Nanoscale Control of Phase Variants in Strain-Engineered BiFeO3

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Nanoscale Control of Phase Variants in Strain-Engineered BiFeO3 Rama K. Vasudevan,† Yunya Liu,‡,§ Jiangyu Li,§ Wen-I. Liang,|| Amit Kumar,^ Stephen Jesse,^ Yi-Chun Chen,# Ying-Hao Chu,|| Valanoor Nagarajan,† and Sergei V. Kalinin*,^ †

School of Materials Science and Engineering, University of New South Wales, Sydney, NSW 2052, Australia Faculty of Materials, Optoelectronics and Physics, and Key Laboratory of Low Dimensional Materials & Application Technology of Ministry of Education, Xiangtan University, Xiangtan, Hunan 411105, China § Department of Mechanical Engineering, University of Washington, Seattle, Washington 98195-2600, United States Department of Materials Science and Engineering, National Chiao Tung University, Hsinchu 30010, Taiwan, Republic of China ^ The Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States # Department of Physics, National Cheng Kung University, No. 1, University Road, Tainan 70101, Taiwan, Republic of China

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bS Supporting Information ABSTRACT: Development of magnetoelectric, electromechanical, and photovoltaic devices based on mixed-phase rhombohedral tetragonal (R-T) BiFeO3 (BFO) systems is possible only if the control of the engineered R phase variants is realized. Accordingly, we explore the mechanism of a bias induced phase transformation in this system. Single point spectroscopy demonstrates that the T f R transition is activated at lower voltages compared to T f T polarization switching. With phase field modeling, the transition is shown to be electrically driven. We further demonstrate that symmetry of formed R-phase rosettes can be broken by a proximal probe motion, allowing controlled creation of R variants with defined orientation. This approach opens a pathway to designing next-generation magnetoelectronic and data storage devices in the nanoscale. KEYWORDS: Bismuth ferrite, mixed phase, cantilever resonance tracking, PFM

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n recent years, much attention has been attracted to novel materials and device concepts enabled by interfaces and domain walls in oxides.1 4 BiFeO3 (BFO) has become one of the foci for these studies, with numerous key developments including magnetoelectric coupling, domain wall conductance, and bias-induced metal insulator transitions.5 8 The recent discovery of a strain-induced morphotropic-like phase boundary (MPB) in BFO films grown on (001) LaAlO3 (LAO) substrates has generated further interest to this material.9 11 The initial report by Zeches et al. showed that compressive strain imposed by the substrate could stabilize the tetragonal-like phase.12 These films also exhibit mixed-phase regions consisting of rhombohedral-like (R) “needle” domains embedded into a tetragonal-like (T) matrix, with ability to selectively switch between the two phases by application of electric fields.13 The T R mixture exhibits a giant piezoelectric coefficient, d33, enabled by phase boundary motion, in contrast to traditional ferroelectric materials in which extrinsic d33 contributions arise from movement of 90 and 180 domain walls under applied fields.14 16 This finding of a strain-stabilized morphotropic-like phase boundary state in a ternary compound is well outside the traditional ferroic- and stress-driven physics of oxides, resulting in strong interest to this system. Very recently it was found that there exists an enhanced magnetic moment in the highly strained R-phase in this structure, with the magnetic moment lying along the needle’s long axis.17 r 2011 American Chemical Society

The strong directional dependence of enhanced properties enabled by T R boundaries necessitates directional control of the R phase, as well as understanding of which R-phase morphologies can be created. If achieved, it will allow nanoscale design of materials with unique electromechanical and magnetic properties controllable by external electric fields. Despite some efforts,13,18 the fundamental understanding of polarization switching and the field-induced T f R transition remains elusive, precluding reliable control of these materials. Here, we explore the key features of the bias-induced phase transformations in BFO, including the phase transformation sequence and domain morphologies, through a combination of single-point band excitation (BE) piezoresponse force spectroscopy, domain imaging, and phase field modeling. We further demonstrate that a high degree of control over the rhombohedral phase morphology can be attained through variation of tip-scan angle, point grid densities and proximal probe motion. By determining the exact driving force for the transition, we develop a technique to control the resulting structures, which ultimately allows selective writing of phase variants. These techniques form

