Probing phonon softening in ferroelectrics by the scanning probe microwave spectroscopy

Abstract

Microwave measurements have recently been successfully applied to measure ferroelectric materials on the nanoscale, including detection of polarization switching and ferroelectric domain walls. Here we discuss the question whether scanning probe microscopy (SPM) operating at microwave frequency can identify the changes associated with the soft phonon dynamics in a ferroic. The analytical expressions for the electric potential, complex impedance and dielectric losses are derived and analyzed, since these physical quantities are linked to experimentally-measurable properties of the ferroic. As a ferroic we consider virtual or proper ferroelectric with an optic phonon mode that softens at a Curie point. We also consider a decay mechanism linked to the conductance of the ferroic, and thus manifesting itself as the dielectric loss in the material. Our key finding is that the influence of the soft phonon dispersion on the surface potential distribution, complex impedance and dielectric losses are evidently strong in the vicinity (10-30 K) of the Curie temperature. Furthermore, we quantified how the spatial distribution and frequency spectra of the complex impedance and the dielectric losses react on the dynamics of the soft phonons near the Curie point. These results set the stage for characterization of polar phase transitions with nanoscale microwave measurements, providing a complementary approach to well established electromechanical measurements for fundamental understanding of ferroelectric properties as well as their applications in telecommunication and computing.

arXiv comment26 pages, including 4 figures and the supplementary materials

References in corpus (16)

• Nanoelectromechanics of Piezoresponse Force Microscopy
• Modeling of a Cantilever-Based Near-Field Scanning Microwave Microscope
• Nanoscale piezoelectric response across a single antiparallel ferroelectric domain wall
• Origin of the "Waterfall" Effect in Phonon Dispersion of Relaxor Perovskites
• Antiferrodistortive phase transition in EuTiO3
• Electromechanical Detection in Scanning Probe Microscopy: Tip Models and Materials Contrast
• Nanoelectromechanics of Polarization Switching in Piezoresponse Force Microscopy
• Low-energy Structural Dynamics of Ferroelectric Domain Walls in Hexagonal Rare-earth Manganites
• Emergence of a Dynamic Super-Structural Order Integrating Antiferroelectric and Antiferrodistortive Competing Instabilities in EuTiO3
• The Piezoresponse Force Microscopy of surface layers and thin films: effective response and resolution function
• Cryogenic Microwave Imaging of Metal-Insulator Transition in Doped Silicon
• The influence of elastic strain gradient on the upper limit of flexocoupling strength, spatially-modulated phases and soft phonon dispersion in ferroics
• Lattice dynamics and antiferroelectricity in PbZrO${}_3$ tested by X-ray and Brillouin light scattering
• Flexocoupling impact on the generalized susceptibility and soft phonon modes in the ordered phase of ferroics
• Sound behavior near the Lifshitz point in proper ferroelectrics
• Flexocoupling induced soft acoustic mode and the spatially modulated phases in ferroelectrics