Ferroics: magnetic-compass lattice and optical phonon dispersions of dipolar crystals

Details Ferroics: magnetic-compass lattice and optical phonon dispersions of dipolar crystals Ferroics: magnetic-compass lattice and optical phonon dispersions of dipolar crystals

2005-12-22

arxiv.org/abs/cond-mat/0512563v2

Physics

Condensed Matter

Materials Science

6 pages, 9 figures, submitted to The American Journal of Physics

Scientific paper

We report a simple safe and attractive pedagogic demonstration with magnetic compasses that facilitates an intuitive understanding of the concept that ferromagnetism and ferroelectricity do not result from dipole-dipole interactions alone. Phonon dispersion relations were calculated for a 3-dimensional simple-cubic dipole crystal and a 2-dimensional square-lattice dipole crystal. The latter calculation corresponds to the compass demonstration that confirm the antiferro ground state structure. A sum rule for the three optical phonon frequencies is discussed. A mathematical non-analyticity in the longitudinal optical phonon are also illustrated.

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