Nanotechnology 18 (2007) 405701 (8pp)


Spatially resolved mapping of ferroelectric switching behavior in self-assembled multiferroic nanostructures: strain, size, and interface effects Brian J Rodriguez1,2 , Stephen Jesse1 , Arthur P Baddorf1,2 , T Zhao3,4 , Y H Chu3,4 , R Ramesh3,4 , Eugene A Eliseev5 , Anna N Morozovska6 and Sergei V Kalinin1,2,7 1

Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA 2 The Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA 3 Department of Materials Science and Engineering, University of California, Berkeley, CA, USA 4 Department of Physics, University of California, Berkeley, CA, USA 5 Institute for Problems of Materials Science, National Academy of Science of Ukraine, 3, Krjijanovskogo, 03142 Kiev, Ukraine 6 V Lashkaryov Institute of Semiconductor Physics, National Academy of Science of Ukraine, 41, Prospekt Nauki, 03028 Kiev, Ukraine E-mail: [email protected]

Received 8 June 2007, in final form 12 July 2007 Published 17 September 2007 Online at Abstract Local ferroelectric polarization switching in multiferroic BiFeO3 –CoFe2 O4 nanostructures is studied using switching spectroscopy piezoresponse force microscopy (SS-PFM). Dynamic parameters such as the work of switching are found to vary gradually with distance from the heterostructure interfaces, while nucleation and coercive biases are uniform within the ferroelectric phase. We demonstrate that the electrostatic and elastic fields at interfaces do not affect switching and nucleation behavior. Rather, the observed evolution of switching properties is a geometric effect of the heterointerface on the signal generation volume in PFM. This implies that the heterostructures can be successfully used in devices, since interfaces do not act as preferential sites for switching. At the same time, small systematic variations of switching properties within the ferroelectric component can be ascribed to the long-range elastic and electrostatic fields in the heterostructure, which can be visualized in 2D. (Some figures in this article are in colour only in the electronic version)

1. Introduction

the most rapidly developing areas of physics and materials science [1–4]. In particular, the electrical control of the magnetic ordering enables new classes of electronics devices [5], e.g. electrically switchable magnetic memories, spin valves, and tunneling junctions. The number of roomtemperature single-phase multiferroic materials is relatively small and is limited to, for example, BiFeO3 , BiMnO3 , and

Multiferroic materials exhibiting coupling between ferroelectric polarization, ferro- or antiferromagnetic ordering, and strain order parameters have recently emerged as one of 7 Author to whom any correspondence should be addressed.



© 2007 IOP Publishing Ltd Printed in the UK

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YMnO3 [2, 3, 6, 7]. In addition, while a number of materials with helical magnetic structures exhibit ferroelectric transitions at low temperatures [8], the coupling coefficients in such multiferroics are usually small. To overcome the scarcity of single-phase multiferroics, a number of groups have suggested the use of ferroelectric–ferromagnetic heterostructures [9] or self-assembled nanostructured films [4]. The development and optimization of multiphase multiferroic nanostructures for functional device applications necessitates understanding (a) the mechanisms of magnetoelectric coupling between dissimilar components, (b) the spatial variability of ferroic properties within a single phase, and (c) the switching mechanisms in single-phase regions and assemblies. The coupling between components can be due to both short-range interface-controlled interactions, such as a directexchange interaction between the ferroelectric antiferromagnet (BiFeO3 ) and the ferromagnet (CoFe2 O4 ), polarizationinduced changes of the valence of the magnetic cation across the interface (electric field effect), and long-range elastic interactions that couple to order parameters through piezoelectric and magnetostrictive effects [3, 6]. In general, a multiferroic assembly is expected to possess long-range elastic fields on the length scale of the film thickness and the size of single-phase regions [10]. In addition, interfaces between dissimilar materials are expected to result in partial charge transfer because of the differences in work functions, interface states, and ferroelectric polarization, resulting in electric fields on the length scale of the Debye length of the material. Short-range interface-mediated interactions and longrange elastic and electric fields can significantly affect the static and dynamic ferroelectric behavior of the ferroelectric component. The interface fields can result in regions with frozen polarization [11, 12]. Long-range elastic and electric fields can break the symmetry between antiparallel polarization states, resulting in ferroelectric imprint. Finally, in multiaxial ferroelectrics, the polarization orientation that minimizes the elastic energy will be favored, resulting in spatial variations of preferred in-plane polarization orientation. These factors will affect the switching behavior within single-phase regions, which ultimately controls the ferroelectric switching, and hence, the functionality of multiferroic assemblies. To achieve a comprehensive understanding of multiferroic nanostructures, the ferroic properties and coupling mechanisms should be investigated at length scales below the size of the constitutive phases (figures 1(a), (b)). The atomic structure of these heterostructure interfaces has been visualized by transmission electron microscopy [4], and theory [4, 13] can predict local order-parameter coupling from observed structure. However, to date, this behavior has been ascertained experimentally only on the macroscopic scale by temperature-dependent magnetization measurements [4]. The ferroelectric polarization reversal in multiferroic structures has been studied locally by piezoresponse force microscopy (PFM), magnetic force microscopy (MFM), and photoemission microscopy [14–19]. However, while the order parameter coupling and switching in self-assembled magnetoelectric structures have been extensively studied on the macroscopic level, and the order parameter coupling has been accessed on the nanoscale by MFM and PFM, little is known about the spatial variability of switching behavior at a length scale below the characteristic size of the

