of the film Bragg peak splitting, and the half-order intensities associated with oxygen octahedra rotations, definitively demonstrate that there is a structural phase transition from the monoclinic M_A phase to a tetragonal symmetry as a function of film thickness. Further investigations on ultra-thin BiFeO₃ films on different substrates are needed to better understand the interplay between structure, film thickness, and the misfit strain. Having established the structural symmetry, a complete determination of the atomic structure, including the oxygen octahedra tilt angles, can be obtained as a function of the strain and thickness by quantitative analysis of crystal truncation rod and half-order peak intensities. This work is ongoing.

The authors wish to thank J. W. Freeland and V. Stoica for helpful discussions. This work was supported by the U.S. Department of Energy (Contract No. DE-FG02-06ER46273). The film synthesis work (at Cornell University) was supported by the Army Research Office through Agreement No. W911NF-08-2-0032. The X-ray diffraction experiments were performed at sectors 13-BMC (GeoSoilEnviroCARS), 33-IDD (XSD), and 33-BMC (XSD) at the APS. Excellent beamline support by P. J. Eng, J. Stubbs, Z. Zhang, E. Karapetrova, and the staff of the APS is gratefully acknowledged. GeoSoilEnviroCARS is supported by the National Science Foundation - Earth Sciences (EAR-0622171) and Department of Energy - Geosciences (DE-FG02-94ER14466). The use of the APS was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357.