Flexible Quasi-Two-Dimensional CoFe2O4 Epitaxial Thin Films for

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Flexible Quasi-Two-Dimensional CoFe2O4 Epitaxial Thin Films for Continuous Strain Tuning of Magnetic Properties Yong Zhang,†,‡,# Lvkang Shen,†,‡,# Ming Liu,*,†,‡ Xin Li,§ Xiaoli Lu,*,§ Lu Lu,† Chunrui Ma,‡ Caiyin You,⊥ Aiping Chen,□ Chuanwei Huang,∥ Lang Chen,△ Marin Alexe,▽ and Chun-Lin Jia†,‡,¶ †

School of Microelectronics and ‡State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Xi’an 710049, China § State Key Discipline Laboratory of Wide Band Gap Semiconductor Technology, School of Microelectronics, Xidian University, Xi’an 710071, China ⊥ School of Materials Science and Engineering, Xi’an University of Technology, Xi’an 710048, China □ Center for Integrated Nanotechnologies (CINT), Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States ∥ Shenzhen Key Laboratory of Special Functional Materials, College of Materials Science and Engineering, Shenzhen University, Nanshan District, Shenzhen 518060, China △ Department of Physics, South University of Science and Technology, Nanshan District, Shenzhen 518055, China ▽ Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom ¶ Ernst Ruska Centre for Microscopy and Spectroscopy with Electrons, Forschungszentrum Jülich, D-52425 Jülich, Germany S Supporting Information *

ABSTRACT: Epitaxial thin films of CoFe2O4 (CFO) have successfully been transferred from a SrTiO3 substrate onto a flexible polyimide substrate. By bending the flexible polyimide, different levels of uniaxial strain are continuously introduced into the CFO epitaxial thin films. Unlike traditional epitaxial strain induced by substrates, the strain from bending will not suffer from critical thickness limitation, crystalline quality variation, and substrate clamping, and more importantly, it provides a more intrinsic and reliable way to study strain-controlled behaviors in functional oxide systems. It is found that both the saturation magnetization and coercivity of the transferred films can be changed over the bending status and show a high accord with the movement of the curvature bending radius of the polyimide substrate. This reveals that the mechanical strain plays a critical role in tuning the magnetic properties of CFO thin films parallel and perpendicular to the film plane direction. KEYWORDS: free-standing thin films, strain tuning, CoFe2O4, magnetic properties, flexible electronics substrates.17−19 The strain in films can also be controlled by the thickness of the epitaxial thin films.20 However, it is widely believed that the effect of partially relaxed strain on the properties is difficult to interpret on the basis of experimental data. The main reason is that ideally defect-free films are hard to obtain experimentally and that the films usually include different types of defects. Furthermore, a specific strain state is hard to achieve since only very limited single-crystal substrates are commercially available.

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undamental understanding of mechanical deformation on the physical properties of ferroelectric and ferromagnetic materials has received significant interest due to the utility of its superior properties and wide range of applications including multiferroics1−4 and sensors.5−7 It has been found that epitaxial strain can dramatically alter the properties of functional oxides,8,9 such as the transition temperatures of superconductors,10,11 ferrimagnets, and ferroelectrics.12−16 Generally, mechanical strain in thin films can be induced by thermal misfit and lattice misfit to the substrates, volume shrinkage or expansion due to recrystallization, phase transformation, and so on. Epitaxial misfit has been frequently used as a primary route for engineering strain and thus tailoring the properties of thin films by the appropriate choice of © 2017 American Chemical Society

Received: April 16, 2017 Accepted: June 28, 2017 Published: June 28, 2017 8002

DOI: 10.1021/acsnano.7b02637 ACS Nano 2017, 11, 8002−8009

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Figure 1. (a) Schematic illustration of transfer processes of CFO thin films on flexible substrates. (b) Free-standing CFO thin film floating on the surface of water. (c) CFO thin film transferred on a PI substrate. (d) SEM image of a transferred CFO thin film. (e) Magnified images of the transferred CFO thin film.

