Abstract
Depolarization in ferroelectric materials has been studied since the 1970s, albeit quasi-statically. The dynamics are described by the empirical Merz law, which gives the polarization switching time as a function of electric field, normalized to the so-called activation field. The Merz law has been used for decades; its origin as domain-wall depinning has recently been corroborated by molecular dynamics simulations. Here we experimentally investigate domain-wall depinning by measuring the dynamics of depolarization. We find that the boundary between thermodynamically stable and depolarizing regimes can be described by a single constant, Pr/ε0εferroEc. Among different multidomain ferroelectric materials the values of coercive field, Ec, dielectric constant, εferro, and remanent polarization, Pr, vary by orders of magnitude; the value for Pr/ε0εferroEc however is comparable, about 15. Using this extracted universal value, we show that the depolarization field is similar to the activation field, which corresponds to the transition from creep to domain-wall flow.
Highlights
Depolarization in ferroelectric materials has been studied since the 1970s, albeit quasistatically
For the ferroelectric random copolymer poly(vinylidenefluoride– trifluoroethylene) [P(VDF–TrFE)], the depolarization field can be estimated as 1 GV/m using a remanent polarization of 7 μC/cm[2] and a static dielectric constant of 10
This circuit yields a relation between depolarization field and suppressed remanent polarization, and has been verified by quasi-static hysteresis loop measurements[3], where the electric field is gradually changed
Summary
Depolarization in ferroelectric materials has been studied since the 1970s, albeit quasistatically. For the ferroelectric random copolymer poly(vinylidenefluoride– trifluoroethylene) [P(VDF–TrFE)], the depolarization field can be estimated as 1 GV/m using a remanent polarization of 7 μC/cm[2] and a static dielectric constant of 10. This field is an order of magnitude higher than the experimental coercive field, Ec, of about 50 MV/m. Depolarization can be modeled using an equivalent circuit comprising a linear capacitor in series with a ferroelectric capacitor[4,5,6] This circuit yields a relation between depolarization field and suppressed remanent polarization, and has been verified by quasi-static hysteresis loop measurements[3], where the electric field is gradually changed. When a high applied electric field is abruptly switched off, the final polarization state is not a priori known; as the polarization is a highly non-linear function of the electric field, one might even expect macroscopic polarization reversal as an overshoot effect
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