Received: May 20, 2011 Revised: June 23, 2011 Published: June 24, 2011 3346

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Figure 1. (a) Virgin AFM topography of the film, showing clear band structures with needle-like R domains. (b) Vertical amplitude PFM image of the region in (a), with higher amplitude response from the needles arising from higher intrinsic d33 of the R phase. Phase-field simulation of R-phase needles embedded in a T-phase matrix is shown in (c). (d) A schematic of the film studied.

a possible basis for high-level control of enhanced magnetic moments in epitaxial films of BFO. PFM Spectroscopy of Phase Transitions in (T) BFO. As a model system, we have chosen the (T) BFO sample grown on LAO substrate having the almost pure T phase in the as-grown film.10,19 To illustrate the phase behavior, Figure 1a is the topography in a 1 μm2 region, showing the banded needle-like structures that comprise the R-phase, as well as the tetragonallike matrix. The characteristic surface corrugations result from the lattice mismatch between R and T phases,20 much like classical ferroelastic domain walls in ferroelectrics. The vertical amplitude PFM image, taken simultaneously with the topography scan, is shown in Figure 1b. Interestingly, the needles appear to show a brighter contrast in the PFM image, a result of higher intrinsic piezoelectric coefficient (d33) of the R phase.11 The morphology of R phase can be understood from the minimization of potential energy of the system, as verified from phase-field simulations showing R-phase needles embedded in a T-phase matrix, illustrated in Figure 1c. Additionally, careful inplane PFM measurements (Supplementary S1, Supporting Information) indicate the presence of weak, striped in-plane domains in the matrix, indicating the presence of a monoclinic distortion within the T phase. These have also been reported elsewhere for similar films.19,21 Since this distortion is small and no effect of monoclinic distortion on phase transition was detected, here for simplicity we refer to the matrix as the T phase. A cross section of the film structure is shown in Figure 1d. Previously, it was shown that application of bias can result in transition between R and T phases.12,13 We note that the transition from the initial as-poled T phase to R phase could occur through three possible routes, as illustrated in Figure 2:

(1) The transition could proceed with simultaneous switching of the polarization and the phase at a critical bias (triggered transition22), T f ( T, R). (2) The phase transition and the polarization switching are independent, with differing onset voltages. In this case it would be possible to obtain a new phase before polarization switching (T f R transition before T f T), or vice versa, depending on which transition has the lower critical bias. (3) It is also possible that the phase transition from T f R may involve an intermediate (i.e., transient) T domain that reverts to the initially poled direction upon removal of the external bias, T f ( T, R)in-field f R. Scenarios 1 and 2 can be directly differentiated through tip pulse-bias experiments with subsequent imaging of resultant domain morphologies. However, scenarios 2 and 3 would result in the same final state, so a spectroscopic experiment, in which in-field data are acquired while the transition is occurring, is necessary. Further, for scenarios 2 and 3 the question arises as to whether mesoscopic areas of the thermodynamically less stable phase can be formed, i.e., if critical bias for T f T transition is larger than for T f R transition, whether pure T or pure R phase regions can be created. Here, we explore the phase transition sequence in T-BFO through PFM single-point switching and spectroscopic experiments. The topography scan prior to the tip-bias experiments is shown in Figure 3a. The tip was then moved to six different sites within the scanned area, and at each site a 1 s pulse of differing amplitude was applied. The results of the experiment are highlighted in the topography and vertical (amplitude) PFM images in panels b and c of Figure 3, respectively. At low bias ( 5, 6 V), there is no evidence of any switching, as can be inferred from the 3347

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Figure 2. Schematic of possible transition pathways. Note that the fully switched case in scenario 3 has not been shown, but it would be identical to that shown in scenario 2. Also, note importantly the same final state in the case of scenario (2) and scenario (3). Thus, determining the mechanism requires a spectroscopic experiment.