Figure 2. XRD patterns of an as-grown CFO thin film and transferred CFO on silicon and PI. (a) XRD θ−2θ scan spectrum of the CFO film on a MgO-buffered STO (001) substrate. (b) ϕ scan spectra of the CFO films, the MgO buffer layer, and the STO substrates. (c) XRD θ−2θ spectrum of the CFO thin films transferred on silicon and PI substrates. (d) ϕ scan measurements of the transferred CFO thin film on silicon and PI substrates.

stabilities,25,26 which allow preparing free-standing thin films through wet etching and measuring the properties at different bending states. In this research, we first transfer CFO epitaxial layers on flexible polyimide (PI) substrates. Further, we investigate the magnetic properties of the CFO layer under mechanical strain, showing excellent mechanical stability and high tunability of magnetic properties. Moreover, the coercive field and magnetization can be effectively tuned by the bending strain, which shows a great potential for applications in flexible electronics, such as magnetic data storage,27 spin-electronic devices,28−30 and so on.

An ideal way to isolate the stress effects from other factors on the magnetic or ferroelectric properties of functional oxide thin films is measuring free-standing thin films under flexibly adjusted strain. Gan et al. have demonstrated how epitaxial strain affects the magnetic and electrical properties of epitaxial SrRuO3 thin films by using a lift-off technique to remove the epitaxial strain of the films.21 This method provides the possibility to study thin film samples at two strain states, before and after strain relaxation. Here, we show a method to prepare free-standing CoFe2O4 (CFO) epitaxial thin films and study the magnetic properties under different mechanical strain states. CFO, as a ferromagnetic inverse spinel, is a promising candidate for spintronic devices and multiferroic applications due to its relative high Curie temperature, large coercivity (Hc), and saturation magnetization (Ms) as well as strong magnetocrystalline anisotropy and large magnetostriction.22,23 In addition, CFO shows excellent mechanical24 and chemical

RESULTS AND DISCUSSION High-quality CFO epitaxial thin films were grown on MgObuffered (001) SrTiO3 (STO) substrates using pulsed laser deposition (PLD) (see Methods). The epitaxial CFO thin films were subsequently transferred onto either silicon or PI 8003

DOI: 10.1021/acsnano.7b02637 ACS Nano 2017, 11, 8002−8009

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ACS Nano substrates, as illustrated in Figure 1a. Polystyrene (PS) is first spun on top of the as-grown thin film as a carrier for handing CFO thin films in a subsequent process and baked at 100 °C for 15 min to enhance the adhesion between PS and the CFO thin films. Then, the sacrificial MgO layer is chemically etched in 10% (NH4)2SO4 solution at 80 °C.31 After almost 12 h of wet etching, the MgO sacrificial layer was completely etched away, leaving CFO films sitting on the top of the STO substrate through van der Waals adhesion force. This is a critical feature used to remove the PS layer in chloroform. When the entire specimen is immersed into chloroform, the CFO thin films are enabled to maintain the integrity during the whole PS dissolution process, which is due to the supporting function of the STO substrates. By utilizing a water-assisted peel-off method, CFO thin films are released onto the surface of water, as shown in the Supporting Information video. To minimize wrinkles, wrapping, and cracks probably induced by the chemical wetting, the CFO thin films remained on the water surface for about a few hours for a slow release (Figure 1b). It can be seen that a damage-free CFO film with a large area (∼2 mm × 2.5 mm) can freely float on the water surface. Then, the floating film on the water surface was scooped up and transferred onto the target substrates (Figure 1c). Although there is no adhesive bonding, the transferred CFO thin films are firmly attached to the PI substrates, leading to excellent mechanical stability. Finally, after multiple cleaning using alcohol and deionized water, the thin films were dried in air. As scanning electron microscope (SEM) (Figure 1d and e) and atomic force microscope (AFM) (Figure S1) investigations showed, the surface of the transferred CFO thin film on a PI flexible substrate is flat and clean, accompanied by only a few wrinkles and cracks. The phase, epitaxial relationship, and crystalline quality of all the as-grown and transferred CFO thin films have been characterized by X-ray diffraction (XRD). Figure 2a shows a typical XRD θ−2θ pattern of an as-grown CFO thin film deposited on a MgO-buffered (001) STO substrate. Only a (004) peak around 43.14° can be found for the CFO thin film along with the (00l) peaks for the MgO buffer layer and STO substrate, indicating that the CFO thin film is c-axis oriented. From the ϕ scan patterns shown in Figure 2b and the epitaxial relationship, the heterostructure is determined to be [001]CFO//[001]MgO//[001]STO and (100)CFO//(100)MgO// (100)STO. Figure 2c and d show the θ−2θ and ϕ of the transferred CFO thin films on silicon and a PI substrate, respectively, which indicate that the crystalline quality of the CFO film is essentially maintained in the transfer process. As a comparison, Figure 3a−c display the full width at half-maximum (fwhm) of the rocking curve of the as-grown CFO films, the transferred CFO on silicon, and the transferred CFO on PI, which are 1.27°, 1.35°, and 1.31°, respectively. This demonstrated that the CFO films essentially retain the single-crystalline quality after the transfer process. Cross-sectional transmission electron microscope (TEM) images were also used to analyze the microstructure of the as-grown CFO films and the transferred CFO films on silicon substrates. As shown in Figure 3d and e, it is clearly seen that both the original surface and the etched interface are sharp and smooth. Figure 3f shows a highresolution TEM image of the interface between the transferred CFO film and the silicon substrate, revealing an excellent contact of the transferred CFO film to the silicon substrate.

