Short range biaxial strain relief mechanism within epitaxially grown BiFeO3

Lattice mismatch-induced biaxial strain effect on the crystal structure and growth mechanism is investigated for the BiFeO3 films grown on La0.6Sr0.4MnO3/SrTiO3 and YAlO3 substrates. Nano-beam electron diffraction, structure factor calculation and x-ray reciprocal space mapping unambiguously confirm that the crystal structure within both of the BiFeO3 thin films is rhombohedral by showing the rhombohedral signature Bragg’s reflections. Further investigation with atomic resolution scanning transmission electron microscopy reveals that while the ~1.0% of the lattice mismatch found in the BiFeO3 grown on La0.6Sr0.4MnO3/SrTiO3 is exerted as biaxial in-plane compressive strain with atomistically coherent interface, the ~6.8% of the lattice mismatch found in the BiFeO3 grown on YAlO3 is relaxed at the interface by introducing dislocations. The present result demonstrates the importance of: (1) identification of the epitaxial relationship between BFO and its substrate material to quantitatively evaluate the amount of the lattice strain within BFO film and (2) the atomistically coherent BFO/substrate interface for the lattice mismatch to exert the lattice strain.

caused by the lattice misfit with the substrate within the identified crystal symmetry, can be further investigated with XRD technique that focuses on highly localized area in reciprocal space with exceptional precision.
It should be noted that the hexagonal notation rather than the pseudocubic one is highly recommended to use to accurately describe structural details of the rhombohedral, i.e., SG of R3c, BFO 21,23,24 . This is because pseudocubic notation disregards the ~0.55° of rhombohedral distortion in BFO unit cell and subsequent rhombohedral shifts in basis atom locations. As a result, the pseudocubic notation cannot interpret some of Bragg's reflections that are specifically related to the rhombohedral characteristic as demonstrated in recent reports 21,23,24 . Thus, hereafter, hexagonal notation is used to accurately describe rhombohedral BFO in this work unless otherwise mentioned. Another parameter to quantitatively evaluate the biaxial strain exerted on BFO films is the misfit lattice strain with substrate materials. Conventionally, the misfit lattice strains are estimated by assuming BFO and the substrate materials as pseudocubic crystals 25 . In this assumption, the growth orientation of BFO film is simply assumed to be the same as that of the substrate material. While this could be reasonable with some substrate materials that have similar lattice parameters as BFO, the possibility of BFO growth having different crystal orientations is excluded. Thus, this assumption is not expected to accurately estimate the misfit lattice strain if a BFO film grows on a substrate having a different crystal orientation from that of the substrate as pointed out previously 21,23 .
In this study, the crystal structures and growth mechanisms of the epitaxial BFO films grown on La 0.6 Sr 0.4 MnO 3 (LSMO)/SrTiO 3 (STO) and YAlO 3 (YAO) substrates are studied using TEM and XRD techniques. The result clearly demonstrates: (1) The importance of the direct observation on the BFO/substrate interface to determine either the biaxial strain evaluated by the lattice mismatch is exerted toward the BFO film with atomistically coherent lattice plane, or it is relaxed by introducing lattice imperfections such as dislocations.
