Exploring Electro‐Thermal Interconversion in Oxide Superlattices Across Polarization Behavior Transition

Due to the great demand for global energy consumption, electro‐thermal energy interconversion has drawn great attention. Ferroelectrics as promising candidates realize energy conversion through pyroelectric and electrocaloric effects, but their efficiency is not sufficiently high. Herein, using phase‐field simulations, it is demonstrated that superlattices with polar topologies tend to have various polarization behaviors, and the antiferroelectric‐ to paraelectric‐like phase transition induces a large polarization change and thus a high pyroelectric response. In KNbO3/KTaO3 superlattices, the pyroelectric energy conversion has a scaled efficiency of 50% and the equivalent ZT of 7.2, and the electrocaloric cooling temperature reaches 40 K. The operation temperature can be tuned by changing the thickness of the superlattice. The results reveal that oxide superlattices are competitive in energy harvesting and conversion, thus creating new application prospects for polar topologies.


Introduction
Highly efficient interconversion of energies in different forms is an important technique for various applications. For example, power generation harvests electric energy from thermal, mechanical, and chemical energies, and refrigeration requires the conversion of heat into another kind of energy. Ferroelectrics (FE) can interconvert electric energy and heat via pyroelectric and electrocaloric effects, making them promising in handling energy harvesting and cooling , where 0 and r are permittivity of vacuum and relative permittivity of the material, respectively. [10] Therefore, a pyroelectric material with high pyroelectric coefficient and low dielectric permittivity is highly desired. Inversely, the electrocaloric effect that converts heat to electricity is realized in an adiabatic condition as electric field (E) induced entropy (S) of dipoles in FEs yields a temperature change. The temperature change ΔT = − ∫ T C(T) dE, where C(T) is the heat capacity of a material. [11] Thus, a high pyroelectric coefficient is a prerequisite to realize high electrocaloric effect.
The two effects both require high pyroelectric coefficients, and the high pyroelectricity in addition prefers suppressed dielectric permittivity. FEs in proximity to phase boundaries are always sensitive to external stimuli such as temperature and electric field. [12][13][14] Along this route, composition-, strain-, temperature-, and electric-field-induced multi-phase coexistence and high susceptibility have been well explored in Pb(Zr,Ti)O 3 , Ba(Zr,Ti)O 3 , PbTiO 3 -Pb(Mg,Nb)O 3 (PMN-PT), etc. [4,8,[15][16][17][18] However, the realization of high-efficiency electro-thermal conversion is still rare, and some of the outperformance was obtained at high temperature. In addition, because high pyroelectric coefficient is always along with high dielectric permittivity, significant enhancement in pyroelectric conversion is much harder. In order to access excellent interconversion ability near room temperature, new approaches should be explored.
Recently, unique polarization structures such as polar vortices, spirals, skyrmions, and merons have been revealed in FE/paraelectric (PE) superlattices, [19][20][21] offering a fertile ground to explore complicated phase coexistence and their response to electric and thermal fields. [22][23] It has been found that polartopology-contained FE/PE multilayers exhibit unique polarization hysteresis loops, indicating ample phase boundaries in terms of polarization behaviors and more chances for large polarization changes to occur. [20] In the meanwhile, FE/PE superlattice should be more FE-like in fields that are far from domain switching, implying relatively low permittivity. However, there lacks a comprehensive study of the thermally-induced phase transition in FE/PE superlattices and how much their electro-thermal interconversion performance can be enhanced. In this work, we use phase-field simulations to study the effects, which have been well proven to be effective and accurate in rebuilding polar-topologycontained superlattices. [24][25][26]

