A Local Approach to Solid State Problems: Pseudo Jahn-Teller origin of Ferroelectricity and Multiferroicity

This is a partially review paper in which, in continuation of previous work, it is shown that in perovskite crystals of ABO(3) type the spontaneous polarization is triggered by local vibronic interactions, the pseudo Jahn-Teller effect (PJTE). The driving force of the latter is added covalency by distortion, which is essentially of local (chemical) origin. The local origin of polar instability in crystals is confirmed by the theorem of structural instability proved earlier. For crystals of BaTiO3 type local PJT interactions of the metal ion with the oxygen environment results in a peculiar adiabatic potential energy surface (APES) which has eight trigonal [111] type minima, twelve [110] type saddle points between them, six higher in energy [100] type saddle points at the top of the barrier connecting four minima, and a maximum at the cubic symmetry. The temperature dependence of the free energy with this potential explains the origin of all the four phases in such crystals; only the lowest rhombohedral phase is fully ordered, the other two ones at higher temperatures are partially disordered, and the paraelectric phase is fully (three-dimensionally) disordered. For BaTiO3 this picture is confirmed by numerical estimates and ab initio DFT calculations. An important further development of this theory was reached recently by showing that not only B ions with electronic d(0) configurations are subject to the PJTE instability to produce ferroelectricity in perovskite crystals (the d(0) mystery), but some other specific d(n) configurations with unpaired electrons may be dipolar active too, the crystal being thus both magnetic and ferroelectric (multiferroic), and the necessary conditions for such multiferroicity are formulated for the whole d(0)-d(n) variety of perovskites. Moreover, the condition of multiferroicity was shown to depend also on the spin state, high-spin or low-spin, which in conditions of spin crossover leads to a magnetic-ferroelectric crossover that can be manipulated by external perturbations.