(2) BFO film grows retaining the rhombohedral symmetry despite a large lattice mismatch of ~6.8% with its substrate, but with an unusual epitaxial relationship. This result is important in that it answers the question that "Does BFO grow another metastable phase if a substrate imparting larger compressive strain than LaAlO 3 is used?" 9,11,16 . (3) The identification of the epitaxial relationship between the BFO film and the substrate material should precede to ensure accurate evaluation of the lattice mismatch. Figure 1(a) is a cross-sectional bright-field (BF) TEM image of the BFO/LSMO/STO sample along [011] STO orientation, which shows overall microstructural characteristics. Note that [011] STO zone axis is chosen because this zone axis is proven to reveal the subtle symmetry difference between rhombohedral, i.e., space group of R3c, and cubicperovskite, space group of Pm m 3 , within BFO films grown on cubicperovskite substrates previously 16,[19][20][21]23 . A BFO layer of ~95 nm is confirmed to grow on a ~50 nm LSMO electrode layer grown directly on the STO substrate. Note that both of the BFO and LSMO layers show stress/strain contrasts as denoted by white arrows, whereas the STO substrate show no such contrast. This implies both of the BFO and LSMO layers could be under the lattice strains caused by the lattice mismatch with STO substrate. In order to investigate the crystal structures of LSMO and BFO, nano-beam electron diffraction (NBED) technique was applied to BFO, LSMO and STO with a probe size of ~40 nm as denoted by the three circles in each material. The corresponding NBED patterns are shown in Fig. 1(b-d), respectively. It should be noted that while the symmetry of the pattern in Fig. 1(d), i.e., STO, matches that of [011] zone axis of cubicperovskite, those in Fig. 1(b), i.e., BFO, and 1(c), i.e., LSMO, correspond to [211] zone axes of rhombohedral with the rhombohedral signature Bragg's reflections such as 213, 113, 213 and 113. Note that the indices for BFO are based on hexagonal notation as mentioned earlier. These reflections have been confirmed to be used as the fingerprints of rhombohedral symmetry within BFO because they show up in rhombohedral BFO only 16,[19][20][21]23 . In other words, they overlap none of Bragg's reflections from the other BFO symmetries (including the pseudocubic) as discussed previously 23  In order to acquire a direct insight about the status of the lattice mismatches among the three materials, the NBED patterns were acquired from the BFO/LSMO and LSMO/STO interfaces as shown in Fig. 2(a,c) respectively. Note that the high index Bragg's reflections from BFO and LSMO (encircled in white) split along out-of-plane orientation in Fig. 2(a). The rectangle areas at the top and bottom are enlarged in supplementary Fig. S1 to show the split clearly. Besides, the in-plane Bragg's reflections from BFO and LSMO (encircled in orange) perfectly overlap with no split, indicating that the in-plane lattice spacing of BFO is forced to match that of LSMO. This strongly suggest that the BFO/LSMO interface is atomistically coherent along in-plane orientation. In other words, the lattice mismatch between BFO and LSMO exerts the lattice strain in the BFO film by forcing the in-plane lattice spacing of BFO, i.e., (120) BFO , to match that of LSMO, i.e., (120) LSMO . In order to visualize how the NBED pattern in Fig. 2(a) is different when no lattice strain exists in the BFO film, the structure factor, F hkl ,

Results and Discussion
hkl n n n n n www.nature.com/scientificreports www.nature.com/scientificreports/ where hkl represents a specific Bragg's reflection; f n is the atomic scattering factor for atom n at fractional coordinates (x n , y n , z n ), was calculated by using the crystallographic data, i.e., space group, lattice parameter, and basis atom locations, of unstrained rhombohedral BFO 26 and unstrained rhombohedral LSMO 27 materials in tandem with epitaxial relationship (1) as shown in Fig. 2(b). Note that the high index Bragg's reflections from BFO and LSMO (encircled in black) split radially with respect to the direct beam located at the center. This is in clear contrast with the splits showing up along only out-of-plane orientation in Fig. 2(a). In addition, the in-plane Bragg's reflections from BFO and LSMO (encircled in orange) in Fig. 2(b) split slightly along in-plane orientation owing to the different in-plane lattice spacings, i.e., d in-plane of BFO = 0.2787 nm 26 and d in-plane of LSMO = 0.2742 nm 27 , whereas the corresponding Bragg's reflections in Fig. 2(a) (encircled in orange) show no sign of splits. Thus, Fig. 2(a,b) clearly demonstrate the difference of the NBED patterns between with strain, i.e., Fig. 2(a), and with no strain, i.e., Fig. 2(b), within the BFO film. Note that the reflections denoted with red arrows in Fig. 2(a,c) are the result of double