Giant electrocaloric effect at the antiferroelectric-to-ferroelectric phase boundary in PbZrTiO$_3$

TL;DR

This study uses molecular dynamics simulations to reveal a giant electrocaloric effect at the phase boundary between antiferroelectric and ferroelectric states in PZT materials, providing atomistic insights into the mechanisms involved.

Contribution

It introduces the first detailed atomistic simulation analysis of the electrocaloric effect at the AFE-FE phase boundary in PZT, highlighting the origin of the giant effect.

Findings

Giant electrocaloric effect occurs at the AFE-FE phase boundary.

AFE materials show a positive-to-negative electrocaloric crossover.

Complex domain patterns are observed at the phase boundary.

Abstract

Molecular dynamics simulations predict a giant electrocaloric effect at the ferroelectric-antiferroelectric phase boundary in PZT (PbTiO$_3$-PbZrO$_3$). These large-scale simulations also give insights into the atomistic mechanisms of the electrocaloric effect in PZT materials. Studying a range of ferroelectric (FE) and antiferroelectric (AFE) PZT materials we found positive electrocaloric effect in FE composites, but AFE ones exhibit a positive-to-negative crossover. At the AFE-FE phase boundary we find complex domain patterns. We demonstrate that the origin of giant electrocaloric change of temperature is related to the easy structural response of the dipolar system to external stimuli the transition region.

Equations

$$\Delta T=-\underset{0}{\overset{E}{\int }}\frac{TV}{C_{p,E}}{\left(\frac{\partial P}{\partial T}\right)}_E\mathrm{d}E,$$

Full text

††preprint: AIP/123-QED

The electrocaloric effect is a reversible temperature change ($\Delta T$) in materials under adiabatic conditions in response to applied electric (or magnetic) field. The discovery of a giant 12 K electrocaloric effect (ECE) in thin films of Zr-rich lead titanate compositions fuelled interest into the development of novel ferroelectric-based ECE materialsMischenko et al. (2006).

Giant and moderate ECE’s have since been reported for classical ferroelectrics like BaTiO3Kar-Narayan and Mathur (2010) and for several relaxor materials Lu et al. (2010). Pb(Zr1-xTix)O3 (PZT) is a disordered solid solution ABO3 perovskite, with Pb atoms occupying the A-site, and Ti and Zr cations randomly arranged among the B-sites. PbTiO3 (PTO), the $x$=0.0 end member of Pb(ZrxTi1-x)O3, is a classical ferroelectric (FE), and the other end member PbZrO3 (PZO) ($x$=1.0) is antiferroelectric (AFE). Near $x$=0.95 there is a phase boundary that separates AFE and FE phasesWoodward, Knudsen, and Reaney (2005). Pb(Zr1-xTix)O3 (PZT) remains an active area of research for novel ECE materialsZhang et al. (2016); Zuo et al. (2015). The response of PZT to the applied electric field in the transition region between its ferroelectric and antiferroelectric phases is of particular interest since a giant electrocaloric response has been found experimentally for compositions close to this regionMischenko et al. (2006). Studies of electrocaloric response of AFE Pb0.97La${}_{0.02}($Zr0.95Ti0.05)O3 have provided an insight into a mechanism for the negative electrocaloric response. Authors suggested that misaligning of non-collinear dipoles provides different entropy contribution depending on the direction of the applied electric field  Geng et al. (2015).

Several theoretical works discuss caloric effects in perovskites. Large electrocaloric effects have been observed in the vicinity of ferroelectric-paraelectric phase transition, however, little is known about the ECE near AFE-FE phase boundary. Recent work with effective Hamiltonians reveals a strong potential of electrocalorics for thin PZO films with FE and AFE phase competitionKingsland, Lisenkov, and Ponomareva (2018). Phenomenological modelling for an AFE system predicted the negative electrocaloric effect in PZO ceramics, which agrees well with direct measurements of the EC temperature change in this systemPirc et al. (2014).

Molecular dynamics (MD) methods, using shell model potentials fit to first principles calculations, are promising models for computing the thermal behaviour of materials, since they do not require assumptions about the important degrees of freedom. Such models have been used to study ECE in LiNbO3, PMN-PT, and BaTiO3Rose and Cohen (2012); *Erratum14; Wu and Cohen (2017a, b). These simulations provide insight into the universal principles related to optimal operating temperature for the electrocaloric effect.

In this work we studied the effects of composition on electrocaloric properties of PZT using large scale MD simulations with first-principles based shell model potentialsGindele et al. (2015). We modelled a wide range of ferroelectric and antiferroelectric compositions of Pb(ZrxTi1-x)O3. We found that the electrocaloric response of PZT correlates with the type of ferroelectric order and that a giant electrocaloric response exists at the phase boundary of PZT, where antiferroelectric and ferroelectric order coexist.