Simulation Setups
Considering that our priority is to obtain high pyroelectric coefficient, only initial large polarization is able to yield large polarization change, so we chose three typical FE/PE superlattices with considerable polarizability, BiFeO 3 /SrTiO 3 (BFO/STO), KNbO 3 /KTaO 3 (KNO/KTO), and PbZr 0.2 Ti 0.8 O 3 /SrTiO 3 (PZT0.8/STO). The superlattice is coherently constructed from a substrate with alternating PE and FE layers, capped with a PE layer on the top. The lattice mismatch between FE and substrate is zero. The number of unit cells (u.c.) in FE layers is 12, and that of PE layers changes (marked as n = 4, 6, 8, 10, and 12). This design can ensure the robust ferroelectricity and regulate the polarization magnitude and domain rigidity. The period is fixed as 5, and the superlattice is abbreviated as (12/n) 5 . The electric field applied is 2 MV cm −1 , and the temperature is set from 300 to 450 K, no more than 150 K higher than the room temperature. A cross-sectional 2D simulation is employed. The detailed phase-field methodology and related constants are included in the Method section.

Thermal Evolution of Polar Topologies and Their Polarization Behaviors
The simulations output the cross-sectional polarization mapping of all three (12/n) 5 superlattices in Figure S1-S5 (Supporting Information), and the representative polarization mappings are presented in Figure 1a. When the PE layer is thin and the temperature is low, the FE layer tends to be purely single domain without any exotic topologies (Figure 1a, first panel) at a cost of higher electric energy because domain walls in this case are more energetically costly. When temperature is elevated or the PE layer is thicker, polar topologies of spiral-like polarization flux occur in FE layers due to the depolarization (Figure 1b, second and third panel). The appearance of single domains and polar spirals is consistent with our previous results and implies the possibility of various polarization behaviors. [20,27] Figure 1b summarizes domain structures of all three superlattices, and clearly demonstrates the tendency that single domain is more stable for thinner superlattices at lower temperatures. PZT0.8/STO, however, seems to contradict this trend, but it still has single domains when n is down to 2 (not shown here).
To understand this trend, we conducted further energetic analysis in FE layers ( Figure 1c) The competition between single domain and polar spirals is dependent on the total energy of domain and domain walls (DWs). Domains have lower Landau energy because of the spontaneous polarization; Landau energy at DWs is basically higher, but the depolarization field lowers the electric energy. If, in total, DWs have lower energy, spirals composed of domain and DWs should be more energetically stable than single domains. In (12/4) 5 superlattices at 300 K, BFO/STO and KNO/KTO show deep Landau potential wells and single domains are more favorable; PZT0.8/STO has lower total energy at DWs, so spirals can be stabilized at 300 K. However, at 400 K, as the domain Landau energy increases with the increased temperature, DW energy is lower than domain energy in KNO/KTO as the electric energy can compensate for the Landau energy, and therefore polar spirals occur. This means that higher temperature do not intrinsically favor long-range FE orders. For BFO/STO, as BFO has an ultrahigh Curie temperature (1103 K), [28] its single domain to spiral transition has not occurred, and according to Figure 1b, the spirals form until the average ferroelectricity is further eliminated in (12/6) 5 . Distinct differences in ferroelectricity maintenance and energy competition between domain and DWs profoundly influences polar topologies in three types of superlattices and further their polarization behaviors. Figure 2a-c displays the simulated P-E hysteresis loops for three superlattices at 2 MV cm −1 , and Figure 2d summarizes the coercive field (for single domains, the coercivity refers to the switching of polarization, and for spirals, it refers to the disruption of topology) and polarization behaviors. For single domains such as (12/4) 5 BFO/STO, they behave just FE-like. Elevated temperatures and increased PE layer thickness suppress the total ferroelectricity, and hence the coercive field reduces (Figure 2d, FE part). For spirals, the increase of electric field induces the spiral to single domain transition, and the removal of field causes a recovery of polar topologies, as is reported before, resulting in antiferroelectric (AFE)-like loops. [20] In this case, the further suppression of ferroelectricity by temperature and PE layers favors the stabilization of PE-like state where polarizations are laid in-plane, bridged by the delayed AFE-FE transition, i.e., increased coercive field for spirals, until the transition is out of the 2 MV cm −1 field range. This transition can be found apparent in KNO/KTO, but is less noticeable in BFO/STO and PZT0.8/STO. BFO has very rigid ferroelectricity due to the high Curie temperature and rhombohedral nature, so out-of-plane polarization behavior barely changes in the AFE region; [28] PZT0.8 has smaller polarization but comparably larger permittivity in the linear segment (Figure 2c), so the AFE-PE change does not lead to an abrupt change in polarization magnitude. By contrast, KNO has relatively large polarization, approaches the orthorhombic-rhombohedral-tetragonal phase boundaries at 300-450 K, [29] and has low permittivity if there is no domain switching. These features endow KNO/KTO not only the largest gradual polarization change caused by temperature and PE layer thickness far from phase boundaries but also the most significant AFE-PE transition, making it appealing for electro-thermal interconversion.

