The soft mode concept and the history of ferroelectricity

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Abstract
I. THE SOFT MODE CONCEPT: In the late fifties ferroelectric research underwent a serious transition. Until that time the theory of ferroelectricity has been either phenomenological or consisted of attempts to develop microscopic theories for specific atomic structures. In 1959 Cochran1 pointed out that at second order ferroelectric transitions where the dielectric constant diverges there must be a transverse optical lattice vibration mode whose frequency goes to zero as the transition is approached. This suggestion turned out to be a tremendous stimulus to ferroelectric theory and research. Many first order transitions which are close to being second order ones also exhibit mode softening as the transition is approached. Whereas the soft mode idea was at first applied only to displacive type ferroelectrics, de Gennes2 extended it to order-disorder type crystals. In these systems one finds instead of soft phonons soft (usually overdamped) pseudo-spin wave type excitations3 or anomalously long relaxation times as the transition is approached.