Figure 1. Schematics showing domain nucleation in BFO–CFO nanostructure samples. (a) The domain nucleation is controlled by the spatial distribution of nucleation centers when a uniform field is applied to a top electrode. When a tip is used as the top electrode, the domains nucleate under the tip, as shown in (b). (c) Line profile of the mixed piezoresponse signal of a domain wall in a BiFeO3 thin film showing ∼15 nm resolution. Mixed PFM image of an as-grown domain is shown as an inset.

single-phase regions. In other words, does the multiferroic heterostructure switch as a single-phase material, or is the switching behavior dominated by short- and long-range effects associated with the interfaces and the inherent spatial inhomogeneity of these systems? Do the interfaces between phases act as preferential nucleation sites, or is nucleation controlled by the intrinsic defects in the ferroelectric? Conversely, do the interfaces preclude nucleation due to the presence of frozen layers or dielectric constant mismatch effects? Would the strain result in strong imprint and polarization back-switching, similar to ferroelectric capacitors [20]? The answers to these questions are crucial for the optimization of devices based on multiferroic heterostructures and the establishment of their scaling limits. Here we investigate local ferroelectric domain structures and polarization switching properties of BiFeO3 –CoFe2 O4 (BFO–CFO) [4] self-assembled nanostructures by PFM and switching spectroscopy PFM (SS-PFM) [21, 22]. In these techniques, a sharp atomic force microscope (AFM) tip is used as a moving electrode that allows local static and dynamic properties of polarization within the heterostructure to be addressed. The information obtained in local and macroscopic techniques is compared in figure 1. When the dc bias is applied to a top electrode, the applied field is uniform and domains nucleate where the activation barrier for nucleation is lowest (nucleation sites). However, when the tip is used as the top electrode, domains can only nucleate beneath the tip due to its highly inhomogeneous field (figure 1(b)). Hence, nucleation activity and switching behavior can be correlated 2

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with materials microstructure in real space. In particular, here we aim to address the role of built-in elastic and electrostatic fields on the relative stabilities of antiparallel polarization orientations and the role of interfaces on domain nucleation and switching.

