Introduction

Solid-state refrigeration has attracted considerable attention due to its potential applications in small-scale cooling technology1,2,3. There are several physical effects that can be utilized for solid-state refrigeration, such as magnetocaloric (MC)4,5, electrocaloric (EC)6,7,8,9, and mechanocaloric (mC) effects10,11. In MC and EC effects, a temperature change is induced by applying a magnetic field and electric field, respectively. However, the MC and EC strengths for typical ferromagnetic/ferroelectric materials are relatively small. For instance, the EC strengths for prototype ferroelectrics such as PbZr0.95Ti0.05O312 and fluorinated polymers13 thin films are less than 1.0 K m MV−1. To achieve a large temperature change, a strong magnetic/electric field is required, which is normally provided by a huge auxiliary device, limiting the practical applications of the MC/EC materials in cooling devices9,14,15.

The mC effect10, the application of a mechanical force that induces thermal cooling, can be divided into two categories, elastocaloric (eC) and barocaloric (BC) effects, for which the driving mechanical forces are uniaxial stress and hydrostatic pressure, respectively. The schematic illustration of an eC refrigeration cycle for thin films is shown in Fig. 1. The refrigeration cycle begins with applying a compressive stress on the film adiabatically (step a), the temperature rises from T0 to Tmax due to the release of latent heat. Then followed by the heat transfer from thin films to the surroundings (step b), with a decrease of temperature while the compressive stress is kept constant. The temperature keeps dropping when the compressive stress is gradually reduced (step c), as a result of the inverse eC effect. Finally, at step d, the compressive stress is fully removed. The film absorbs heat from the surroundings where the temperature rises back to T0 after a full refrigeration cycle.

Fig. 1: Schematics of an eC refrigeration cycle.
figure 1

The cycle is divided into four steps: (a) compressive stress applying on the elastocaloric material, the release of latent heat and related temperature rise, (b) heat transfer to the surroundings when the stress is fixed at σmax, (c) compressive stress removed gradually, uptake of latent heat and related temperature drop, (d) heat transfer to the elastocaloric material when the stress is fixed at 0. Elevated temperatures are represented in red and orange, decreased temperatures are in blue.

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To maximize the temperature change and improve the energy efficiency for the cooling cycle, materials with high eC strength are required. Previously, high eC strength with ΔTeC/Δσ of 0.7 K GPa−1 has been predicted for ferroelectric oxide heterostructures such as BaTiO3 thin films1. One key factor limiting the eC performance of the oxide ferroelectrics is their low compressibility with strong ionic bonds. Even though a high adiabatic temperature change might be obtained by applying large external stress, the eC strength is quite small which gives rise to low energy efficiency for a refrigeration cycle.

Recently, Wang et al. predicted extraordinarily large EC strengths, 18 J m kg−1 K−1 MV−1 for the isothermal ΔSEC/ΔE and 8.06 K m V−1 for the adiabatic ΔTEC/ΔE, of a metal-free perovskite ferroelectric material [MDABCO](NH4)I3 (MDABCO stands for N-methyl-N′-diazabicyclo[2.2.2]octonium)16, which is superior to the prototype perovskites1,17,18,19,20,21 such as BaTiO3 and PbTiO3. For instance, the EC strength of [MDABCO](NH4)I3 is three times higher than the largest reported values of BaTiO3, which could be attributed to the larger Curie–Weiss constant and smaller mass density of [MDABCO](NH4)I3. In addition to the smaller mass density, the molecular ferroelectric material has a much smaller elastic stiffness (~1 GPa) in comparison to typical ferroelectric oxides (~100 GPa). Therefore, it is rational to believe that large volume and entropy changes could be induced by applying external mechanical stimuli to [MDABCO](NH4)I3, which may generate a significant mC effect.

The very large BC effect was also reported in plastic crystals which are featured by the extensive disorder and giant compressibility22,23. For example, The BC strength ΔS/Δσ for NPG plastic crystals can reach 961.5 J K−1 kg−1 GPa−1 at 320 K22. The metal-free organic perovskite ferroelectric [MDABCO](NH4)I3 is held together by both ionic and hydrogen-bonding interactions, which has considerably large compressibility. Large piezoelectric response was also predicted in [MDABCO](NH4)I3 from first-principles calculations24. Moreover, [MDABCO](NH4)I3 also has advantages of high polarization, mechanical flexibility, low weight, and low processing temperatures25,26,27,28,29,30,31, as compared to other organic ferroelectric systems.