diffraction 28,29 . Now let us turn our attention to the underlying LSMO/STO interface. An NBED pattern from the interface is shown in Fig. 2(c). It is readily noticed that the Bragg's reflections from LSMO and STO overlap completely with no sign of splits. This result is similar to the structure factor calculation for the unstrained LSMO/STO interface that uses the crystallographic data of unstrained LSMO 27   www.nature.com/scientificreports www.nature.com/scientificreports/ In order to acquire more direct information about the structural detail about the BFO/LSMO interface, an atomic resolution high angle annular dark field (HAADF)-scanning TEM (STEM) image was acquired along [011] STO zone axis, i.e., the same zone axis as in Figs 1 and 2, as shown in Fig. 3. The image readily shows that the (120) BFO lattice planes runs smoothly across the BFO/LSMO interface through (120) LSMO lattice plane with no sign of lattice imperfections such as dislocations or stacking faults that could be the sources of the strain relaxation at the interface. This directly demonstrates that the lattice strain caused by the lattice misfit between BFO and LSMO is exerted in BFO with no strain relaxation. Thus, the HAADF-STEM image is consistent with the strain contrasts shown in Fig. 1(a) and the NBED analysis result discussed with Fig. 2. Now that the lattice misfit is proved to be stored as the elastic energy, i.e., the lattice strain, within the BFO layer, it is worth focusing more on the details about the behavior of the lattice strain. In Fig. 4 is shown a wide range X-ray reciprocal space mapping (XRSM) that includes the Bragg's reflections from BFO, LSMO and STO. Note that while a rhombohedral signature Bragg's reflection, i.e., 213, are clearly visible for both of BFO and LSMO (see the inset at the right-bottom for more details), this reflection does not exist for STO. This is consistent with the NBED result in Fig. 2 and further verifies the rhombohedral crystal structure identified for BFO. It is worth noting that the crystal structures together with ferroelectric polarization orientation within the BFO films grown on LSMO/STO was previously investigated by using quantitative aberration-corrected STEM technique which directly measures the locations of the Bi and Fe atoms in a HAADF-STEM image with pico-meter accuracy 31,32 . The BFO films were suggested to have either rhombohedral or tetragonal symmetries 31,32 . On the other hand, our result demonstrates that the www.nature.com/scientificreports www.nature.com/scientificreports/ rhombohedral symmetry of BFO can be unambiguously verified by using the conventional techniques of NBED and XRSM.
Another characteristic worthy of notice is that in-plane Bragg's reflections for BFO, LSMO and STO are all lined up along out-of-plane orientation, indicating in-plane lattice planes, i.e., (120) BFO , (120) LSMO and (011) STO , have the same lattice spacing. This is consistent with the NBED results shown in Fig. 2. Since x-ray diffraction based techniques provide the superior accuracy to NBED in determining lattice spacings, the 306 and 426 Bragg's reflections are used to accurately derive the in-plane lattice spacings of (120) for the BFO and LSMO. As a result, they turn out 0.2759 for BFO and 0.2750 nm for LSMO, which match 0.2759 nm of (011) lattice plane distance in  www.nature.com/scientificreports www.nature.com/scientificreports/ unstrained STO 30 . This confirms that the lattice spacings of BFO and LSMO are the same as that of STO along in-plane orientation. Note that the measured 0.2759 nm of (120) BFO is ~1.0% smaller than 0.27870 nm of the corresponding lattice plane spacing in unstrained bulk BFO 26 . This indicates compressive strain is applied in BFO layer along in-plane orientation. Now let us consider how the ~1.0% of the in-plane compressive strain affects the lattice plane along out-of-plane orientation by measuring the lattice plane distance along out-of-plane orientation. By using 306 reflection of BFO, the lattice plane distance of 102 is precisely calculated to be 0.4058 nm. This value is in good agreement with the out-of-plane lattice spacing, i.e., ~0.406 nm, measured for a BFO film grown on LSMO/STO by using quantitative STEM technique 33 . Note that this value is ~2.4% larger than 0.3961 nm of (102) lattice plane distance in unstrained bulk BFO 26 . The larger tensile strain value of ~2.4% along out-of-plane orientation than the ~1.0% of the compressive strain along in-plane orientation is considered to be associated with the fact that two-dimensional, i.e., biaxial, in-plane compressive strain effect shows up as one-dimensional, i.e, uniaxial, tensile stress along out-of-plane orientation. This is in agreement with the similar trend, i.e., the in-plane biaxial tensile strain causing a larger amount of uniaxial compressive strain along out-of-plane orientation, found