Topography, PFM amplitude, and PFM phase for a BFO– CFO nanostructure sample are shown in figures 2(a)–(c). As expected, the ferromagnetic nanopillars do not exhibit piezoelectricity, while the ferroelectric BFO thin film does. The SS-PFM maps of the work of switching, PNB, and NNB are shown in figures 2(d)–(f), respectively. Characteristic loops are shown from the BFO, CFO, and BFO–CFO interface regions in figure 2(g), and corresponding bias parameters are defined in figure 2(h). Note that for this material the well-saturated hysteresis loops and subsequent PFM imaging strongly suggest that the switching process is complete. Note that there is no hysteresis in the CFO loop, and the BFO loop appears to be slightly imprinted, but there is no vertical shift in the loop. The loop from the interfacial region has a slightly larger coercive field and lower magnitude of piezoresponse, but is still symmetric along the response axis. Corresponding line profiles of the work of switching and other switching properties are shown in figures 3(a) and (b). Note that the coercive biases and the imprint vary weakly with position (figure 3(a)), while the work, remanent piezoresponses, and the switchable piezoresponse all follow the same trend across the line profile (figure 3(b)). The similar behavior of parameters that scale with maximal response strength (i.e. the work of switching, remanent response, and PFM signal) suggests that the dominant effect that influences the loop shape is the presence of an interface with a non-piezoelectric material that reduces the signal generation volume. In other words, the observed evolution of switching properties can be a purely geometric effect. To verify this assumption, we develop a phenomenological approach for the interpretation of the hysteresis loop data beyond the characteristic biases. Briefly, we assume that for an ideal material away from defects and interfaces, the hysteresis loop shape is given by the phenomenological − functions PR+ 0 (V ) for the forward branch and PR0 (V ) for the reverse branch. The exact functional form of PR+ 0 (V ) and PR− (V ) is determined by the nanoelectromechanics of 0 the polarization switching for a given tip geometry and contact conditions and is not discussed here. In a realistic material, the presence of long-range electrostatic and strain fields produced by the interfaces will renormalize the effective piezoelectric constants, and result in layers with frozen polarization and the presence of a built-in electrostatic field in the material. In addition, the electrical contact conditions can vary along the surface. To account for these factors, we introduce a model in which the local hysteresis loop can be represented as a linear transformation of an ideal loop (figure 4(a)), i.e.

2. Experimental details The domain structure of BFO–CFO nanostructured films, grown as discussed elsewhere [16], is studied by PFM implemented on a commercial AFM system (Veeco MultiMode NSIIIA) equipped with a function generator and a lock-in amplifier (DS 345 and SRS 844, Stanford Research Systems) and an external signal generation and data acquisition system. Measurements were performed using Au–Cr coated Si tips (Micromasch, spring constant k ∼ 0.65 N m−1 ). In PFM, the tip is biased with Vtip = Vdc + Vac cos(ωt), brought into contact with the surface, and the electromechanical response of the surface is detected as the first harmonic component of the bias-induced tip deflection, d = d0 + d1ω cos(ωt + ϕ). The phase of the electromechanical response, ϕ , yields information on the polarization direction below the tip. For c− domains (polarization vector pointing downward) the application of a positive tip bias results in the expansion of the sample and surface oscillations are in phase with the tip voltage, ϕ = 0. For c+ domains ϕ = 180◦ . The PFM signal is plotted either as a pair of amplitude–phase, A = d1ω /Vac , ϕ , images, or as a mixed piezoresponse (PR) signal representation, PR = A cos ϕ .

3. Results and discussion The spatial resolution PFM can be determined from the half width at half maximum of a 180◦ domain wall [23, 24]. A mixed PFM signal of a domain in BFO is shown in the inset of figure 1(c). The line profile across the domain wall (figure 1(c)) is fitted to a phenomenological hyperbolic tangent function, y = A1 + (A2 − A1 ) tanh(2(x − x0 )/w) and the width, w, is 13.6 nm. The penetration depth of the electric field is expected to be comparable to the resolution, γ w, where γ is the dielectric anisotropy (γ ∼ 1 for BFO). Hence, the resolution is a measure of the signal generation volume, and in this case, the penetration depth is ∼15 nm. To address the spatially resolved switching behavior, we employ SS-PFM. In SS-PFM, electromechanical hysteresis loops are acquired on a 2D mesh of points in space yielding a 3D spectroscopic data array [25, 26]. The 3D data arrays are analyzed to yield 2D maps of parameters describing the local polarization switching properties. In particular, parameters such as imprint, positive and negative coercive bias (PCB and NCB, respectively), remanent responses, etc, can be determined directly from the intersections of the loop with the axes. The work of switching can be determined as the area under the loop [26]. These global parameters can be defined for any single-value response function in the positive and negative directions. In addition, by fitting the corners of the loops, it is possible to extract values for positive and negative nucleation biases (PNB and NNB, respectively). These parameters provide local analogs of switching parameters that can be determined for macroscopic switching loops.

