Typical spontaneous symmetry breakdown in solid state as revealed by Fe₃O₄

Several of our experimental results, as seen from the side of the symmetry breakdown of this most characteristic material, will be shown. X-ray study reveals that the lattice constant decreases approximately by 7×10 ^-6 per degree from room temperature to the Verwey temperature T _v. At T_v, the cell volume increases by about 6×10^-4, suggesting the presence of covalent nature in the crystal. At T_v, the crystal transforms to monoclinic. Although there is a report of another transition at about 12°K, very careful work by X-ray and NMR showed no discontinuous change in this temperature region in the accuracy up to 10^-4. Detailed measurements of magnetoelectric effect were performed at 4.2°K and up to 34°K statically and dynamically. The induced electric potentials between the two planar electrodes formed parallel to a-, b-, or c-plane were observed as a function of the direction of the magnetic field in a-plane. Magnetic field cooling along [112], squeezing along [111] and electrically polarizing along a-, b-, or c-axis were simultaneously performed. We found that the electrically polarizing at and below T_v is only effective along a-axis. The crystal symmetry revealed is nearly monoclinic and may be triclinic. Again no appreciable discontinuous signal is observed near 12°K.