Figure 3. Rocking curves of (a) the as-grown and the transferred CFO on (b) silicon and (c) PI. Cross-sectional TEM of (d) the CFO/MgO/STO multilayer films and (e) CFO thin film on silicon. (f) Magnified TEM image of the interface of the CFO/Si heterostructure. In-plane and out-of-plane M−H hysteresis loops of (g) an as-grown CFO thin film and (h) a transferred CFO thin film at room temperature.

To further analyze the functional properties of transferred CFO thin films, a vibrating sample magnetometer (VSM) was employed to measure the magnetic properties of the as-grown and transferred CFO thin films on PI substrates, respectively (see Figure 3g and h). The measurements were performed at room temperature with an applied magnetic field parallel and perpendicular to the film surface. Both as-grown and transferred films exhibit clear magnetic hysteresis loops, which indicate that the transfer process does not chemically affect the CFO thin films. It is important to note that for the as-grown CFO thin film, hysteresis loops illustrate the existence of a strong perpendicular magnetic anisotropy, which disappeared in the transferred films. For the as-grown film, the out-of-plane Hc is estimated at 2.740 kOe, while that along the in-plane direction is about 800 Oe, whereas in the transferred CFO films the Hc along both the out-of-plane and in-plane directions are almost equal to each other and estimated at 1.340 kOe. One reason might be the strain relaxation of the free-standing CFO thin film after removing of the substrate constraint, which greatly weakens the magnetic anisotropy induced by the substrate clamping effect.32 Both the in-plane (100) and the out-of-plane (001) tests are along the same crystal plane groups, thus leading to similar magnetic properties after removing the clamping effect. The above measurements indicate that this transfer procedure has an obvious tuning effect on the magnetic properties, which can be used to study the magnetic films without the clamping effect from a rigid substrate. 8004

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CFO thin films on the PI substrates in the bending direction is given by33

On the basis of the work mentioned above, we continued to study the effect of strain on free-standing CFO single-crystalline films. Unlike in traditional film/substrate systems, where a high concentration of interface states and interfacial dislocations would obfuscate intrinsic strain effects, in the present case, the variable strains can be induced to the CFO films exclusively by a direct application of external mechanical stress to the thin film. Figure 1c shows that a stress-free CFO film has attached to a PI substrate that is elastically deformable. Considering the excellent contact between the CFO thin film and PI substrate, the film is elastically strained to match the substrate. This means that the strain state of the CFO film can be effectively controlled by the deformation states of the PI substrate. This method can disentangle strain effects from other factors, such as variation of the crystalline quality with substrates and the presence of impurities arising from interdiffusion with the substrates, which can effectively affect the film properties and induce false strain-related effects. Details about the sample mounting within the measurement system and the method to apply different mechanical strains on the films are shown in Figure S2. The CFO thin films transferred on PI substrates were fixed on the convex molds (acrylonitrile butadiene styrene plastic (ABS)), where a large and controllable strain can be applied to the transferred CFO thin films. The physical maps and schematic diagrams of the sample mounting can be found in Figure S2. The strain is determined by changing the radius of curvatures of convex molds. This system allows a systematic study of the effects of the strain on the magnetic properties of the CFO thin films in both the perpendicular and parallel directions to the film plane. Figure 4 illustrates two