PR+ (V ) = df + α PR+ 0 (β V + Vi ) ,

(1a )

PR− (V ) = df + α PR− 0 (β V + Vi )


where df is the vertical shift of the hysteresis loop proportional to the thickness of a frozen polarization layer, α is the scaling factor related to the changes in the signal generation volume or effective coupling constant, β is the horizontal scaling factor related to contact quality, and Vi is the imprint bias in the film. Experimentally, the ideal switching functions PR+ 0 (V ) and PR− (V ) are not known. Hence, we define the average 0 + − hysteresis loop as PR+ a (V ) = PRi (V ), PRa (V ) = 3

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Figure 2. (a) Topography of multiferroic BFO–CFO nanostructures and the corresponding PFM, (b) amplitude, and (c) phase images. The ferroelectric and antiferromagnetic BFO shows a piezoresponse, while the ferromagnetic CFO spinels show no piezoresponse. (d) SS-PFM map of the work of switching and (e), (f) maps of the positive and negative nucleation biases, respectively. (g) Representative loops from BFO (), CFO (), and the BFO–CFO heterostructure interface (). (h) Fit of the loop shape with coercive and nucleation biases indicated. The work of switching is defined as the area within a loop.


0.8 0.6 0.4 0.2 0.0

PFM NCB PCB Imprint 10



normalized line profile

normalized line profile


0.8 0.6

PFM PR rem


+ PR rem PR Switch.



0.0 15







Figure 3. (a) Normalized line profiles of PFM, positive and negative coercive biases, and imprint, and (b) normalized line profiles of PFM, positive and negative remanent piezoresponses, switchable piezoresponse, and work for the dashed line shown in figure 2(d).

PR− i (V ), where averaging is taken over the ferroelectric part of the surface (defined as Ri > 0.5Ri , where Ri is the saturated response at a given location). The parameters df , α , β , and Vi are determined using a phenomenological function

fitting method. The normalized residuals (the ‘goodness’ of the fit) is shown in figure 4(b). Note that there are no systematic trends within the image over the ferroelectric part, suggesting that the loop shape follows a universal form 4

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Figure 4. (a) Schematic showing the scaling of a hysteresis loop and (b) the ‘goodness’ of the fit. (c), (d) α and df , respectively. Note the features in the white circle. (e), (f) β and Vi , respectively. (g) Loops from red and blue circles in (e) and (f). (h) Line profiles of the parameters along the line marked in (c). Note the relative contrast in grains shown in red and blue circles.

vertical shifts within the non-ferroelectric CFO regions. This behavior is due to the detection of a non-local response by PFM, as discussed below. The behavior of voltage-dependent scaling parameters is illustrated in figure 4(e). The β map (coercive biases) is relatively featureless, and illustrates a relatively uniform response without large-scale variations. The noise level is higher in the CFO region, when the fitting is less reliable. In comparison, the imprint bias map (figure 4(f)) clearly illustrates the presence of large (∼2 V) imprint biases. The spatial variability of the signal suggests that it differs between different BiFeO3 regions, but is relatively weakly dependent on separation from the interface. From the imprint data in figure 4(f), we conclude that the heterostructure interface does not affect the internal bias, which would result in systematic changes of imprint voltage with distance from the interface. Furthermore, there is no evidence that domain nucleation is affected by the interface. Finally, we observe weak (5–10%) long-range variations in the switching behavior in the SS-PFM data (e.g. figure 2(d)). While determining the mechanism of this variability requires more systematic studies, it can be argued that these variations represent the effect of long-range elastic fields that renormalize the piezoelectric constants in the film and hence can be used to reconstruct the former.

everywhere in the ferroelectric phase. In analyzing the 2D data, we considered the systematic changes across the interfaces (i.e. similar behavior along the circumference of the pillars), and large-scale (>2–3 pixels) variations within single-phase regions. While point by point variations can be significant and reproducible (i.e. represent real data, rather than thermal noise), they were ignored. Thus, only the long-range (>2 times the pixel size, i.e. 100 nm) effects were addressed. Note that the characteristic probed volume determined from the domain wall width is ∼15 nm, and its effect on measurements will be considered below. The resulting parameter maps are shown in figures 4(c)– (f). The switchable response map (figure 4(c)), α , shows variation from a nearly zero response in the CFO regions to a nearly uniform response in the BFO regions. A number of points on the boundary show an intermediate response, corresponding to reduced hysteresis loops similar to that in figure 2(g). The image analysis illustrates a number of features with reduced switchable response (white circles in figures 4(c), (d)), located where high strains can be anticipated. The polarization activity in the heterostructure can be further elucidated from the vertical shift map, df , shown in figure 4(d). In this case, long-range (∼2–3 pixels, corresponding to 150 nm) vertical shifts of the hysteresis loops are observed as a function of distance from the interfaces. Note that the analysis suggests the presence of a finite response with anomalous 5

