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

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.