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## Creator

[Yukiya Tanaka](https://orcid.org/0009-0002-3209-9925), [Ryo Iguchi](https://orcid.org/0000-0002-8112-4608), [Takashi Teranishi](https://orcid.org/0000-0001-8755-1224), [Shinya Kondo](https://orcid.org/0000-0002-6194-4879), [Akira Kishimoto](https://orcid.org/0000-0003-4949-2723)

## Rights

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Yukiya Tanaka, Ryo Iguchi, Takashi Teranishi, Shinya Kondo, Akira Kishimoto; Permittivity and remanent polarization contributions to the electrocaloric effect in (Ba, Sr)TiO3 under unipolar field. Appl. Phys. Lett. 31 March 2025; 126 (13): 132902 and may be found at https://doi.org/10.1063/5.0259805.[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)

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[Permittivity and remanent polarization contributions to the electrocaloric effect in (Ba, Sr)TiO3 under unipolar field](https://mdr.nims.go.jp/datasets/fdd49d3d-135e-4ee7-93e8-b6e4bf21b2d5)

## Fulltext

Tanaka et al ECE_MDRPermittivity and remanent polarization contributions to the electrocaloric effect in (Ba, Sr)TiO3 under unipolar field  Yukiya Tanaka1, Ryo Iguchi2*, Takashi Teranishi1, 3*, Shinya Kondo1, Akira Kishimoto1,   1Graduate School of Natural Science and Technology, Okayama University, 3-1-1 Tsushima-naka, Kita, Okayama 700-8530, Japan 2National Institute for Materials Science, 1-2-1 Sengen, Tsukuba 305-0047, Japan 3Laboratory for Materials and Structures, Tokyo Institute of Technology, 4259 Nagatsuta, Midori, Yokohama 226−8503, Japan  a)Authors to whom correspondence should be addressed: IGUCHI.Ryo@nims.go.jp, terani-t@cc.okayama-u.ac.jp  Abstract The electrocaloric effect (ECE)-induced temperature change (ΔT) in (Ba, Sr)TiO3-based ferroelectrics under unipolar electric fields was analyzed from the separate contributions of the dielectric constant (ε) and remanent polarization (Pr) based on the Maxwell relation. Consideration of the contributions of both ε and Pr is particularly important in a unipolar electric field operation, such as on/off field switching used in device applications. Direct ΔT measurements were also performed based on the lock-in thermography technique to verify the accuracy of the ΔT intensity estimated by the indirect method. The indirect and direct ΔT values were largely consistent. The ΔT intensity near the peak temperature of ΔT was dominated by the Pr contribution; a large  𝜕𝑃!/𝜕𝑇 was necessary to increase the overall ΔT magnitude. In contrast, a large 𝜕𝜀/𝜕𝑇 was essential to expand the operating temperature range of ΔT at temperatures higher than the dielectric maximum temperature. Quantitative understanding of the contributions of both ε and Pr to ΔT in unipolar electric fields is expected to guide the search for materials with a superior ECE.  A cooling system based on the electrocaloric effect (ECE) is a promising candidate for next-generation environmentally friendly electronic modules to replace the current vapor compression cycle-based systems, which use fluorite-based gases.1,2 The ECE is a heat absorption/generation phenomenon that results from variation in polarization entropy under a changing external electric field.3-9 The ECE can induce a temperature change (ΔT) under adiabatic conditions. The current highest value is approximately 10 K,10 which has been observed in ferroelectric thin films near the ferroelectric–paraelectric phase-transition temperature (Tc). Additionally, the coefficient of performance has been reported to exceed 10 for prototypical devices.11,12 The ECE is discussed on the basis of ∆T under the external electric field.13 It is maximized around the dielectric maximum temperature (Tm), which involves the ferroelectric–paraelectric phase transition.14-16 The dielectric polarization includes the permittivity response and the remanent polarization (Pr). Thus, both