Hidden variable in the electrocaloric effect of ferroics

Caloric effects allow for temperature control through adiabatic application of external fields and are actively explored for solid-state refrigeration. The common wisdom is that the application of ultrahigh fields enhances the effects, thus providing a route to their practical applications. Using the ferroelectric relaxor (Ba, Ca)(Ti, Zr)${\mathrm{O}}_3$, we demonstrate that in ferroics, which are the prime candidates for such application, this is not true in general and that caloric effects can be enhanced through the reduction of the applied field. The explanation of such a counterintuitive response is in the dependence of the electrocaloric effect on the effective poling field that can be regarded as a “hidden” variable of the caloric effects.

Figure 1

Polarization as a function of applied electric field (a), temperature (b), and electrocaloric change in temperature as a function of temperature in bulk BCZT (c). Panels (d)–(f) present the same dependencies but for 100-nm-thick BCZT film.

Figure 2

Ferroelectric hysteresis loops obtained in MD simulations with different range of electric fields: [–50:50] kV/cm (a), [–500:500] kV/cm (b), and [–5000:5000] kV/cm (c). In (c) left inset gives zero-field dipole distribution function at 520 K for two different values of the poling field. Right inset is schematic free-energy landscape in the vicinity of first-order phase transition. Dependence of polarization on temperatures (d)–(f) obtained from the data of panels (a)–(c), respectively. Electrocaloric change in temperature (g)–(i) computed from dependencies of panels (d)–(f) using Eq. (1). Electrocaloric change in temperature as a function of temperature due to application of 50-kV/cm field (j). Different curves correspond to different values of the poling field as given in the legend. Electrocaloric $\mathrm{\Delta }T\left(T\right)$ obtained from direct adiabatic simulations for different value of $E_0$ as given in the titles (k)–(l).

Figure 3

Hysteresis loops (a) and associated temperature dependence of polarization (b) in 100-nm BCZT thin film for poling field of 500 kV/cm. Electrocaloric $\mathrm{\Delta }T$ computed from experimental data using the approach of Eq. (1) (c). For comparison we include data for $E_0=1000$ kV/cm and $\mathrm{\Delta }E=$ 100 kV/cm (blue squares) and 500 kV/cm (blue circles). The peak electrocaloric temperature $\mathrm{\Delta }{T}_{\max }$ and its position $T_{\max }$ as a function of the poling field for the case $E_0=\mathrm{\Delta }E$ for both bulk ceramics and thin film (d). Open symbols correspond to the largest values in the given temperature range when the peak is outside the range.