ε = (tCFO + t PI)/2R

(1)

where tCFO and tPI are the thickness of the CFO thin film and PI substrate, respectively. R is the radius of the convex molds. Since the film thickness (∼100 nm) is far less than that of the PI substrate (∼20 μm), eq 1 can be simplified as ε = tPI/2R, and the neutral plane, where there is no stress, can be taken to be at the middle of the PI substrate, indicating that the strain in the CFO films can be assumed to be uniform across the film thickness. ε is positive for outward/tensile bending and negative for inward/compressive bending. To understand the mechanical strain effect on magnetic properties of free-standing CFO thin films, we conduct magnetization measurements in a superconducting quantum interference device (SQUID) and VSM at different strain states. To investigate the repeatability and accuracy, we prepared three CFO film samples and carried out successive measurements with SQUID and VSM. The in-plane and out-of-plane magnetization versus applied magnetic field (M−H) hysteresis loops were measured with magnetic fields parallel and perpendicular to the film plane, respectively. Figure 5a−c depict in-plane M−H hysteresis loops of a transferred CFO thin film under different compressive strain, unstrained, and different tensile strain states, respectively, whereas the corresponding out-of-plane M−H hysteresis loops are shown in Figure 6a−c. The in-plane and out-of-plane M−H hysteresis loops for other samples are shown in Figures S3−S6. All hysteresis loops exhibit similar shapes and saturate at a field of 1.5 T, even for those bent with a large angle. Figure 5d and Figure 6d show, respectively, the in-plane and out-of-plane magnetic properties (Ms and Hc) of the CFO films depending on the strain. The values of Ms and Hc were averaged over the data of three samples, which are shown in Figures S9 and S10. Obviously, the strain dependence of Ms and Hc are monotonic. Meanwhile, both the in-plane and out-of-plane directions seem to have the same tendency even with closed Ms and Hc values. With increasing the tensile strain along the bending direction, the Hc of CFO thin films decreases and the corresponding Ms increases, while the compressive strain along the bending directions results in the opposite effect on Ms and Hc. Moreover, from the data of individual samples, which are illustrated in Figures S9 and S10, the Ms and Hc values are reproducible on successive measurements. Especially, separate measurements by SQUID and VSM of an identical sample have resulted in nearly the same magnetic behavior. However, it should be noted that fluctuations of the Hc and Ms values appeared for the out-of-plane direction probably due to large background signals in the measurement (see Figure S7). Although no adequate theory has been developed and no detailed relationship between strain and coercivity and magnetization has been set up, in particular when it relates to a free-standing thin film without the influence of substrate clamping, a tremendous number of experiments have been reported that study the effect of strain on coercivity and magnetization in epitaxial magnetic thin films. As shown in Figure 7a, in a general epitaxial spinel ferrite thin film, the clamping effect often induces a tetragonal distortion of the lattice, which plays an important role in magnetic anisotropy of CFO films and contributes a lot to the alignment of the easy axis through magnetoelastic effects.34−37 According to Schulz and Baberschke38 and Thamankar39 et al., the magnetoelastic

Figure 4. Two position configurations of the transferred CFO thin film with respect to the PI substrate. (a) CFO thin film with a tensile strain from the outward bending position. (b) CFO thin film with a compressive strain from the inward bending position. For both cases, the magnetic field is applied parallel to the film planes, corresponding to in-plane magnetization measurements. Out-ofplane hysteresis M−H loops are obtained when the magnetic field is applied perpendicular to the film plane.

configurations of the film position with respect to the PI substrate, corresponding to tensile and compressive strain states. When the film sits above the PI substrate with an outward bending direction (Figure 4a), it undergoes a tensile strain along the crystallographic direction (100). In contrast, when the film sits under the PI substrate with an inward bending (Figure 4b), it will result in a compressive strain along the same crystallographic direction (100). In this way, the outward and inward bending of the PI substrates induce, respectively, tensile and compressive strains in the transferred CFO thin films along the bending directions. The strain of the 8005

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Figure 5. In-plane M−H hysteresis loops of the CFO thin films measured by VSM (a) under different inward bending strains, (b) without bending strain, and (c) under different outward bending strains. (d) Hc and Ms measured on different strain states after successive measurements by VSM and SQUID. The values of Hc and Ms were obtained by averaging the data of three film samples.