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x + CFO


+ 0






(b) Tip position

0 10


-10 1




0.8 a/d=0.3


Normalized PRD



(c) 0.6



a/d=0 0

a/d= -3 a/d= -0.3




0 -4







10 -2






10 2

Domain radius r/d

Figure 5. (a) Scheme of calculations and upper insets I–VI: cross-sections of cylindrical domain or its segment appearing near the CFO–BFO boundary at different tip positions. (b) Normalized on the bulk value piezoresponse PRQS (a) from a homogeneously polarized BFO quarter-space (domain is absent) via the tip coordinate a/d from the BFO–CFO boundary. (c) Relative contributions of different components w3i j (a, r) to the PFM response of a cylindrical cluster of radius r as the function of the distance a from the boundary with a non-piezoelectric medium. Solid and dashed curves present exact numerical and approximate (3b) calculations, respectively, for parameters r/d = 10, γ ∼ = 1, ∗ ν ≈ 0.35. (d) Normalized piezoresponse PRD (a, r) via the domain radius r/d for d15 = d33 ,γ ∼ = 1, ν ≈ 0.35 and different tip coordinate a/d denoted by labels near the curves.

from the CFO boundary. The BFO quarter-space is located at a  0, as shown in figure 5(a). The normalized piezoresponse, PRQS (a), from the polarized BFO quarter-space versus the coordinate a/d is shown in figure 5(b). As expected, the normalized wall profile tends to zero as a/d → −∞. The effect of the boundary on the PFM hysteresis loop can be analyzed assuming that the interface limits the size of an inverted domain formed by the probe electric field below the tip apex, as illustrated by the upper insets in figure 5(a). The piezoresponse, PRD (a, r ), in the center of a cylindrical domain with radius r or its segment located in the BFO depends on the tip apex coordinate x = a counting from the BFO–CFO interface (x = 0) as:

To analyze the interface effect on PFM data quantitatively, we consider the 3D geometry of the PFM experiment. The electric field formed below the tip extends radially, and hence a fraction of the signal generation volume is excluded in the vicinity of a domain wall or a grain boundary with a nonpiezoelectric material, resulting in the reduction of the overall signal. Note that when the field is concentrated in the surface area, polarization switching results in elongated domains, as shown by Molotskii [27] and Morozovska [28]. Hence, the domain radius is the primary parameter determining the PFM signal. The evolution of the PFM signal across the interface can be obtained using a decoupled approximation for PFM in the limit of elastic and dielectric anisotropy, as described in [29], as a linear superposition of the response across an antiparallel domain wall and a vertical offset as   a 3 ∗ PRQS (a) ≈ − d33 +1 |a| + d/4 8   a 1 +1 . (2) − d15 | a| + 3d/4 8 Equation (2) is valid for an infinitely thin CFO–BFO boundary and a dielectric anisotropy γ ∼ = 1, as is the case for BFO (arbitrary anisotropy is considered in detail in [29]). ∗ Here, the piezoelectric coefficient d33 = d33 + (1 + 4ν)d31 /3, ν ≈ 0.35 is the Poisson ratio, d is the effective separation between the charge representing the tip and the surface, and a is the coordinate from the tip center projection determined

PRD (a, r ) = (1 + 4ν) d31 w313 (a, r ) + d33 w333 (a, r )

+ d15 w351 (a, r ), w333 (a, r ) ≈ 3w313 (a, r ) ≈

(3a )

3 8r g(r, a, 4) 8 2r + π d/4

 a , |a| + d/4  1 8r w351 (a, r ) ≈ g(r, a, 4/3) 8 2r + 3π d/4  a , −1− |a| + 3d/4 −1−



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1 µm





1 µm



Figure 6. (a), (d) Topography, (b), (e) PFM amplitude, and (c), (f) PFM phase images of a BFO–CFO nanostructured film before and after the application of ±20 V, respectively. The dashed line in (a) and (d) is shown as a guide. After the dielectric breakdown, the tip became damaged, resulting in significant broadening of features in the image; however, electromechanical data can still be obtained.