Computational methods such as thermodynamic calculations have emerged as powerful tools to the understanding of eC effects,1,32,33,34,35,36 which could help to explain and design materials with high eC effects. In this work, we employ thermodynamic calculations to study the polarization properties and phase transitions of (111)-oriented ferroelectric [MDABCO](NH4)I3 thin films under different combinations of in-plane misfit strains and out-of-plane stresses, from which the eC properties are calculated. As compared to the bulk system, thin films are much smaller in size which is beneficial to the miniature of the device, while also providing an extra degree of freedom (the substrate strain) in the design of the cooling device. It is revealed that the isothermal ΔSeC/Δσ and adiabatic ΔTeC/Δσ for a [MDABCO](NH4)I3 thin film under an out-of-plane compressive stress of 1.28 GPa and in-plane isotropic misfit strain of 0.01 at 300 K can reach as high as −60.0 J K−1 kg−1 GPa−1 and 17.9 K GPa−1, respectively, much superior to the traditional ferroelectric oxides. The giant eC effect is found to be attributed to the low Young’s modulus and high thermal expansion coefficient of [MDABCO](NH4)I3.

Results

Phase transitions and phase diagram

The detailed procedure for developing a thermodynamic potential energy density function for (111)-oriented [MDABCO](NH4)I3 film is described in the Theoretical Method Section and Supporting Information. The parameters for this study are all taken from the previous report16. We first calculate the analytical equilibrium polarization for the (111)-oriented [MDABCO](NH4)I3 thin film under different in-plane misfit strains and out-of-plane stresses at room temperature. Consider a single-domain (111)-oriented thin film epitaxially grown on a cubic substrate with in-plane coherency, the schematics is given in Fig. 2a. The stress and strain components in the global coordinate system satisfy the mixed mechanical boundary condition: \(\sigma _4^\prime = \sigma _5^\prime = {\mathrm{0,}}\,\sigma _3^\prime = \sigma\) and \(\varepsilon _1^\prime = \varepsilon _2^\prime = u_m, \,\varepsilon _6^\prime = 0\). The calculated stress and misfit strain intervals are 0.01 GPa and 0.001, respectively. Supplementary Fig. 2 shows the contour plots for the equilibrium polarization components Px, Py, and Pz in the pseudocubic system as a function of the misfit strain and external stress. It can be observed that the Px, Py, and Pz components have finite values at the low-stress region (see the R and M parts of the contour plot). In the high stress and high misfit strain regions, the cubic phase is stable where all polarization components vanish (the C-region in the phase diagram). In the O region (orthorhombic phase), the Px and Py components are in the same magnitudes while Pz equals zero.

Fig. 2: Thin film model and misfit strain-stress phase diagram for (111)-oriented [MDABCO](NH4)I3 thin film at room temperature.
figure 2

a Schematic illustration of the thermodynamic calculation model. b In-plane misfit strain versus out-of-plane stress phase diagram of single-domain (111)-oriented [MDABCO](NH4)I3 thin film. The inserts are schematics of the polarization direction for each phase.

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Figure 2b shows the stable phases for (111)-oriented [MDABCO](NH4)I3 thin films under different in-plane misfit strains and out-of-plane stresses at room temperature. There are four stable phases in total, depending on the misfit strain and applied stress. When the in-plane misfit strains are zero, the stable phase is orthorhombic O (Px2 = Py2 ≠ 0, Pz2 = 0) for σ33 < −2.0 GPa, monoclinic M (Px2 = Py2 > Pz2 ≠ 0) for −2.0 GPa ≤ σ33 ≤ 0.0 GPa, and rhombohedral R (Px2 = Py2 = Pz2 ≠ 0) for σ33 ≥ 0.0 GPa, respectively. In the region where both the in-plane misfit strain and the out-of-plane stress are highly negative, the cubic phase C (Px2 = Py2 = Pz2 = 0) is stable. In this case, the mechanical condition applied to the material is similar to a hydrostatic pressure, which could favor the paraelectric cubic phase. Notably, no stable T-phase can be observed in the entire phase diagram. This can be understood since R-phase is the ground state for [MDABCO](NH4)I3 and the film is (111)-oriented. T-phase has much higher energy as compared to the O phase according to the calculations from Wang et al.16, which is difficult to stabilize via strain engineering in (111)-oriented [MDABCO](NH4)I3 thin films.