Figure 6. Out-of-plane M−H hysteresis loops of the CFO thin films measured by VSM (a) under different inward bending strains, (b) without bending strain, and (c) under different outward bending strains. (d) Hc and Ms measured on different strain states after successive measurements by VSM and SQUID. The values of Hc and Ms were obtained by averaging the data of three film samples.

be positive and the magnetoelastic anisotropy will be confined perpendicular to the film plane and, thus, dominates the magnetocrystalline anisotropy. Conversely, the Ks will be negative under compressive strain and generate in-plane anisotropy. This formula shows a high accord with various spinel ferrite thin films,32,40−43 whereas for the transferred CFO films, the results are expected to be different due to different orientations of the bending strain inducing tetragonal distortion. Typically, for the case of homogeneous elastic materials, e.g., PI, an applied external force would merely lead to uniaxial strain in a film. However, for the free-standing CFO thin films transferred on PI, the uniaxial stress along the (100)

anisotropy energy associated with the tetragonal distortion of the lattice in a (100) oriented film is formulated as36 K s = −3/2λ100(C11 − C12)(a − a⊥)/a

(2)

where λ100 is the magnetostriction constant along the (100) crystallographic direction and C11 and C12 are the elastic constants. The strain-induced magnetoelastic energy could easily be calculated for the present case by assuming the bulk phase of cobalt ferrite (C11 = 2.7 × 1012 dyn/cm−2, C12 = 1.06 × 1012 dyn/cm−2, and λ100 = −5.9 × 10−4). Since CFO exhibits a negative large magnetostriction, under tensile strain, the Ks will 8006

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Figure 7. (a) Biaxial stress in a CFO thin film deposited on a rigid substrate. (b) Mechanical bending of a transferred CFO thin film produces a uniaxial strain along the bending direction and a biaxial strain state perpendicular to the bending direction.

such as magnetic-controlled switches, electronic circuitry, magnetoelectronics, spintronics, and memory devices. More importantly, the strong strain−anisotropy correlation further confirms the essential role of strain in tuning the magnetic properties of oxide thin films.

direction would contribute to biaxial stress perpendicular to the moment of force due to the bending Poisson effect.44 As shown in Figure 7b, bending deformation can be approximated as a tetragonal distortion with a uniaxial strain along the (100) direction, while the strains along the (010) and (001) directions might gain a close value. This is consistent with the results discussed above that the strain-induced magnetic properties behave almost in the same way in the (010) and (001) crystallographic directions. Thus, in the transferred CFO film under outward bending (tensile strain along the (100)), Ks will be positive and the magnetoelastic anisotropy will be confined along the (010) and (001) directions, and the corresponding Hc along the (010) and (001) directions will decrease to about 872 and 714 Oe, respectively. Similarly, under inward bending (compressive strain along the (100)), Ks will be negative and lead to a magnetic anisotropy along the bending (100) direction, and the corresponding Hc will increase to about 1.947 and 1.878 kOe. However, the scenario described above might be too simple; the evolution and mechanism for strong mechanical strain− anisotropy correlation are still not well understood yet. In order to understand the origin of such phenomena, it is important to explore the underlying mechanisms to explain the magnetic properties of the films. Recently, Liu et al.45 measured CFO thin films under different bending-induced strain by magnetic force microscopy (MFM) and found the magnetic anisotropy is probably related to randomly distributed upward and downward magnetic domains observed in the MFM images. Further investigation is needed to understand the strain effect.

METHODS Fabrication of Epitaxial CFO Films. CFO thin films were epitaxially grown on MgO-buffered (001) STO substrates using a PLD system with a 248 nm KrF excimer laser. The epitaxial MgO buffer layer with a thickness of 50−100 nm was first grown at 600 °C in an oxygen pressure of 20 mTorr. CFO thin films with a thickness of ∼100 nm were subsequently grown at 700 °C at an oxygen pressure of 50 mTorr. The repetition frequency is 5 Hz, and the laser energy is fixed at 650 mJ for both layers. After depositions, the films were in situ annealed in pure oxygen with a pressure of 200 Torr for 15 min and then slowly cooled to room temperature. CFO Thin Film Characterization and Magnetic Measurement. The crystalline phase, quality, and interface relationship of the thin films were characterized by high-resolution X-ray diffraction using a PANalytical X’Pert MRD (λ = 1.5406 Å) and by TEM performed on a JEOL ARM 200F. The large controllable strains of the CFO thin films were induced by fixing the CFO/PI sample on convex molds with a radius of curvature of 1, 2, and 4 mm, respectively. The convex molds are made from ABS plastic. The inward and outward bending of the PI substrates induce, respectively, compressive and tensile strains in the transferred CFO thin films along the bending direction. The magnetic properties of the CFO thin films under different strain states were systematically studied using SQUID and VSM measurement systems at room temperature.