in epitaxial BFO films previously 21,34 . Based on the results from NBED, HAADF-STEM and XRSM, it is concluded that the ~1.0% compressive strain exerted in BFO along in-plane orientation causes ~2.4% of tensile strain in BFO along out-of-plane orientation. Note that the current conclusion of rhombohedral crystal structure found within BFO film grown on LSMO/STO is in agreement with the previous works in that ~1.0% of the compressive strain imparted from LSMO/STO substrate is within the biaxial lattice strain range, i.e., between ~2.5% compressive and ~0.35% tensile strains, in which the rhombohedral crystal structure is found to be stable 23 . It is also noteworthy that the rhombohedral crystal structures found within the current BFO film could be slightly different in terms of the lattice parameter and rhombohedral distortion angle, i.e., α angle, from those found in other BFO films and bulk BFO. This is because the crystallographic details of the rhombohedal BFOs in terms of α angle, lattice parameter, and the locations of basis atoms depend on the characteristic lattice strain statuses, i.e., the amount and type of the particular lattice strain, induced by the particular lattice mismatch with the substrate material 23,24 . www.nature.com/scientificreports www.nature.com/scientificreports/ Now let us turn our attention to the BFO film grown on YAO substrate. Figure 5(a) is a cross-sectional BF TEM image of a BFO layer grown on (100) YAO substrate, showing that a ~90 nm thick BFO layer grows on the YAO substrate. Note that the BFO layer shows the contrasts presumably associated with either low-angle grain boundaries or ferroelectric domain walls (denoted by white arrows) 35 , and the dislocations populated area (denoted by blue lines) at the BFO/YAO interface. The NBED patterns from BFO and YAO are shown in Fig. 5(b,c), respectively. Figure 5(c), i.e., for YAO, corresponds to that of [010] YAO zone axis, whereas the four-fold symmetry showing up in Fig. 5(b), i.e., for BFO, could be interpreted for either [010] zone axis of cubicperovskite or [421] zone axis (in hexagonal notation) of rhombohedral as discussed previously 16,19,21 . Note that the red arrows in Fig. 5(c) indicate the reflections caused by double diffraction 28,29 . The characteristics of Bragg's reflections in Fig. 5(b,c) are consistent with those in XRSM data (see Supplementary Figure S2), indicating that TEM data in Fig. 5 represent volume-averaged characteristics within the BFO film grown on YAO substrate.
In order to determine the crystal symmetry of BFO, another cross-sectional TEM sample is prepared along [001] YAO zone axis as shown in Fig. 6. The BF image in Fig. 6(a) show highly similar characteristics with those found in Fig. 5(a) in terms of the contrasts attributable to either low-angle grain boundaries or ferroelectric domain walls (denoted by white arrows), and the area with high density of dislocations (denoted by blue lines) at the BFO/YAO interface. While the NBED pattern of YAO shown in Fig. 6(c) corresponds to [001] YAO zone axis as expected, the NBED pattern of BFO in Fig. 6(b) clearly shows the rhombohedral signature Bragg's reflections such as 213, 113, 213 and 113. These unambiguously identify the crystal symmetry of BFO as rhombohedral rather than cubicperovskite or others. Another NBED pattern is acquired at the BFO/YAO interface to investigate the lattice mismatch-induced strain status in BFO layer as shown in Fig. 6(d). Note that the reflections denoted with red arrows are resulting from double diffraction 28,29 . Unlike the NBED pattern at the BFO/LSMO in which the Bragg's reflections from BFO and LSMO lined up along out-of-plane [(see Fig. 2 In order to add more insight, an atomic resolution HAADF-STEM image was acquired at the BFO/YAO interface as shown in Fig. 7. Unlike the atomic resolution HAADF-STEM image at the BFO/LSMO interface in which the lattice planes of both BFO and LSMO are lined up with no sign of lattice imperfections (see Fig. 3), the BFO lattice plane along in-plane orientation, i.e., (102) BFO , clearly show the existence of the dislocations as indicated by white arrows. This clearly indicates that ~6.8% of the lattice mismatch calculated between (102) BFO and (020) YAO is confirmed to be too large to be stored as the elastic energy, i.e., the lattice strain, within BFO layer except for a couple of nano-meter of the strained area denoted by the blue lines. On the other hand, ~1.0% of the lattice mismatch between (120) BFO and (120) LSMO along [011] STO zone axis (see Fig. 3) turned out to induce the lattice strain with no sign of lattice imperfections. Thus, the current HAADF-STEM results in Figs 3 and 7 clearly demonstrate the importance of the atomistically coherent BFO/substrate interface for the lattice mismatch to be stored as the elastic energy, i.e., the lattice strain, in BFO film.
