2005/12/22 by Takeshi Nishimatsu, Nishimatsu, Takeshi, Umesh V. Waghmare +10
Chemistry · Engineering · Physics and Astronomy · #Acoustic Wave Resonator Technologies #Advanced Physical and Chemical Molecular Interactions #Mechanical and Optical Resonators #cond-mat.mtrl-sci
paper · pdf · doi:10.48550/arxiv.cond-mat/0512563
6 pages, 9 figures, submitted to The American Journal of Physics
arxiv created 2006/01/03 · arxiv updated 2009/12/01
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.