Equation (4) is exact at a > r  0 (full domain in BFO, tip positions I and II), a = 0 (half-domain in BFO, g = 0.5 at tip position IV), and a < −r (no domain in CFO at tip position VI). Thus, in accordance with the adopted model of signal generation volume exclusion and equations (3) and (4), one should expect the PFM signal to be reduced by half when the tip apex is located at the CFO–BFO interface (a = 0, g = 0.5) in comparison with the case of a domain far from the boundary (a d ), and that the piezoresponse almost disappears in the CFO at a < −d . The prediction is corroborated by the obtained piezoresponse loops at different locations (see figure 2). In fact, the maximal relative piezoresponse near the BFO–CFO interface is about 1.3 au, whereas the response inside the BFO region is about 2.7 au.

where the function g(r, a, f ) determines the piezoresponse of the cylindrical cluster itself:

g(r, a, f ) ⎧ 1, a > r  0 (tip position I, II) ⎪ ⎪  ⎪ ⎪ ⎪ r 2 a 2 a 4 1 ⎪ ⎪ 1 − arctan − 1 − − ⎪ ⎪ π a r r ⎪ ⎪ ⎪ ⎪ ⎪ fd ⎪ ⎪ 0  a < r (tip position III, IV) , ⎨ × |a| + f d  ≈ (4) ⎪ r 2 a 2 a 4 1 ⎪ ⎪ arctan −1− − ⎪ ⎪ ⎪ π a r r ⎪ ⎪ ⎪ ⎪ ⎪ fd ⎪ ⎪ × , −r  a < 0 (tip position V) ⎪ ⎪ |a| + f d ⎪ ⎩ 0,

a < −r (tip position VI).

fd in equation (4) reflects the The function |a|+ fd inhomogeneous electric field distribution inside the signal generation volume. Numerical calculations of the exact expressions for w3i j (a, r ) show that the factor f = 1/4 for the w333 (a, r ) and w313 (a, r ) contributions is related to the features of the probe electric field normal component; while the factor f = 3/4 for the w351 (a, r ) contribution is related to the transverse component of the probe electric field, as illustrated in figure 5(c). The same factors f determine the response of the polarized BFO quarter-space PRQS (a), reflecting the universal nature of the local piezoresponse of an infinitely thin domain wall. The normalized piezoresponse PRD (a, r ) via the domain radius r/d for different tip coordinates, a/d , is shown in figure 5(d). For the cases a/d = 10 and 0.3, the domain growth passes through the successive stages I at r < a , II at r = a , and III at r > a ; the case a/d = 0 corresponds to an arbitrary domain radius at stage IV. For the cases a/d = −0.3 and −3 the domain growth passes through the successive stage VI when the domain is absent or too far from the tip (r < −a) and then stage V at r > −a (see upper insets).

Remarkably, the interface effect is observed for distances of the order of 100–200 nm from the interface, while the effective resolution of the PFM is ∼10–20 nm. A similar effect was observed by Kholkin, who observed the saturation of PFM hysteresis loops for domains as large as 200–300 nm, while the spatial resolution could be estimated as 20–40 nm [30]. This indicates that the signal generation volume addressed in the hysteresis loop is significantly larger than anticipated based solely on the tip radius. In fact, this conclusion agrees with the analysis above, which demonstrated that the Greens function in this case, and hence the hysteresis loop tail, saturates as a/r , where a is the characteristic tip size (reflected in resolution), and r is the domain radius. Hence, SS-PFM signals achieve 90% of the value corresponding to a free film for a domain size r = 10a . This extremely slow saturation accounts for the experimentally observed behavior. Attempts to achieve complete saturation of the hysteresis loops typically resulted in dielectric breakdown, presumably due to the increased conductivity of the CFO (figure 6). 7