It is interesting to note that while some previous works have found the crystal structure of BFO grown on YAO as so called "supertetragonal" or "T-like" with the out-of-plane (c)/in-plane (a) lattice vector ratios ranging from ~1.23 to ~1.27 9,11 , the BFO grown on YAO in the current work turns out to have rhombohedral crystal structure. The discrepancy is considered to be associated with the different growth surfaces of the YAO substrates that provide different templates, i.e., different atomistic structures, for BFO to grow onto. For example, the in-plane lattice vectors of b and c for the (100) YAO used in the current study are ~0.7371 nm and ~0.5180 nm whereas the (110) YAO with a pseudocubic in-plane lattice parameter of 0.3704 nm (which is equivalent to the (010) YAO with in-plane lattice parameters of ~0.5330 nm and ~0.5180 nm in orthorhombic notation) was used in the previous works 9, 11 . In fact, a very recent study showed that the crystal structure of the BFO grown on (100) YAO is rhombohedral 37 , which is in good agreement with the current study. This clearly demonstrates that: (1) the lattice strain status and the following crystal structure in BFO film are highly affected by the types of growth planes as well as the types of substrate materials; (2) the epitaxial relationship between BFO and substrate should be identified to quantitatively evaluate the misfit strain applied in BFO film.

summary
The crystal structures as well as lattice strain status were investigated for the BFO films grown on LSMO/STO and YAO substrates using ultra high vacuum r.f. magnetron sputtering. For the BFO film grown on LSMO/STO, the TEM and NBED results indicate that its crystal structure as rhombohedral. The epitaxial relationship identified by the NBED and precise lattice spacing measurement using the XRSM reveal that the BFO film is under ~1.0% of compressive lattice strain. The HAADF-STEM technique confirms the applied compressive lattice strain in BFO by directly showing the atomistically coherent BFO/LSMO interface. On the other hand, the crystal structure within the BFO film grown on YAO turns out rhombohedral with no sign of lattice strain from the NBED and structure factor calculation results although the lattice mismatch is estimated ~6.8% on the basis of the epitaxial relationship identified. HAADF-STEM technique clearly show the sign of the lattice strain relaxation, i.e., the dislocation formation at the BFO/YAO interface. This indicates that ~6.8% of lattice mismatch is too large to exert the corresponding amount of compressive lattice strain within the BFO film.
The current work demonstrates the highly synergetic combination effect of the TEM and XRSM techniques to precisely determine the crystal symmetry, epitaxial relationship, and lattice strain status within BFO films. The www.nature.com/scientificreports www.nature.com/scientificreports/ experimental results clearly show the importance of: (1) identifying the epitaxial relationship between the BFO film and the substrate material for the precise evaluation of the lattice mismatch, and (2) the atomistically coherent BFO/substrate interface for the lattice mismatch to exert the lattice strain.

Methods
The BFO thin films were grown on a (102) LSMO buffered (100) STO and a (100) YAO substrates using ultra-high vacuum (<2 × 10 −6 Pa) r.f. magnetron sputtering (ULVAC Co. Ltd.) at 550 °C. The detail about the deposition of the LSMO bottom electrode layer on STO substrate is given elsewhere 38 . The cross-sectional TEM samples were prepared by the focused ion beam technique, FEI Nova 600, with Ga ion beam. ~1 μm-thick Pt thin film was deposited on the surface of the sample to prevent the possible surface damage and re-deposition during the milling process. Then, the Ga ion beam energy gradually decreased from 30 to 1 keV to minimize ion beam induced damage. For atomic resolution HAADF-STEM analysis, a Cs-corrected TEM of JEOL JEM-ARM200F operated at 200 keV was used. For BF and NBED, a 200 keV JEOL JEM-2100F was used together with a Gatan Orius 833 CCD camera specifically designed with electron beam damage resistant scintillator. XRSM was performed using Rigaku SmartLab diffractometer with CuKα radiation.