Pyroelectric Performance
The room-temperature pyroelectric performance of (12/8) 5 superlattices is further studied by extracting important parameters from hysteresis loops. Figure 3a shows hysteresis loops at 300 and 310 K. The relative dielectric permittivity arises from the differential of P with respect to E, r = dP 0 dE , as shown in Figure 3b. The subtraction of the two gives the polarization change at room temperature and is used to calculate the pyroelectric coefficient , as shown in Figure 3c. The dielectric permittivity of all superlattices generally has four peaks, in accordance with the field-induced polar topology disruption and recovery. However, KNO/KTO has two more small peaks, indicating its topology recovery is a two-step process and also rendering more susceptible polarization characteristics. All high-field permittivity is low, which is not surprising because, unlike relaxor FEs, FEs are usually easier to reach the polarization saturation. Among the three, KNO/KTO has the lowest high-field permittivity (85 for BFO/STO, 62 for KNO/KTO, and 80 for PZT0.8/STO), and the largest switching-field responses. As for pyroelectric coefficients, KNO/KTO superlattices are the highest in magnitude, being −1.67×10 −3 C m −2 K −1 , while BFO/STO and PZT0.8/STO are −8.2×10 −4 C m −2 K −1 and −8.9×10 −4 C m −2 K −1 , respectively. This means that even at room temperature that is far from the phase boundary, KNO/KTO are the most responsive to temperature, possibly owing to the close energy of different phases. [29] Using dielectric permittivity and pyroelectric coefficient, one can anticipate its room temperature pyroelectric performance by calculating the FoM (Figure 3d), and the results turn out undoubtfully that KNO/KTO is the most outperforming one, by combining the two advantages. The FoMs of BFO/STO, KNO/KTO and PZT0.8/STO are 900, 5100, and 1100 C V m −3 K −2 , respectively. All FoMs are at least 10 times of the outstanding PMN-PT, and the KNO/KTO superlattice can be 50 times superior than that result. [8] The above merits quantitatively evaluating the pyroelectric performance of superlattices, but only by letting the pyroelectrics undergo cycles will we know their real operation capability. Figure  4a shows the adapted Ericsson cycle we use here. The pyroelectric is electrically poled at a low temperature T low from a starting electric field E 1 to the ending electric field E 2 , followed by an isoelectric process with the temperature elevated to T high . Then, the pyroelectric is de-poled at this high temperature to E 1 , and the material is cooled to T low . The green shadowed area represents the conversed energy density by calculating the loop integral. The efficiency of this conversion is calculated by the division of conversed energy and input heat energy  [30] The heat capacity of BFO, KNO, PZT0.8, STO and KTO are taken from existing results with appropriate approximations for PZT0.8. [31][32][33][34][35] Figure 4b-d exhibits the conversed energy density, scaled efficiency, and equivalent ZT of (12/8) 5 Figure 5. Optimization of operation temperature by the PE layer thickness. a) Conversed energy density, b) scaled efficiency, and c) equivalent ZT for (12/n) 5 superlattices starting from 300 K (room temperature), 350 K and 400 K at a temperature difference of 50 K. d-e) Equivalent ZT for (12/n) 5 (d) BFO/STO, (e) KNO/KTO, and f) PZT0.8/STO superlattices with starting temperature ranging from 300 to 400 K at a temperature difference of 50 K. The electric field range in these cycles is 1.5-2.0 MV cm −1 .
superlattices starting from 300 K with various temperature differences, respectively. In good agreement with parameterized pyroelectric evaluations, the results confirmed the excellent pyroelectric energy conversion ability of KNO/KTO. The conversed energy density, as calculated from the loop integral, maximizes for KNO/KTO (9.3 J cm −3 for 300-350 K and 15.0 J cm −3 for 300-450 K, over 3 times higher than BFO/STO and PZT0.8/STO) because the temperature range from 300 K to 450 K has crossed the AFE-PE transition and enjoyed the huge polarization decline (Figure 2b). Note that although the polarization monotonously decreases and hence the energy density increases in the same fashion, the temperature difference of 50 K has the highest efficiency since further increase of temperature do not substantially reduce the polarization. Indeed, the scaled efficiency and the equivalent ZT of KNO/KTO at a temperature difference of 50 K are the highest, being 46% and 5.7, respectively, and are ≈4 times higher than that at a temperature difference of 150 K and over 4 times higher than BFO/STO and PZT0.8/STO. The equivalent ZT surpasses all thermoelectric materials ever explored, to say nothing of such a low working temperature. [36] These impressive results indicate that KNO/KTO owns compelling pyroelectric energy conversion efficiency.
Taking a look back at Figure 2a-c, the AFE-PE transition temperature can be tuned by the PE layer thickness, which can be used as a modulator for the pyroelectric operation temperature. Especially for KNO/KTO, the transition of (12/4) 5 occurs between 400-450 K, that of (12/6) 5 occurs between 350-400 K, and that of (12/8) 5 occurs between 300-350 K. Thus, fixing the temperature difference at 50 K, the conversion energy and efficiency of KNO/KTO superlattices that start from 300 K, 350 K, 400 K peak at PE layer thickness of 8 u.c., 6 u.c., 4 u.c., respectively (Figure  5a-c). The highest energy density, scaled efficiency and equivalent ZT are 9.5 J cm −3 , 50% and 7.2 at the temperature of 350-400 K, respectively. PZT0.8/STO also has AFE-PE transitions, although less conspicuous, and left-shifted peaks of the PE layer thickness with the increase of starting temperature. BFO/STO, however, does not show this trend because of the absence of AFE-PE transition. The higher efficiency relies on larger PE layer thickness, possibly because the weakened ferroelectricity is more vulnerable to the temperature.
Figure 5d-f shows a panorama of how the efficiency changes as a function of starting operation temperature and the PE layer thickness, with the temperature difference being 50 K. As stated, given the lack of AFE-PE transition, BFO/STO with thicker PE layers is more responsive, so the equivalent ZT reaches the maximum at (12/12) 5 (≈0.7, Figure 5d). PZT0.8/STO with thinner PE layers has more noticeable AFE-PE transitions, so the equivalent ZT reaches the maximum at (12/4) 5 (≈ 0.7, Figure 5f). KNO/KTO seems to combine the features of BFO/STO and PZT0.8/STO, as the temperature of noticeable AFE-PE transition is coupled with the PE layer thickness, rendering an inclined belted region where the equivalent ZT is the highest (≈7, Figure 5e).

