Step-by-step first order antiferroelectric-paraelectric transition induced by frustration and electric field

In this work we show analytically that even not too strong frustrating next neighbour interaction strongly affects first order antiferroelectric-paraelectric transition in an external electric field. We apply mean-field Landau theory. In the electric field a single phase transition at $T_0$ splits into a step-by-step staircase with a series of intermediate phases. Unexpectedly enough we found that the equilibrium structures of the phases differ substantially from structures formed at low temperature both without field and in field. Polarization of intermediate structures decreases with temperature in a stepwise manner. Similar step-by-step transitions can occur also in magnetic materials with frustrating interaction.