To model the electrocaloric properties of PZT we use a core-shell force field, which includes all degrees of freedom. This $ab$  $initio$ based interatomic potential reproduces a set of temperature and composition induced phase transitions characteristic of Pb(ZrxTi1-x)O3Gindele et al. (2015). The potential model underestimates the Curie temperatures with respect to experiment for PbTiO3 (600 K versus 750 KWoodward, Knudsen, and Reaney (2005)) and PbZrO3 (400 K versus  507 KPirc et al. (2014)), which is a reasonable error for this type of force field.

A set of Pb(ZrxTi1-x)O3 compositions were modelled using the DL$\textunderscore$POLY codeTodorov et al. (2006). We study AFE and FE compositions with $x$ equal to 0.5, 0.9, 1 (corresponds to AFE PbZrO3), together with $x$=0 (that corresponds to FE PbTiO3), 0.7, 0.8, 0.85, 0.95 shown in Supplementary Information (SI). The B-site cations, Ti and Zr, were randomly distributed over the B-sites. We use the adiabatic shell model (also known as dynamical model Fincham and Mitchell (1993)) as a method of incorporating polarisability into a molecular dynamics simulation with the shell masses varying as 3.5 %, 8.3 %, 17.12 % and 12.5 % of the atomic mass of Pb, Ti, Zr and O, respectively. We used relatively large 20 $\times$ 20 $\times$ 20 super-cells (80 000 core and shell particles). Each composition was equilibrated at 100 K for 40 ps, followed by application of an electric field along the polar axis. The direction of the polar axis depends on the composition of Pb(ZrxTi1-x)O3  and was taken as [001] for PZO, [111] for the Zr content from 0.95 to 0.50, and as [001] for $x>=0.4$ . The strength of the applied electric field was 0, 5, 10, 15, 20, 25, 50, 75, 100 MV/m. We used a 0.2 fs timestep and NST ensemble with the Nosé-Hoover thermostat (0.01 ps) and barostat (0.5 ps) for equilibration of individual systems during 8 ps. The equilibration was followed by a 12 ps production run over which the polarisation value was calculated.

To study the electrocaloric effect we used the indirect method, where the change of temperatures were calculated from Maxwell related expression:

[TABLE]

Here, $E$ is the applied electric field, $T$ is the temperature, $V$ is the volume of the simulation cell and $C_{p,E}$ is the heat capacity per cell under constant electric field and pressure. We calculate the ECE change of temperature ($\Delta T$), by integrating equation (1) numerically. The values of $C_{p,E}$ were calculated as the derivative of the total energy with temperature ($\frac{\partial E_{tot}}{\partial T}$) at a given value of electric field, $E$ and are in agreement with experiment  Morimoto et al. (2003) (See Supplementary Information).

The temperature and field dependence of the electrocaloric change in temperature, $\Delta T$, were calculated for FE PTO via expression eq. (1) ( see Supplementary Information Fig. 1a.) A characteristic dominant peak at 650 K (the PTO Curie temperature reproduced by our force field) moves towards higher temperatures for larger applied electric fields, typical for ferroelectrics Rose and Cohen (2012); *Erratum14. The magnitude of electrocaloric effect calculated for PTO is good agreement with similar method computations for LiNbO3 that gives 17 K at applied 50 MV/m field versus 16 K in our computations for PTORose and Cohen (2012).

The morphotropic phase boundary (MPB) is found in a narrow compositional range around $x$=0.5, where the FE phase with rhombohedral symmetry transforms to the tetragonal phase. It is now known that there is a monoclinic transition region between the rhombohedral and tetragonal phases  Noheda et al. (1999); Cohen2018; Glazer2014; Bogdanov2016; FuCohen2000; Ahart2008. We found that the electrocaloric effect in FE Pb(ZrxTi1-x)O3  with $x$ = 0.5 and 0.7 exhibits very similar behaviour. The peaks of $\Delta T$ broaden, which reflects the B-site cations disorder and reduction of the correlation length in the material Guzman-Verri and Littlewood (2016) (See Fig. 1a, b and Supplementary Information, Fig. 1b, c). The $\Delta T$ curves peak above Tc* with increasing electric field (Fig. 1b), similar to what was computed for LiNbO3Rose and Cohen (2012).

The transition boundary between AFE and FE phases in Pb(ZrxTi1-x)O3  has been shown to exist within a composition region around $x$=0.95-0.9Woodward, Knudsen, and Reaney (2005). It is challenging to identify the precise composition of the transition region between AFE and FE phases experimentally, due to purity of the samples, composition variance, especially for solid solution materials, and the presence of surface effects that may stabilise the FE phase. The force field used in this work is able to reproduce the composition induced AFE-FE phase boundary, but the model gives a boundary wider than seen experimentally – we find composites with $x>$0.8 exhibit antiferroelectric propertiesGindele et al. (2015). Further, we have performed calculations of the electrocaloric properties for several of the AFE PZT compositions with $x$ of 0.9, and 1 (PbZrO3), while the result for 0.85, 0.95 are given in Supplementary Information.