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4. Conclusions

[7] Viehland D 2005 Smart Materials—Fundamentals and Applications: Multiferroics Tutorial (Warrendale, PA: Materials Research Society) [8] Spaldin N A and Fiebig M 2005 Science 309 391 [9] Dong S, Li J-F and Viehland D 2003 Appl. Phys. Lett. 83 2265 [10] Slutsker J, Levin I, Li J, Artemev A and Roytburd A L 2006 Phys. Rev. B 73 184127 [11] Alexe M, Harnagea C, Hesse D and G¨osele U 2001 Appl. Phys. Lett. 79 242 [12] Ma W and Hesse D 2004 Appl. Phys. Lett. 84 2871 [13] Ederer C and Spaldin N A 2005 Curr. Opin. Solid State Mater. Sci. 9 128–39 [14] Zavaliche F, Das R R, Kim D M, Eom C B, Yang S Y, Shafer P and Ramesh R 2005 Appl. Phys. Lett. 87 182912 [15] Zavaliche F, Shafer P, Ramesh R, Cruz M P, Das R R, Kim D M and Eom C B 2005 Appl. Phys. Lett. 87 252902 [16] Zhao T et al 2006 Nat. Mater. 5 823–9 [17] Zavaliche F et al 2005 Nano Lett. 5 1793 [18] Zheng H, Zhan Q, Zavaliche F, Sherburne M, Straub F, Cruz M P, Chen L-Q, Dahmen U and Ramesh R 2006 Nano Lett. 6 1401 [19] Zhao T, Scholl A, Zavaliche F, Zheng H, Barry M, Doran A, Lee K, Cruz M P and Ramesh R 2007 Appl. Phys. Lett. 90 123104 [20] Gruverman A, Rodriguez B J, Kingon A I, Nemanich R J, Cross J S and Tsukada M 2003 Appl. Phys. Lett. 82 3071 [21] G¨uthner P, Glatz-Reichenbach J and Dransfeld K 1991 J. Appl. Phys. 69 7895 [22] Alexe M and Gruverman A (ed) 2004 Nanoscale Characterization of Ferroelectric Materials (Berlin: Springer) [23] Kalinin S V, Jesse S, Rodriguez B J, Eliseev E A, Gopalan V and Morozovska A N 2007 Appl. Phys. Lett. 90 212905 [24] Rodriguez B J, Jesse S, Baddorf A P and Kalinin S V 2006 Phys. Rev. Lett. 96 237602 [25] Jesse S, Lee H N and Kalinin S V 2006 Rev. Sci. Instrum. 77 073702 [26] Jesse S, Baddorf A P and Kalinin S V 2006 Appl. Phys. Lett. 88 062908 [27] Molotskii M 2003 J. Appl. Phys. 93 6234 [28] Morozovska A N, Eliseev E A and Kalinin S V 2006 Appl. Phys. Lett. 89 192901 [29] Morozovska A N, Eliseev E A, Bravina S L and Kalinin S V 2007 Phys. Rev. B 75 174109 [30] Kholkin A L, Bdikin I K, Shvartsman V V, Orlova A, Kiselev D, Bogomolov A A and Kim S-H 2004 Mater. Res. Soc. Symp. Proc. 839E O7.6

To summarize, polarization switching in multiferroic BFO– CFO structures has been studied by SS-PFM. The SSPFM maps illustrate that coercive and nucleation biases are uniformly distributed within the ferroelectric regions and do not exhibit any systematic trends in the vicinity of the interface. The imprint bias shows large-scale variations between the grains. The work of switching and the electromechanical response are reduced in the vicinity of the interfaces. However, we believe this is a purely geometric effect due to the reduction of the domain volume. Small (5–10%) variations of switching behavior within the BFO are observed that can be attributed to long-range strain fields. Based on these observations, the switching behavior and domain nucleation in multiferroic heterostructures is determined by the ferroelectric component, and is unaffected by the presence of the heterostructure interfaces, suggesting the applicability of these systems for devices.

Acknowledgments Research sponsored by the Division of Materials Sciences and Engineering (BJR, SJ), Oak Ridge National Laboratory, managed and operated by UT-Battelle, LLC for the Office of Basic Energy Sciences, US Department of Energy. A portion of this research (APB, SVK) was conducted at the Center for Nanophase Materials Sciences, which is sponsored at Oak Ridge National Laboratory by the Division of Scientific User Facilities, US Department of Energy. Three authors (TZ, YHC, RR) acknowledge the support of an LBL LDRD.

References [1] Wang J et al 2003 Science 299 1719 [2] Ederer C and Spaldin N A 2004 Nat. Mater. 3 849 [3] Lottermoser T, Lonkai T, Amann U, Hohlwein D, Ihringer J and Fiebig M 2004 Nature 430 541 [4] Zheng H et al 2004 Science 303 661 [5] International Technology Roadmap for Semiconductors http:// [6] Eerenstein W, Mathur N D and Scott J F 2006 Nature 442 759


Spatially resolved mapping of ferroelectric switching ...

