Higher order harmonic detection for exploring nonlinear interactions with nanoscale resolution

Nonlinear dynamics underpin a vast array of physical phenomena ranging from interfacial motion to jamming transitions. In many cases, insight into the nonlinear behavior can be gleaned through exploration of higher order harmonics. Here, a method using band excitation scanning probe microscopy (SPM) to investigate higher order harmonics of the electromechanical response, with nanometer scale spatial resolution is presented. The technique is demonstrated by probing the first three harmonics of strain for a Pb(Zr1-xTix)O3 (PZT) ferroelectric capacitor. It is shown that the second order harmonic response is correlated with the first harmonic response, whereas the third harmonic is not. Additionally, measurements of the second harmonic reveal significant deviations from Rayleigh-type models in the form of a much more complicated field dependence than is observed in the spatially averaged data. These results illustrate the versatility of nth order harmonic SPM detection methods in exploring nonlinear phenomena in nanoscale materials.

[1]  Seung Eek Eagle Park,et al.  Relaxor-based ferroelectric single crystals for electromechanical actuators , 1998, Smart Structures.

[2]  N. Sherlock,et al.  Large signal response and harmonic distortion in piezoelectrics for SONAR transducers , 2012, Journal of Electroceramics.

[3]  S. Trolier-McKinstry,et al.  Piezoelectric nonlinearity due to motion of 180° domain walls in ferroelectric materials at subcoercive fields: A dynamic poling model , 2006 .

[4]  Fei Xu,et al.  Domain wall motion and its contribution to the dielectric and piezoelectric properties of lead zirconate titanate films , 2001 .

[5]  F. Kremer,et al.  Giant lateral electrostriction in ferroelectric liquid-crystalline elastomers , 2001, Nature.

[6]  U. Böttger,et al.  Effects of ferroelectric switching on the piezoelectric small-signal response (d33) and electrostriction (M33) of lead zirconate titanate thin films , 2004 .

[7]  Dragan Damjanovic.  Hysteresis in Piezoelectric and Ferroelectric Materials , 2006 .

[8]  H. Kumar Wickramasinghe,et al.  High‐resolution capacitance measurement and potentiometry by force microscopy , 1988 .

[9]  John William Strutt,et al.  Scientific Papers: Notes on Electricity and Magnetism.—III. On the Behaviour of Iron and Steel under the Operation of Feeble Magnetic Forces , 2009 .

[10]  J. Petzelt,et al.  The giant electromechanical response in ferroelectric relaxors as a critical phenomenon , 2006, Nature.

[11]  S. Trolier-McKinstry,et al.  Longitudinal piezoelectric coefficient measurement for bulk ceramics and thin films using pneumatic pressure rig , 1999 .

[12]  S. Trolier-McKinstry,et al.  Piezoelectric nonlinearity in ferroelectric thin films , 2006 .

[13]  D. Hall.  Review Nonlinearity in piezoelectric ceramics , 2001 .

[14]  Dragan Damjanovic,et al.  STRESS AND FREQUENCY DEPENDENCE OF THE DIRECT PIEZOELECTRIC EFFECT IN FERROELECTRIC CERAMICS , 1997 .

[15]  Tagantsev,et al.  Phenomenological model of dynamic nonlinear response of relaxor ferroelectrics , 2000, Physical review letters.

[16]  Y. Shapir,et al.  Interface pinning and dynamics in random systems. , 1990, Physical review. B, Condensed matter.

[17]  O. Boser.  Statistical theory of hysteresis in ferroelectric materials , 1987 .

[18]  Amit Kumar,et al.  Nonlinear phenomena in multiferroic nanocapacitors: joule heating and electromechanical effects. , 2011, ACS nano.

[19]  S. Trolier-McKinstry,et al.  Strain-modulated piezoelectric and electrostrictive nonlinearity in ferroelectric thin films without active ferroelastic domain walls , 2011 .

[20]  Rayleigh Lord,et al.  XXV. Notes on electricity and magnetism.—III. On the behaviour of iron and steel under the operation of feeble magnetic forces , 1887 .

