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Materials like iron, nickel, and cobalt consist of magnetic domains, within which the magnetic dipoles are arranged parallel to each other. The magnetic dipoles are rigidly aligned in the same direction within a domain by quantum mechanical coupling among the atoms. This coupling is so strong that even thermal agitation at room temperature cannot break it. The result is that each domain has a net dipole moment. However, some materials have weaker coupling, and are ferromagnetic at lower...
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The Fermi-Dirac function is represented by an S-shaped curve indicating the probability of an energy state being occupied by an electron at a given temperature. The Fermi level is the energy level at which there is a fifty percent chance of finding an electron, and it is positioned between the lower-energy valence band and the higher-energy conduction band.
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An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔHlattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid sodium chloride, the lattice energy is the enthalpy change of the process:
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Related Experiment Video

Updated: Jul 19, 2025

Measuring Magnetically-Tuned Ferroelectric Polarization in Liquid Crystals
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Measuring Magnetically-Tuned Ferroelectric Polarization in Liquid Crystals

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Lamellar Fluctuations Melt Ferroelectricity.

G G Guzmán-Verri1, C H Liang2, P B Littlewood3

  • 1Centro de Investigación en Ciencia e Ingeniería de Materiales, Universidad de Costa Rica, San José 11501, Costa Rica; Escuela de Física, Universidad de Costa Rica, San José 11501, Costa Rica; and Department of Materials Science and Metallurgy, University of Cambridge, Cambridge CB3 0FS, United Kingdom.

Physical Review Letters
|August 11, 2023
PubMed
Summary
This summary is machine-generated.

Thermal and quantum fluctuations destabilize long-range modulated order in ferroelectrics, even at low temperatures. Systems like SrTiO3 and KTaO3 are likely "melted" states driven by fluctuations.

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Area of Science:

  • Condensed matter physics
  • Materials science
  • Solid-state physics

Background:

  • Flexoelectric interaction couples electrical polarization to elastic strain gradients.
  • This coupling hybridizes acoustic and optic phonon modes.
  • It can lead to modulated lattice structures preceding ferroelectric transitions.

Purpose of the Study:

  • Investigate the impact of thermal and quantum polarization fluctuations on hybridized phonon modes.
  • Determine the stability of flexoelectric-induced modulated phases.
  • Understand the behavior of nearly ferroelectric materials like SrTiO3 and KTaO3.

Main Methods:

  • Utilized the Ginzburg-Landau model for ferroelectrics.
  • Employed the self-consistent phonon approximation.
  • Calculated the effects of fluctuations on bare hybridized modes.

Main Results:

  • Long-range modulated order, driven by flexoelectricity, is found to be unstable at all temperatures.
  • Thermal and quantum fluctuations disrupt the formation of these ordered phases.
  • The underlying modulated state is dominated by nonzero momentum thermal fluctuations.

Conclusions:

  • The observed modulated phases are unstable due to fluctuations.
  • Nearly ferroelectric materials (SrTiO3, KTaO3) are proposed to be 'melted' versions of these unstable modulated states.
  • Nonzero momentum thermal fluctuations are key, except at very low temperatures.