the dielectric constant (ε) and Pr contribute to the polarization entropy change. It has been discussed that the Pr contribution is significant for the unipolar operation, such as on/off field switching.17 However, only a few studies have been dedicated to the indirect ECE measurements under unipolar electric fields18-20, and the contributions of ε and Pr to the ECE have not yet been quantified. Herein, we quantify the contributions of ε and Pr to ΔT in ECE materials under unipolar electric fields via a modified indirect ECE measurement (Fig. 1). The ∆T values are calculated from the temperature dependence (T-dependence) of the ε and Pr values obtained from P–E measurements under unipolar and bipolar electric fields. The estimated ∆T values are also compared with the directly measured ΔT using a field-modulated lock-in thermography technique (LIT),21-23 which is performed simultaneously with the unipolar P–E measurements. In the indirect measurement, the adiabatic ΔTindirect due to the ECE is described by the Maxwell relation.24,25 Based on the decomposition of polarization P with P(E) = Pr + ε0(ε-1)E, it can be described by Equation (1) as follows:19 ∆𝑇"#$"%&'( = −𝑇𝜌 ∙ 𝐶)×.𝜕(𝜀*(𝜀 − 1)𝐸 + 𝑃!)𝜕𝑇 𝑑𝐸,+!"#*         (1) where ρ is the density, Cp is the specific heat, E (Emax) is the (maximum) electric field, and ε0 is the vacuum permittivity. The T-dependences of ε and Pr are measured by a Sawyer–Tower circuit,26 and each contribution is estimated in Equation (1). ε and Pr are estimated as follows. To determine ε, a sinusoidal waveform that varies from 0 to Emax at the freqyency, f, is used as an AC electric field according to Equation (2), as follows: 𝐸(𝑡) = 𝐸,-. × 7sin ;2𝜋𝑓𝑡2 ? +12@ .        (2) Here, the obtained P–E hysteresis is unipolar. The waveform corresponds to turning the electric field on and off (as in real devices),12,27 and thus our direct measurements were also performed under this electric field. ε is estimated according to the approximation of P(Emax) – P(0) = ε0(ε-1)Emax. Pr cannot be estimated for a unipolar hysteresis since the Sawyer–Tower circuit only measures the change in polarization. Thus, to estimate Pr, bipolar hysteresis, where the electric field varies from –Emax to Emax, was also measured.28 Bipolar hysteresis enables estimation of the absolute P value at Emax (Pmax). The Pr value is estimated as Pr = Pmax – ε0(ε-1)Emax (see Fig.1).  In the experiment, Ba0.8Sr0.2TiO3 (08BST) was used because its Tm is in the vicinity of room temperature, i.e., 340 K; it was synthesized via a conventional solid-state reaction.29 X-ray diffraction (Mini Flex, Rigaku) confirmed that the material was single phase, had tetragonal symmetry, and was impurity-free. The density was 5.56 × 103 kg/m3 measured by Archimedes method and the relative density was 95.2%. Figure 2(a) shows the T-dependence of Cp measured using Differential Scanning Calorimetry (DSCvesta, Rigaku). Pellets of 08BST were cut into cuboid pieces of dimensions 2.0 × 2.0 × 1.0 mm3 using a step cutter for direct and indirect ECE measurements. Then, the specimens were polished using lapping films of grits ranging from #400 to #10,000. Au electrodes (100-nm-thick) were sputter-deposited on the 2.0 × 2.0 mm2 surfaces, and 50-μm-thick Au wires were attached to the electrodes using Ag paste. The 08BST specimen was connected to a Sawyer–Tower circuit equipped with a 0.1-μF reference capacitor and placed on a temperature-controlled stage equipped with a Peltier module. The surface between the Au electrodes (2.0 × 1.0 mm2) was observed using an infrared camera. The static component of the captured thermal image is used to determine the sample temperature, and the dynamic component is used to directly measure ΔT through LIT. The values in the following are averaged over the entire sample surface. Since it was confirmed that the sample surface exhibited sufficiently high