We found that the electrocaloric response of AFE’s is very different to that of the FE systems. In AFE’s the applied electric field causes $T_{c}$ to decrease (Fig. 1c-f, SI Fig. 2), whereas ferroelectric materials show the opposite tendency. A common feature of all studied AFE PZT is a negative-to-positive crossover that varies with temperature and composition. Positive values of the EC $\Delta T$ are related to the reduction of isothermal entropy. In classical FE’s this is related to the drop of macroscopic polarisation with rising temperature. However, in AFE’s the polarisation may exhibit an opposite behaviour, i.e. increasing with rising temperature under applied field. This occurs simply because the applied field favours net polarisation and dielectric susceptibility then increases with temperature. The latter results in negative change of isothermal entropy, and reverse electrocaloric effect (See SI).

PZO does not exhibit a macroscopic polarisation at zero field, as expected for an AFE. Applied electric field induces a polarisation that increases up to the critical temperature, $T_{c}$, and then falls with further temperature rise (see Fig.  1 e, f). However, the induced polar state of PZO at an applied field of 100 MV/m is only 18 $\mu$ C/m2, which is 40 % lower than that of PTO. Ferroelectrics can also show negative ECE originated from polarisation rotation, where the polarisation along the field direction increases with temperature due to approaching phase transition  Wu and Cohen (2017a, b) Calculated behaviour of $\Delta T$ for PZO exhibits a crossover from negative to positive values in the vicinity of $T_{c}$ as shown in Fig. 1f. For applied electric fields $<$50 MV/m the EC change in temperature exhibits negative values below $T_{c}$ (at T=250 K the values of ECE are -0.7 K with applied field of 25 MV/m ).

At zero applied field AFE PZT ($x$=0.95, 0.9, 0.85, 0.8) shows zero macroscopic polarisation, but local dipoles, as will be shown later, form competing AFE and FE domains. Application of an electric field enhances the polarisation, which reaches its maximum at temperatures of 400 K, 350 K and 300 K characteristic for each composition with $x$=0.85, 0.90, 0.95, respectively (Fig. 1c, d, SI Fig. 2b, c, d).

The electrocaloric response of studied AFE’s is characterised by the negative-to-positive crossover. In PZO the EC $\Delta T$ changes its sign once, whereas AFE PZT exhibits more complex EC behaviour.

We have found that, in general, the EC effect in FE and AFE Pb(ZrxTi1-x)O3  with $x>0$ is smaller compared to the pure FE PTO (22.01 K at 100 MV/m of applied field (See SI Fig. 2a)), but at lower temperatures and, thus, more usable under ordinary conditions. At the AFE-FE boundary an enhanced caloric response comparable to MPB PZT. The smallest EC response is observed in the pure AE PZO of about 5 K at 100 MV/m of applied field. The AFE PZT with $x=0.8$ exhibits the EC effect of 6.1 K at a similar field (See SI, Fig. 1). Meanwhile, PZT with $x$=0.95, 0.9 exhibit values of EC $\Delta T$ of about 10 K (SI Fig. 2), which is comparable with the EC response of MPB PZT at similar stimuli.

To understand the origin of the giant EC effect and negative-to-positive crossover at the AFE-FE phase boundary we analysed the evolution of local dipoles in response to applied fields. We found that an AFE system may adopt complex dipole arrangements with a variety of possible states, such as dipole FE order, dipole disorder, and various AFE dipole arrangements characterised by zero macroscopic polarisation.

In particular, at small applied fields and low temperatures the AFE PbZr0.95Ti0.05O3  exhibits a dynamically stable 2$\times$1 pattern (Fig. 2a). Here, the local dipoles are arranged as antiparallel double pairs along $X$ cartesian direction, and single antiparallel arrangement along $Z$ axis (See directing arrows in the inset of Fig. 2a). At higher temperatures the order of local dipoles changes to a 1$\times$1 pattern, where single antiparallel dipoles are alternating with the sites of dipole disorder (Fig. 2b). Increasing the applied field to the critical value of 25 MV/m leads to the rotation of local dipoles, so the system turns into an induced polar FE state.

Increasing the Ti content leads to stabilisation of a zig-zag pattern of AFE local dipoles (Fig. 2c). Here, the local dipoles are arranged into antiparallel pairs. As the field increases the system develops competing AFE and FE domains, with widths which correlate with the strength of applied field. The critical field of 50 MV/m switches the system to an induced polar FE monodomain state.