Electrocaloric Performance
Having studied the pyroelectric energy conversion, let us now investigate its inverse effect, electrocaloric cooling. The adiabatic entropy change for an electrocaloric generator from electric field dE and the cooling temperature Figure 6a shows the temperature change (solid line, left axis) and entropy change (dashed line, right axis) of (12/8) 5 superlattices at room temperature with an electric field from 2 ΔE to 2 MV cm −1 . The electrocaloric effect only relies on the pyroelectric coefficient, given the fixed electric field and operation temperature. Therefore, KNO/KTO should be the most excellent superlattice. It realizes a cooling temperature of 20 K with an electric field of 1.5-2.0 MV cm −1 , and a higher cooling temperature of 35 K, which is ≈3-4 times that of BFO/STO and PZT0.8/STO. All three superlattices show increased ΔT and ΔS in magnitude, indicating that broader electric field range is beneficial to the cooling temperature. However, if ΔT is divided by the operating electric field range ΔE, the obtained parameter represents the field efficiency of electrocaloric cooling. The field efficiency of cooling reaches the highest when ΔE is 0.5 MV cm −1 , and that of KNO/KTO is ≈40 K cm MV −1 . Similarly, since pyroelectric energy conversion has a tunable operation temperature given the AFE-PE transition, electrocaloric effect does the same as shown in Figure 6b,c. In Figure 6b, given the fixed electric field of 1.5-2 MV cm −1 , the best operation temperature of KNO/KTO superlattices is elevated as the PE layer thickness goes smaller, while BFO/STO and PZT0.8/STO remains almost intact. Figure 6c shows a similar mapping to Figure 5e, locating the best cooling effectiveness as a function of operation temperature and the PE layer thickness. The inclined region has the highest cooling temperature when the operation temperature is exactly the AFE-PE transition. The performance can be as high as 40 K for cooling temperature and ≈80 K cm MV −1 with the consideration of the field efficiency at an operation temperature of 310 K for (12/8) 5 , being higher than most state-of-the-art electrocaloric materials. [3,11,37]