emissivity, no coating was applied.23  The measurements were carried out while the temperature was increased from approximately 320 to 350 K. Prior to the measurements, depolarization was achieved by increasing the temperature above the Curie temperature and then decreasing it to 320 K in the absence of an electric field. Subsequently, at each temperature, the unipolar hysteresis was measured along with simultaneous LIT-based direct measurements, followed by the bipolar hysteresis measurement. The frequency was set to 20 Hz, and the voltage was fixed at Emax = 500 V, except during the electric field dependence measurements. In the data analysis, smoothing splines were used to determine the T derivative of the ε and Pr values. Figure 2(b) shows the T dependence of ε and ECE-induced ΔT calculated only from ε (ΔTε) at Emax = 500 V/mm. The T dependence of ε reached a maximum in the measurement temperature range, and Tm of 335.4 K was obtained by fitting the ε values around the peak with a quadratic function. In contrast, since ΔTε is proportional to 𝜕𝜀/𝜕𝑇, ΔTε shows negative and positive peaks, respectively, below and above Tm. Figure 2(c) shows the Pr at Emax = 500 V/mm and ECE-induced ΔT calculated only from Pr (ΔTPr). The Pr value decreased with increasing T. The graph shows a peak maximum at about Tm. The actual peak temperature of ΔTPr was 333.5 K, which is lower than Tm. Next, the T dependence of ΔTindirect was calculated by adding ΔTPr and ΔTε [Figure 2(d)]. The ΔTindirect displayed a positive peak with a maximum at 334.2 K. Notably, the peak temperature for ΔTindirect differed from those for ΔTPr and ΔTε. Therefore, the contributions from both ε and Pr are indispensable when discussing the overall ECE. Below Tm, ΔTPr and ΔTε had opposite signs and thus weakened each other, whereas above Tm, the contributions were additive. The maximum ΔTindirect value was primarily determined by the maximum ΔTPr value, since ΔTε was about zero near Tm. The contributions of ε and Pr to ΔTindirect are explained by the vanishing of Pr at elevated temperatures and the enhancement of ε near the Curie temperature. The Pr value kept decreasing with increasing temperature, and after the ferroelectric–paraelectric phase transition, the values became almost zero. In contrast, ε reached its maximum value at the Tm where the Pr was almost zero. This behavior is attributed to an electric field-induced phase transition in the BST at the Tm or higher temperature. Namely, dipole clusters originating from Ti displacement along the <111> orientation30 are transformed into the macrodomain under the application of the high-intensity E field. The increment in the dipole contribution increased the ΔTε at higher temperatures, i.e., above the Tm.  We also performed LIT-based thermographic measurements to confirm the accuracy of the magnitude of the ΔTindirect values. The LIT measurements were performed simultaneously with the unipolar P-E measurements at the lock-in frequency of 20 Hz. The lock-in frequency was confirmed to be sufficiently high to separate the contributions from leakage-induced Joule heating and thermal loss effect based on the frequency-dependence measurements conducted prior to the T-dependence measurements.23 The ΔT obtained by direct measurement was defined as ΔTdirect; Figure 2(d) indicates that the magnitudes of ΔTdirect and ΔTindirect were comparable and in better agreement compared to previous study.19 The effect of Emax variation in the range of 100–1,000 V/mm on ECE characteristics was also investigated. A change in Emax changes both the amplitude and DC bias of the applied electric field waveform. It has been established that the dielectric properties of ferroelectrics are significantly affected by DC bias, particularly due to the changes in dipole contributions associated with the domain structure.31,32 Thus, substantial changes in the ECE were expected when Emax was changed.  