lack of any contrast around those sites in the vertical PFM image. At 7 V, however, a single needle of R phase appears in the topography image; however, no other changes in topography or PFM image are observed (Supplementary S2, Supporting Information). At higher bias, however, clear evidence of 180 (T f T) domain switching accompanied by the precipitation of the needle-like R phase is observed. Similar behavior was observed for positive bias pulsing of prepoled T regions (Supplementary S3, Supporting Information). These results confirm that scenario 1 outlined above can be ruled out. However, the possibility of a transient T domain (scenario 3) cannot be ruled out in this manner. To further investigate the in-field behavior, we performed single-point spectroscopic experiments in which a unipolar triangular waveform of increasing amplitude was applied to the tip and the response was measured over a range of frequencies using the band-excitation (BE) method.23 We note that pure PFM signal (electromechanical response amplitude) is insufficient to unambiguously differentiate the R and T phases due to the presence of the multiple domains and domain walls in the

proximity of the tip resulting in variation of signal amplitude and convolution between vertical and lateral PFM signals.24 However, nucleation of the R phase is associated with strong changes in strain state of the system (as exemplified by the presence of topographic corrugations in Figure 1), and this can be expected to result in changes in tip surface contact geometry. The latter can be established from the changes in cantilever resonant frequency, providing a yet-unexplored approach for probing local bias-induced transitions. The waveform applied to the tip is drawn in Figure 3d. The BE response was tracked over the frequency spectrum and fitted to a simple harmonic oscillator (SHO) model.25 After SHO fitting, the resonance, maximum amplitude and phase at each bias point in the sweep cycle could all be extracted. A spectrogram of the amplitude and phase response at a particular point is shown in Figure 3e. The result of the SHO fitting is shown in the plot of resonance and phase in Figure 3f. A significant resonant frequency shift at the relative (absolute) maxima (red dotted lines on the graph) during each voltage sweep is readily apparent. These frequency shifts in cantilever resonance thus are the fingerprints of the 3348


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Figure 3. Topography scan of the film before (a) and after (b) pulse experiments. Pulses greater than 7 V generated a topographical change consistent with formation of the R-phase. Vertical PFM Amplitude image (c) in the same region indicates that a 180 polarization switch did not occur for the 7 V pulse. Single point spectroscopy data were captured while sending the dc waveform drawn in (d) to the tip. The (absolute) maxima on some sweeps are indicated by vertical red dashed lines. The captured spectroscopic data from one point are displayed in (e), with amplitude (above) and phase (below) as a function of frequency. This was then fitted to an SHO model; the results are displayed in (f) with cantilever resonance (phase) plotted on the left (right) axis. Resonance shift before a phase flip indicates a phase transition prior to polarization switching. (g) Histogram of first incidence of frequency shift and phase flip voltages, discerned from 100 measurements. (h) Thermodynamic analysis showing trends in polarization components as a function of electric field.

formation of the R-phase needles. Histograms for first incidence of frequency shift and phase flip are provided in Figure 3g, indicating the T f R transition (critical bias ∼ 1.9 V) occurs well before T f T switching (as indicated by phase flip) at ∼ 6 V (Supplementary S4, Supporting Information). In addition, the constancy of the measured phase at the voltages at which frequency shift occurs further suggests that there is no transient T domain formed. These observations are corroborated by the thermodynamic analysis, suggesting that the T f R transition is expected at ∼4.2 108 V/m, while T f T polarization switching requires a higher coercive field of ∼8.9 108 V/m, as shown in Figure 3h. Given the film thickness of 20 nm, these analyses are consistent with the critical fields estimated for phase transformation

and domain switching from the SPM experiments. Thus, through this combination of thermodynamic modeling, spectroscopic data, and PFM tip-bias experiments, we can conclude that scenario 2 is most plausible for the transition; i.e., the phase transition proceeds prior to any ferroelectric switching and, hence, it is possible to form the R phase without 180 tetragonal switching. Rosette Formation. Understanding of the structural pathway of the local bias-induced transition in T-BFO now provides an avenue to determine the collective interactions and domain morphologies in this system. As an initial test, we select a 2 2 μm2 region and apply a 5 5 grid of pulses ( 10 V for 200 ms). The results are shown in the topography in Figure 4a. This grid displays a striking pattern, with needles forming around the tip 3349


