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Potential Due to a Polarized Object01:29

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A neutral atom consists of a positively charged nucleus surrounded by a negatively charged electron cloud. When placed in an external electric field, the external electric force pulls the electrons and nucleus apart, opposite to the intrinsic attraction between the nucleus and the electrons. The opposing forces balance each other with a slight shift between the center of masses of the nucleus and the electron cloud, resulting in a polarized atom. On the other hand, a few molecules, like water,...
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The coupling interactions of nuclei across four or more bonds are usually weak, with J values less than 1 Hz. While these are usually not observed in spectra, the presence of multiple bonds along the coupling pathway can result in observable long-range coupling.
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In bromoethane, the three methyl protons are coupled to the two methylene protons that are three bonds away. In accordance with the n+1 rule, the signal from the methyl protons is split into three peaks with 1:2:1 relative intensities. The methylene protons appear as a quartet, with the relative intensities of 1:3:3:1.
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Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Crystallography

Background:

  • Lattice vibrations (phonons) are fundamental to material properties.
  • Macroscopic polarization in crystals is typically associated with ferroelectric or piezoelectric effects.
  • Understanding the coupling between lattice dynamics and electronic/magnetic properties is crucial.

Purpose of the Study:

  • To investigate the induction of macroscopic polarization by lattice modes of arbitrary symmetry.
  • To identify and characterize the nature of these polarization contributions.
  • To develop a computational framework for calculating the relevant coupling parameters.

Main Methods:

  • Theoretical derivation of polarization response to lattice distortions.
  • Identification of symmetric (flexoelectric-like) and antisymmetric (Dzialoshinskii-Moriya-like) terms.
  • Development of a first-principles computational methodology.

Main Results:

  • Lattice modes induce macroscopic polarization at first order in momentum and second order in amplitude.
  • A symmetric flexoelectric-like contribution, dependent on boundary conditions, was identified.
  • An antisymmetric Dzialoshinskii-Moriya-like term, independent of boundary conditions, was also found.

Conclusions:

  • Lattice dynamics can directly lead to macroscopic polarization through novel mechanisms.
  • The developed first-principles method allows for the quantitative prediction of these effects in any crystal.
  • The findings are exemplified by calculations for the antiferrodistortive order parameter in SrTiO3.