Figure 3(a) shows ε for Emax, ranging from 100 to 1,000 V/mm. With increasing Emax, the ε value decreased, the peak intensity diminished, and the estimated Tm shifted to higher temperature. These behaviors are consistent with previous research.31,32 In normal ferroelectrics possessing a typical domain configuration, increasing the DC bias field intensity decreases ε as the domain wall motions.31,33,34 Although ε was lower at the elevated Emax values, ΔTε still increased with increasing Emax [Figure 3(b)]. This is because ΔTε is proportional to E2, as described in Equation (2). Another effect of Emax is that the positive and negative peaks in ΔTε were shifted to higher temperatures.  Figure 3(c) and (d) show Pr and ΔTPr with Emax ranging from 100 to 1,000 V/mm. The values of both Pr and ΔTPr increased with increasing Emax; the peak temperature of ΔTPr increased by about 1.5 K over this range of Emax. The ΔTindirect value for each Emax value is presented in Figure 4(a). As expected, increased Emax resulted in increased ΔTindirect and peak temperature. Figure 4(b) shows ΔTdirect, which well reproduces the intensities and peak temperature shifts of ΔTindirect. The relative contributions of ε and Pr depends on T and Emax. Near Tm, the peak magnitude of the ΔTindirect is governed by the peak magnitude of ΔTPr. This feature is unchanged even when the Emax value changes. In contrast, the ΔTε contribution is important at T > Tm. Figure 4(c) shows the ratio of ΔTε to ΔTindirect above Tm. Near Tm, the ratio is zero, indicating the dominance of ΔTPr in ΔTindirect. When T increases, the ratio increases and exceeds 0.5 because the greater Emax decreases the ratio. Summarizing, the overall ΔT was quantified by incorporating Pr and ε into the Maxwell relation. The overall ΔT near the Tm was governed by the contribution of Pr, while the contribution of ε was small. The contribution of ε steadily increased with temperature, and the ratio of ΔTε and overall ΔT increased to about 0.5 above Tm. These behaviors indicate that to increase the magnitude of ΔT derived from the ECE, it is necessary to increase 𝜕𝑃!/𝜕𝑇 near Tm. To expand the ECE operating temperature range, it is necessary to adjust 𝜕𝜀/𝜕𝑇. To design ECE materials, their Pr and ε must be selected according to the required ECE characteristics. We expect that the results of this study will stimulate the search for ECE materials and thereby advance the development of micro-cooling devices.  Acknowledgement The authors thank K. Uchida, T. Hirai, and M. Isomura for the equipment and technical support. This work was partially supported by Aid for Scientific Research (B) (24K01334, 24K01162), Aid for Scientific Research (S) (22H04965), and NIMS Joint Research Hub Program.  Figure caption  Figure 1. Experimental setup for LIT measurement and Sawyer Tower circuit. Thermal image, P-E hysteresis and indirect ΔTε, ΔTPr and overall ΔT with temperature were incorporated into the figure.   Figure 2. T-dependences of (a) ε and ΔTε, (b) Pr and ΔTPr at Emax=500V/mm and (c) the comparison between ΔTindirect (ΔTε + ΔTPr) and the ΔTdirect measured by the LIT.  Figure 3. T-dependences of (a) ε, (b) ΔTε, (c) Pr and (d) ΔTPr at various Emax  Figure 4. T-dependences of (a) the ΔTindirect, (b) the ΔTdirect at various Emax and (c) the ΔTε contribution ratio to the total ΔTindirect above the Tm.       AUTHOR DECLARATIONS Conflict of Interest The authors have no conflicts to disclose.  DATA AVAILABILITY The data that support the findings of this study are available from the corresponding authors upon reasonable request.  References 1E. Defay, R. Faye, G. Despesse, H. Strozyk, D. Sette, S. Crossley, X. Moya and N. D. Mathur, Nat. Commun. 9, 1827 (2018). 2J. Li, A. Torelló, V. Kovacova, U. Prah, A. Aravindhan, T. Granzow, T. Usui, S. Hirose and E. 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