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Figure 4. Elementary switching and formation of rosette structures. (a) Topography after a 5 5 grid of pulses. Vertical PFM amplitude of the same area as displayed in (b), with a schematic of the morphology in the white boxed region drawn in (c). Phase-field modeling (d) reveals four R variants encase the switched T region in the rosette. The R variants couple with in-plane components of the tip field, as the driving force for the transition is electrical in nature.

sites. The vertical amplitude PFM image, in Figure 4b, shows that the R-phase needles form around the switched T phase and tend to assemble in rosette-like structures. This is illustrated in the diagram in Figure 4c. Thus a single point elementary switching event leads to formation of all four R variants, as would be expected for an electrically driven transition in a rotationally symmetric field.26 The phase-field simulation, shown in Figure 4d confirms this; the formation of an R phase rosette is driven by the tip-induced electric field adjacent to the tip, which has both inplane and out-of-plane components that favors the formation of R phase. On the other hand, the electric field directly underneath the tip has only an out-of-plane component that favors the T domain, as observed in the center of the simulation. The fact that rosettes (as opposed to complete circular rings) of R phase are formed is due to elastic interactions; i.e., compressive strain due to the surrounding T matrix is too large to allow formation of large continuous regions of pure R phase. We also note here that it is also possible to reverse this transition—i.e., applying positive bias will flip the polarization of the T phase, as well as delete any nearby rhombohedral variants (Supplementary S5, Supporting Information). Control of BFO Patterns. Implementation of R T interfacebased magnetoelectronic and electromechanical devices necessitates deterministic control of phase morphologies, i.e., orientation and density of R-phase bands. Here we explore the possibility of stabilizing certain orientations and deleting others by moving the tip at different biases and orientations,27 as well as

patterning dense grids, to break the tip-induced field’s rotational symmetry. The ubiquitous aspect of the R phase is the formation of the banded structures formed by the closely spaced lamellae of the R phase, stabilized by the elastic interactions. The orientation of the R T lamellae was explored by Kuo et al.11 who showed that the in-plane normal to the bands are aligned subject to minimization of elastic and depolarization energies. The band direction generally follows in-plane angles within ∼15 of the [100]/[010] axes of the host lattice. The formation of the R-phase lamella minimizes one of the components of the stress (along the band direction) and defines the periodicity of R T lamellae and relative fractions of the phases. However, minimization of the second strain component limits the width of the band and necessitates the formation of a band system in orthogonal direction. This two-level instability necessitated by strain compensation should be considered in analyzing the possible degrees of control of R T morphologies. We further note that in the ideal case we aim to control (a) the direction of the bands (between equivalent directions) and (b) orientation of R-phase lamella within the bands (see Supplementary S6 in the Supporting Information for more information and schematics). Here, we explore the universality of the band formation and presence of alternative domain morphologies. To explore the collective interactions between the rosettes, we select a 2 2 μm2 region in the sample and apply a grid of 50 50 pulses, each 10 V for 200 ms. The results of such an 3350


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Figure 5. a Topography after a grid of 50 50 pulses was applied in a 1.5 μm2 region, showing bands of needles forming in the switched region. (b) Phase-field simulation of R-phase band induced by broken symmetry due to proximal probe motion along grid points. To study angle dependence, an array of 30 30 10 V/200 ms pulses were applied to a 2 μm2 with the tip scan angle at (c) 0, (d) 45, and (e) 60 (Topography is shown in each case, and Fourier transforms are shown inset.)

