Scaling behavior of an antiferroelectric hysteresis loop

Abstract

A double hysteresis loop of an antiferroelectric betaine phosphate-arsenate mixed crystal (${\mathrm{BP}}_{0.9}$${\mathrm{A}}_{0.1}$) was studied as a function of applied frequency \ensuremath{\Omega} and field amplitude ${\mathrm{E}}_{0}$. A scaling analysis of the antiferroelectric hysteresis loop was given to show ${\mathrm{A}}_{\mathrm{H}}$\ensuremath{\propto}(${\mathrm{E}}_{0}$-${\mathrm{E}}_{\mathrm{c}}$${)}^{0.50}$${\mathrm{\ensuremath{\Omega}}}^{0.40}$, where ${\mathrm{A}}_{\mathrm{H}}$ represents the area of the hysteresis loops and ${\mathrm{E}}_{\mathrm{c}}$ a threshold field for observing the hysteresis curves. The scaling exponents are found to be close to the reported theoretical results of the two-dimensional ferromagnetic Ising models. We have also found a different scaling behavior for the antiferroelectric minor loops as ${\mathrm{A}}_{\mathrm{m}}$\ensuremath{\propto}(${\mathrm{E}}_{0}$-${\mathrm{E}}_{\mathrm{c}}$${)}^{2.12}$${\mathrm{\ensuremath{\Omega}}}^{0.28}$, where ${\mathrm{A}}_{\mathrm{m}}$ represents the area of the minor loops.