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(2) where kq is wavenumber of the qth source and rm is the mth sensor location. Using a circular symmetric complex c 2012 IEEE

Nanoscale Electromechanics of Ferroelectric and ...
Feb 26, 2007 - 2Department of Mathematics and Computer Science, Suffolk University, Boston, .... Table 1 Electromechanical coupling in crystals and molecules .... (c) Ferroelectric tunneling barriers allow an additional degree of .... on scanning pro

Effect of Mo substitution on ferroelectric properties of ...
School of Materials Science and Engineering, Wuhan University of ... (Received 1 September 2008; accepted 9 December 2008; published online 31 December 2008) ..... Z. Simoes, C. S. Riccardi, L. S. Cavalcante, E. Longo, J. A. Varela, B.

Piezoresponse force spectroscopy of ferroelectric ...
much attention for electronic device applications such as nonvolatile memories,1 ferroelectric data storage,2,3 or as a platform for nanofabrication.4 This has ...

Characterization of ferroelectric material properties of ...
Jan 5, 2011 - as energy harvesting,1,4,7–10 energy storage,10–13 and nonvola- tile information .... (Color online) Structural characterization of sol-gel PZT. (a) SEM of metal ( ... mittivity of free space, and s11 is the lateral strain. In deduc

Resolved designs viewed as sets of partitions - QMUL Maths
(I am grateful to D. A. Preece for this suggestion.) The design in Figure 1.2 is resolved. .... The definitions of VF , PF and orthogonality may be extended to partitions whose class sizes are unequal: see [5]. ..... To exclude designs like that in F

Ferroelectric characterization of highly „0001…-oriented YMnO3 thin ...
ous vapor deposition techniques, the CSD is not atom-by- atom growth, and ... by scanning electron microscope revealed distribution of grains of an average ...

Angle-resolved photoemission spectroscopy of the ...
Sep 28, 2005 - and WO3 as described by Shanks.17 The resistivity measure- ments and Laue diffraction pattern show that the crystals are metallic with a ...

Homogenization for a nonlinear ferroelectric model
We call (u, D, q) an energetic solution of the problem associated with E and R, if the stability condition (S) and the energy balance. (E) hold for every t ∈ [0,T]:.

1 if replacement is realized between missions k and k + 1,. 0 otherwise. Total time TMR(k) and total cost CMR(k) nec- essary to minimal repairs are given by:.

Site-resolved measurement of water-protein ...
Jan 2, 2011 - 2011 Nature America, Inc . All rights reserved. NATURE STRUCTURAl & MolECUlAR BIoloGy ADVANCE ONLINE PUBLICATION. TECHNICAl ...

Fabrication of metallic nanowires on a ferroelectric ... - CiteSeerX
Sep 15, 2006 - Fabrication of silver nanowires on a domain-patterned lithium niobate template by inducing a photochemical reaction in an aqueous solution is.

Angle-resolved and resonant photoemission ...
did not use the second derivative method to map out the band .... electronlike band in the band mapping. .... graphic Data for Intermetallic Phases, 2nd ed.

Quantitative time-resolved measurement of membrane ...
Jan 18, 2009 - ... †These authors contributed equally to this work; *e-mail: Martin. ... subsequent in-batch incubation of cantilevers in a T5 phage suspen-.

Ordered Ferroelectric Lead Titanate Nanocellular ...
Mar 14, 2009 - [b)]T. Furukawa, N. Seo, Jap. J. Appl. Phys. 1990, 29, 675. [3] D. Damjanovic, Rep. Prog. Phys. 1998, 61, 1267. [4] K. Lefki, G. J. M. Dormans, ...

Spatially explicit approach to estimation of total ...
examined an extensive data set of 1068 passerine birds in sub-Saharan ..... Instead, we apply an approximated pdf of the Thomas process ..... Encyclopedia of.

FIRe seveRITy mAPPIng: mAPPIng THe - Bushfire CRC
financial support was provided by Bushfires Nt and student support from Charles darwin university. ... mapping system ( enhancing the ...

Unidirectional Pinning and Hysteresis of Spatially ...
Mar 8, 2012 - alternans increasing with the degree of ..... parameters to change, including the degree of Cai-driven .... basic cycle length ¼ 340 ms, DV=ءx.