experiment are shown in the topography image in Figure 5a. The evolution of the morphology is striking, with two key features to note. First, there appears to have formed bands of R/T lamellae growing in perpendicular directions, much like the ground state of the mixed phase regions. Second, the vertical boundaries of the grids show a braided structure. This latter feature is even more apparent in switching experiments where boxes are written by the moving SPM tip (Supplementary S7, Supporting Information). Overall, the result implies very strong collective interactions when the spacing between points is kept small. Phase-field simulations of a closely spaced grid also predict this result, as shown in Figure 5b. Since the dense grid of points produces banded structures of R-phase needles, we then explore the variation in the final structure while altering the scan angle of the tip. The topography scans of 3 μm2 regions after applying a grid of 50 50 10 V (for 200 ms) points within a 2 μm2 box are shown in Figure 5 for scan angles of 0 (Figure 5c), 45 (Figure 5d), and 60 Figure 5e). In each case, some bands of needles can be seen to form, and the structure is highly complex. However, it appears that in the case of the higher scan angle (60), the structure is unable to form as many bands. To further explore this, fast Fourier transforms (FFT) of the topography images were calculated (processing described in Supplementary S8, Supporting Information). Two sets of intensity peaks can be found in the Fourier plot in panels c and d of Figure 5, corresponding to spacing between the needles and the spacing between the bands

of needles, respectively. Analysis reveals the spacing of the needles is ∼15 20 nm and the spacing between bands is ∼35 nm. In the case of Figure 5e, the Fourier plot is more diffuse. Although the spots corresponding to the periodicity of the needles can be readily seen, the spots expected for the spacing between bands are not. Indeed, the diffusive plot suggests little periodicity in the bands. This confirms that altering the scan angle in this fashion reduces the ability of the structure to form bands, and hence forces the adoption of a kind of frustrated geometric structure. The grid orientation therefore provides another level of control of the resulting morphology. SPM Based Control of R Phase Variants. Noting that some degree of band control has been established, we determine whether we can selectively write rhombohedral variants by writing pulses along a line for differing sample orientations. Since the formation of the R phase is electrically driven, the variants couple with the in-plane components of the tip field, and hence it is probable that some control may be established through breaking the tip-field’s radial symmetry via motion of the biased tip in different orientations. The results of writing lines of 30 pulses (each 10 V for 200 ms) over a ∼1.5 μm length for differing sample orientations are shown in the topography images in Figure 6a d. In the first case, the sample was oriented parallel to the cantilever, i.e., along the [100] axis, and then in subsequent experiments the sample was rotated clockwise 30 (Figure 6b) and 60 (Figure 6c) and counterclockwise 90 (Figure 6d). 3351


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Figure 6. Topography after a single line of 30 pulses ( 10 V/200 ms, across ∼1.5 μm) was applied to the sample with the sample oriented at (a) 0, (b) 30 (c) 60 and (d) 90, with respect to the cantilever, which was along [100]. To demonstrate control, vertical lines of one particular variant were written by biasing the tip at 9V and writing three closely-spaced lines, by moving the tip vertically downwards at 200nm/s, as shown in (e). To demonstrate writing of two phase variants, the letter ‘T’ was formed by writing rectangles with scan angle 0 and 90 with the tip biased at 9V. This is shown by the vertical (amplitude) PFM image in (f) (close-ups of the two variants are shown (boxed) as inset). The top horizontal stroke is (predominantly) one variant; the vertical stroke is (predominantly) the other. A single line written at 200nm/s, with the tip biased at 10V, is shown in the topography (g) and vertical PFM amplitude image (h). The black circles indicate secondary orthogonal bands forming to reduce strain in the system.

From the topography images it is clear that needles form parallel to the step edges in Figure 6a, whereas the alternative arrangement, where the needles are roughly perpendicular to the step edge, is favored in Figure 6 c,d. In Figure 6b, however, we notice that both possible variants are formed. Thus, by simply varying the orientation of the sample with respect to the tip, it becomes possible to select which R-phase variants are formed. This technique can be extended for multiple lines, wherein closely spaced unidirectional lines are written by the biased tip. As shown in Figure 6e, this results in the formation of just one R-phase variant. Similarly, selection of phase variants is also possible by writing boxes and altering the scan angle, an example of which is shown in the “T” in Figure 6f. In this instance, one variant group (with needles oriented predominantly vertically) comprises the top section of the “T”, while another variant group (with needles aligned horizontally) comprises the bottom section. The increase of the bias during line writing results in the insignificant increase of the R band and formation of T switched core. At the same time, it leads to the formation of the secondary R bands perpendicular to the initial orientation.