Conclusion
In summary, we demonstrate the effectiveness of enhancing electro-thermal interconversion efficiency by using the polarization behavior transition originating in polar topologies. Thermal evolution of polarization structures and their corresponding P-E hysteresis behaviors are investigated, and the AFE-PE tran-sition causes a huge polarization change and leads to a large electro-thermal response. KNO/KTO superlattice has the most conspicuous AFE-FE transition, along with its multiphase competition and small dielectric permittivity, making it the most efficient pyroelectric material. The room temperature pyroelectric FoM, scaled efficiency, and equivalent ZT can be as high as 5100 C V m −3 K −2 , 50%, and 7.2. Similarly, the electrocaloric effect is also remarkable; the KNO/KTO superlattice can create a 40 K temperature for cooling with a field efficiency of 80 K cm MV −1 near room temperature. The operation temperature of the electro-thermal interconversion can be tuned by AFE-PE transition as determined by the PE layer thickness. Our results reveal that superlattices with polar topologies are competitive in energy harvesting and conversion, and thus creating possibilities of replacing traditional FE materials.

Experimental Section
Phase-field Simulation: In the modeling, the ferroelectric polarization vector P = (P 1 ,P 2 ,P 3 ) is chosen as the only order parameter. The energy distribution and domain structure are obtained by solving the time-dependent Ginzburg-Landau equation P t = −L F P , where L is the kinetic coefficient, t is the time, and F is the free energy expressed as the integral of individual energy densities F = ∭ (f Landau + f gradient + f elastic + f electric )dV. The free energy terms can be found in previous literature. [20,24] All materials constants are taken from existing reports. [20,29,38,39] Since there is no potential for KTO, so we use that of STO as a substitution. [27] The 2D cross-sectional simulation of the superlattice total grid is sized 100Δ × 1Δ × [20 + 5(n + 12 + 2) + n + ]Δ in x, y, and z, where Δ = 0.4 nm is the grid spacing. In z direction, 20, 5, n, 12, 2, n, and represent the substrate, superlattice period, PE layers, FE layers, interfacial layers, top capping layers, and the air above the film, respectively. The parameters of the interfacial layer are the average of the adjacent two layers. A short-circuit boundary condition is set to obtain domain structures and P-E loops.
[50] The mechanical boundary condition is that the out-of-plane stress on the top of the film equals zero, whereas the displacement is zero at the bottom of the substrate. Periodic boundary conditions along x and y directions are used. The initial polarization nuclei are randomized noises within 0.01 C m −2 in magnitude. The phase-field simulation was conducted using the commercial mu-pro package (http://mupro.co/).

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.