Higher Ti content in PbZr0.85Ti0.15O3 increases the correlation length of the material,Guzman-Verri and Littlewood (2016) which leads to the formation of stripe ordering, with AFE dipole arrangement alternating with FE stripes (Fig. 2d).

We suggest that the nature of giant EC temperature change, $\Delta T$, in AFE PZT is related to the formation of competing AFE and induced FE orders that respond easily to applied fields and temperature. In ferroelectrics the configurational entropy is related to the order maintained by a dipolar system. In the absence of the applied field the change of polarisation with temperature, $\frac{\delta P}{\delta T}$, is relatively small, except the vicinity of the critical temperature, where this value is large. Thus, the maximum of EC $\Delta T$ in ferroelectrics occurs when the system switches from FE to PE.

An AFE system may adopt complex configurations with a variety of possible dipole states - as dipole FE order, dipole disorder, and various AFE dipole arrangements with zero macroscopic polarisation (as shown in Fig. 3, where the system maintained 2$\times$1, 1$\times$1 patterns). We suggest that in AFE systems the change from AFE to FE order happen via a sequence of local minima with a partially preserved AFE order and the formation of competing AFE and FE domains.

We assume that at applied field the aligned dipole configurations may became more advantageous to anti-polar configurations. This leads to destabilisation of anti-aligned arrangements of local dipoles in an AFE material leading to their partial, or complete alignment, and, consequently formation of competing antiferroelectric and induced ferroelectric domains. The transition process may happen through initial canting as proposed in ref. Geng et al., 2015, and follows complete rotation similar to the mechanism proposed for FE’s in ref. Wu and Cohen, 2017b.

In bulk PZO the change of polarisation $\frac{\delta P}{\delta T}$, is relatively small (SI Fig. 2), because our system is free of defects, and grain boundaries and electrode contacts. Thus, each local dipole has to overcome a barrier for rotation. However, in AFE Pb(ZrxTi1-x)O3  the presence of different types of B-site cations increases the configurational entropy of the system, and supports multiple domain configurations. The Ti sites act as nucleation centres for the FE phase, facilitating fast response of local dipoles to applied electric fields. At the AFE-FE phase boundary the concentration of Ti centres is such that there are no FE ordered regions in the absence of an applied electric field, however, the application of an external electric field gives rise to FE ordering, which competes with the AFE order (FIG. 3d). The maximum of EC $\Delta T$ in AFE composites occurs when the system switches to an induced polar FE monodomain.

We have studied the electrocaloric effect in PZT using molecular dynamics simulations with shell model forces fields. Our results show giant electrocaloric effects for FE PTO, in good agreement with similar calculations performed for FE LiNbO3Rose and Cohen (2012). We found a crossover from negative to positive EC temperature change for all studied AFE PZT. The crossover temperatures correlate with composition, which we believe to be related to the correlation length increase in the materialGuzman-Verri and Littlewood (2016). We have found that compositions close to the AFE-FE boundary of PZT exhibits an enhanced caloric response, comparable to that of MPB PZT but with the maximum EC temperature change occurring at temperatures closer to ambient temperatures. Our methodology allows to to investigate the details of the polarisation response at an atomistic level. Close to the AFE-FE boundary we identified complex dipole configurations, with competing FE and AFE domain patterns. We postulate that the small energy barriers associated with growing/ reducing these domains are responsible for the easy response of the polarisation to the applied field and temperature and, hence, for the enhanced calorific response. Despite the high EC response, the critical temperature in many ferroelectric materials is considerably higher than room temperature, which substantially limits the potential for the application in solid-state devices. We have found that AFE PZT exhibits extrema of EC $\Delta T$ close to room temperature, in the range 300-400 K. In addition, solid solution Pb(ZrxTi1-x)O3  offers great variability in critical temperatures and in ECE magnitude, which allows for compositional engineering of materials for electrocaloric applications. In summary, our findings suggest pathways for tuning the operating temperatures of ECE devices and find solutions for a broad range of operating conditions.

Supplementary Information

We show calculated heat capacity, and isothermal change of entropy in AFE and FE Pb(ZrxTi1-x)O3. We also calculated electrocaloric effect in FE PbTiO3, FE PbZr0.7Ti0.3O3, together with polarisation and electrocaloric temperature change in AFE PbZr0.95Ti0.05O3, and AFE PbZr0.85Ti0.15O3.

Authors acknowledge UCL computational facilities LEGION and MYRIAD. AK is supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Sk$\l$odowska-Curie grant agreement No 796781. REC was supported by the U. S. Office of Naval Research Grants No. N00014-12-1-1038, N00014-14-1-0516, and N00014-17-1-2768, the Carnegie Institution for Science, and the European Research Council Advanced Grant ToMCaT.