This behavior is shown in (topography) Figure 6g and (vertical PFM amplitude) Figure 6h of a single line written by slowly moving the tip biased at 10 V. The secondary bands forming are circled in the PFM amplitude image. We note that this behavior reflects the elastic instability if the material, i.e., formation of the band in one direction, minimizes the strain along the band axis. However, it leads to the increase of the driving force for the formation of perpendicular R-phase lamellae. This instability mechanism is highly reminiscent of that involved in solidification and viscous fingering, and leads to comparable dendrite-like morphologies.28 The ability to control the T f R transition is instrumental for a number of device applications, in addition to providing an ideal model system to study the fundamentals of bias-induced phase transitions. Here we have presented controlled, field-induced writing and deletion of selected phase variants (as opposed to domain variants in ordinary ferroelectrics) through probe motion, which represents a new paradigm for information storage. The unique properties of the R phase in these structures could also be utilized for a wide variety of magnetoelectric devices, wherein controlled writing of the needle structures could be used 3352


Nano Letters to align magnetic moments in coupled layers. Finally, the induced formation of frustrated geometric structures in these systems, wherein bands of lamellae are unable to form, provides key insights into mechanisms of disordered and frustrated systems. Indeed, the engineering of highly unfavorable and frustrated structures could result in both new symmetry and new material properties unavailable in the ground state. Conclusions. In summary, through tip-bias experiments, phasefield modeling, and cantilever resonance shift, we shed light on the electric-field-induced phase transformation within multiphase BFO grown epitaxially on LAO substrates. From observation of simple switching forming rosettes, we then explore collective interactions that lead to formations of T/R lamellae for dense grids and subsequently discover a method of stitching nonground-state phases. It is found that the critical bias for T f R transformation is well below that for T f T switching. Further experiments indicate that control over the resulting morphology is readily achieved through three main methods, namely, changing the density of pulses applied by the tip, adjusting the scan angle, and altering the tip movement direction to write desired patterns. These control mechanisms pave the way for reliable and controlled writing of domains exhibiting enhanced magnetic moments within strain-engineered BFO and provide a model platform to study both field-induced phase transitions and disordered and frustrated systems. Methods and Materials. A 20 nm thick sample of BiFeO3 was grown on (001) LaAlO3 with a 15 nm thick buffer layer of LaNiO3 (to act as the bottom electrode), through pulsed laser deposition assisted with high-pressure reflection high energy electron diffraction. The growth mode was tuned to be layer-bylayer and then step flow modes. The sample was then studied using a commercially available scanning probe microscope (Asylum Research, Cypher model) equipped with NI PXI based band excitation controller to enable band-excitation (BE) measurements, with the data analyzed using MATLAB software (v7). Some images were also captured with a Veeco MultiMode AFM with Nanonis V controller. Image processing was carried out using WSxM v5.0,29 and graphs were made using GraphPad Prism v5.03. Thermodynamics analysis was carried out using Landau Devonshire phenomenological theory,12 and the phase field simulation was carried out using characteristic functions of variants as variables, as detailed elsewhere.30

’ ASSOCIATED CONTENT

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Supporting Information. Additional data sets and more detailed analysis. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT R.K.V. and V.N. acknowledge ARC Discovery Project DP1096669. The research at ORNL (A.K., S.J., S.V.K.) was conducted at the Center for Nanophase Materials Sciences, which is sponsored at Oak Ridge National Laboratory by the Division of Scientific User Facilities, U.S. Department of Energy. J.Y.L. acknowledges support of NSF (DMR#1006194) and ARO

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(W911NF-07-1-0410), and Y.Y.L. acknowledges support of NSFC (10732100 and 10972189). Y.H.C. would like to acknowledge the support of the National Science Council, R.O.C., under Contract No. NSC-99-2811-M-009-003.

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Nano Letters

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