[21]  Thomas R. Shrout,et al.  Relaxor based ferroelectric single crystals for electro-mechanical actuators , 1997 .

[22]  Jacob L. Jones,et al.  Origins of Electro‐Mechanical Coupling in Polycrystalline Ferroelectrics During Subcoercive Electrical Loading , 2011 .

[23]  K. Seeger,et al.  Nonlinear electronic transport in TTF-TCNQ observed by microwave harmonic mixing , 1978 .

[24]  T. Nattermann.  Interface roughening in systems with quenched random impurities , 1987 .

[25]  S. Adler,et al.  Measurement of Oxygen Exchange Kinetics on Thin-Film La0.6Sr0.4CoO3 − δ Using Nonlinear Electrochemical Impedance Spectroscopy , 2007 .

[26]  Jacob L. Jones,et al.  Subcoercive Cyclic Electrical Loading of Lead Zirconate Titanate Ceramics I: Nonlinearities and Losses in the Converse Piezoelectric Effect , 2009 .

[27]  Isaak D. Mayergoyz,et al.  The science of hysteresis , 2005 .

[28]  Y. Avishai,et al.  Nature of the superconductor–insulator transition in disordered superconductors , 2007, Nature.

[29]  Zhimin Xue,et al.  Electrochemistry , 2012, Proceedings of the National Academy of Sciences.

[30]  D. Schwartz,et al.  Nonlinear electrochemical impedance spectroscopy for solid oxide fuel cell cathode materials , 2006 .

[31]  G. Arlt,et al.  Forced translational vibrations of 90° domain walls and the dielectric dispersion in ferroelectric ceramics , 1993 .

[32]  Daniel J. Inman,et al.  Powering pacemakers from heartbeat vibrations using linear and nonlinear energy harvesters , 2012 .

[33]  M. Fiebig,et al.  Second-harmonic generation as a tool for studying electronic and magnetic structures of crystals: review , 2005 .

[34]  S. Parkin,et al.  Magnetic Domain-Wall Racetrack Memory , 2008, Science.

[35]  C. C. Wang,et al.  Nonlinear optics. , 1966, Applied optics.

[36]  O. Boser.  Electromechanical resonances in ceramic capacitors and evaluation of the piezoelectric materials' properties , 1987 .

[37]  Sharon C. Glotzer,et al.  Measurement of growing dynamical length scales and prediction of the jamming transition in a granular material , 2007, 1012.4830.

[38]  J. Scott,et al.  Ferroelectric memories , 1997, Science.

[39]  Sergei V. Kalinin,et al.  Nanoscale Origins of Nonlinear Behavior in Ferroic Thin Films , 2013 .

[40]  Sergei V. Kalinin,et al.  Collective dynamics underpins Rayleigh behavior in disordered polycrystalline ferroelectrics , 2010, Proceedings of the National Academy of Sciences.

[41]  Boehmer,et al.  Electric-field-dependent dielectric constant and nonlinear susceptibility in SrTiO3. , 1995, Physical review. B, Condensed matter.

[42]  Stephen Jesse,et al.  Principal component and spatial correlation analysis of spectroscopic-imaging data in scanning probe microscopy , 2009, Nanotechnology.

[43]  王祖浩 孙丹儿 杨惠仙.  Chemistry:The Molecular Nature of Matter and Change评述 , 2007 .

[44]  Dragan Damjanovic.  LOGARITHMIC FREQUENCY DEPENDENCE OF THE PIEZOELECTRIC EFFECT DUE TO PINNING OF FERROELECTRIC-FERROELASTIC DOMAIN WALLS , 1997 .

[45]  S. Leary,et al.  Harmonic analysis of the polarization response in Pb(Mg/sub 1/3/Nb/sub 2/3/)O/sub 3/-based ceramics-A study in aging , 1998, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[46]  Amit Kumar,et al.  Mapping piezoelectric nonlinearity in the Rayleigh regime using band excitation piezoresponse force microscopy , 2011 .