ASSOCIATED CONTENT

CONCLUSIONS In summary, we have shown a process enabling transferring of high-quality epitaxial magnetic oxide films onto flexible substrates. We also have shown that the magnetic properties of the transferred CFO thin films are well preserved after film transferring. The magnetic properties of epitaxial CFO thin films can be tuned by large and controllable mechanical strain, induced by bending the flexible substrate, making them potential and competitive alternatives in frontier technologies

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsnano.7b02637. More detailed set of data for the M−H hysteresis loop curves of the transferred CFO thin films under different strain states (PDF) Supporting movie (AVI) 8007

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AUTHOR INFORMATION Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Ming Liu: 0000-0002-4392-9659 Chunrui Ma: 0000-0002-7824-7930 Aiping Chen: 0000-0003-2639-2797 Author Contributions #

Y. Zhang and L. Shen contributed equally to this work.

Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS This research was supported by the Natural Science Foundation of China (Nos. 51390472, 51572211, 51371140), National “973” projects of China (No. 2015CB654903), China Postdoctoral Science Foundation (No. 2015M582649), and Fundamental Research Funds for the Central Universities. The effort at Los Alamos National Laboratory was supported by NNSA’s Laboratory Directed Research and Development (LDRD) Program and was performed, in part, at the CINT, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science. Los Alamos National Laboratory, an affirmative action equal opportunity employer, is operated by Los Alamos National Security, LLC, for the National Nuclear Security Administration of the U.S. Department of Energy under contract DE-AC52-06NA25396. M.A. acknowledges the financial support of the Royal Society via Wolfson Research Merit and Theo Murphy Blue Sky Awards. REFERENCES (1) Ramesh, R.; Spaldin, N. A. Multiferroics: Progress and Prospects in Thin Films. Nat. Mater. 2007, 6, 21−29. (2) Qin, W.; Jasion, D.; Chen, X.; Wuttig, M.; Ren, S. ChargeTransfer Magnetoelectrics of Polymeric Multiferroics. ACS Nano 2014, 8, 3671−3677. (3) Tsai, C.; Chen, H.; Chang, F.; Tsai, W.; Cheng, H.; Chu, Y.; Lai, C.; Hsieh, W. Stress-Mediated Magnetic Anisotropy and Magnetoelastic Coupling in Epitaxial Multiferroic PbTiO3-CoFe2O4 Nanostructures. Appl. Phys. Lett. 2013, 102, 132905. (4) Eerenstein, W.; Mathur, N.; Scott, J. F. Multiferroic and Magnetoelectric Materials. Nature 2006, 442, 759−765. (5) Gautschi, G. Piezoelectric Sensors. In Piezoelectric Sensorics: Force, Strain, Pressure, Acceleration and Acoustic Emission Sensors, Materials and Amplifiers; Gautschi, G., Ed.; Springer: Berlin, 2002; pp 73−91. (6) Darlinski, G.; Böttger, U.; Waser, R.; Klauk, H.; Halik, M.; Zschieschang, U.; Schmid, G.; Dehm, C. Mechanical Force Sensors Using Organic Thin-Film Transistors. J. Appl. Phys. 2005, 97, 093708. (7) Qin, Y.; Peng, Q.; Ding, Y.; Lin, Z.; Wang, C.; Li, Y.; Xu, F.; Li, J.; Yuan, Y.; He, X. Lightweight, Superelastic, and Mechanically Flexible Graphene/Polyimide Nanocomposite Foam for Strain Sensor Application. ACS Nano 2015, 9, 8933−8941. (8) Ederer, C.; Spaldin, N. A. Effect of Epitaxial Strain on the Spontaneous Polarization of Thin Film Ferroelectrics. Phys. Rev. Lett. 2005, 95, 257601. (9) Zayak, A.; Huang, X.; Neaton, J.; Rabe, K. M. Structural, Electronic, and Magnetic Properties of SrRuO3 under Epitaxial Strain. Phys. Rev. B: Condens. Matter Mater. Phys. 2006, 74, 094104. (10) Sato, H.; Naito, M. Increase in the Superconducting Transition Temperature by Anisotropic Strain Effect in (001) La1. 85Sr0. 15CuO4 Thin Films on LaSrAlO4 Substrates. Phys. C 1997, 274, 221−226. 8008

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DOI: 10.1021/acsnano.7b02637 ACS Nano 2017, 11, 8002−8009