Elastocaloric effect

With the knowledge of the dependence of stress and epitaxial strain on the polarization, now we proceed to calculate the eC properties. Figure 3 shows the eC entropy change ΔSeC and temperature change ΔTeC versus the out-of-plane compressive stress for various [MDABCO](NH4)I3 thin films under different misfit strains (um). To calculate the variations of the ΔSeC and ΔTeC with the phase change, compressive stress is applied on top of the thin film. With the increase of the applied stress, phase transitions from rhombohedral (R) to monoclinic (M) or cubic (C) and finally to orthorhombic (O) occur. According to the previous report37, [MDABCO](NH4)I3 undergoes a plastic deformation when the unidirectional compressive stress is above 1.28 GPa, which is set as the upper limit of the applied stress for the calculations in this study. Note that to sustain 1.28 GPa for the whole thin film device, one has to find either suitable oxide wafers or ductile metals as substrate, or even freestanding film without substrate. Assuming a constant heat capacity of 1000 J K−1 kg−1 for [MDABCO](NH4)I3 at room temperature16, the maximum adiabatic temperature change ΔTeC ~18.7 K occurs with um = −0.01. In most cases, with the highest applied stress, the adiabatic temperature change can reach 10–20 K as shown in Fig. 3a, while the maximum adiabatic temperature change is 22.9 K with a tensile misfit strain of 0.01 as shown in Table 1. Interestingly, at the large compression side (e.g., um = −0.05 and −0.03), ΔSeC (ΔTeC) shows a nonlinear relationship with the external stress while for all the other cases mainly linear dependency is obeserved.

Fig. 3: The eC performance of the [MDABCO](NH4)I3 thin film as a function of external stress and substrate misfit strain.
figure 3

The eC entropy change ΔSeC and the eC temperature change ΔTeC under external stress for [MDABCO](NH4)I3 thin film with a compressive misfit strains and b tensile misfit strains. The gray, white, and yellow regions mark different phases. The blue line shows the entropy change, while the red line indicates the temperature change. The pink dash line marks the maximum nonuniform directional stress −1.28 GPa above which the system undergoes plastic deformation.

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Table 1 Comparison of elastocaloric properties for different materials from previous literature and [MDABCO](NH4)I3 thin films in this study.
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Table 1 and Supplementary Fig. 4 summarize the eC properties for [MDABCO](NH4)I3 and other ferroelectrics that has been reported recently. For the polyvinylidene fluoride (PVDF) based ferroelectric polymers, the polar to the nonpolar phase transition is very sensitive to external mechanical stresses. High eC effects have been reported and adiabatic temperature changes of ~2 K were measured directly in PVDF polymers near room temperature under uniaxial stresses of ~10 MPa38,39. Meanwhile, some typical ferroelectric perovskite thin films also present finite eC effects at room temperature. For instance, BaTiO3 thin films show a ΔTec~ 5 K under huge uniaxial stress of 6.5 GPa1,21. On the other hand, PbTiO3 thin film exhibit a maximum adiabatic temperature change of ~20 K18, which has been ascribed to the mixed ferroelastic and ferroelectric behaviors. However, such a giant eC effect can only occur at ~700 K, which is too high for practical applications. In comparison, [MDABCO](NH4)I3 displays considerably high eC strength, which is much higher than traditional lead-free ferroelectric perovskites, as shown in the light gray area of Supplementary Fig. 4. Polymer-based ferroelectrics have been found to exhibit higher temperature change ΔTec, but they have a very low refrigerant capacity (RC = |ΔT*ΔS|). The calculated RC performance of [MDABCO](NH4)I3 thin film is 1760 J kg−1, much superior to other ferroelectrics as reported in the previous literature. The coefficient of performance (COP) is another commonly used metric to describe the efficiency of the cooling cycle, which is defined as the ratio of the cooling power (Q) to the input work (W) required to perform a thermodynamic cycle. As listed in Table 1, the calculated COP of [MDABCO](NH4)I3 thin film is about 1.11, which is much higher as compared to the other ferroelectrics such as BaTiO3 and comparable to the widely used eC materials such as TiNiFe shape memory alloys32.

Now we further turn to discuss the detailed underlying mechanisms for the superior eC performance of [MDABCO](NH4)I3. Figure 4 demonstrates the eC entropy change ΔSeC, and the eC temperature change ΔTeC for [MDABCO](NH4)I3 thin films under different in-plane misfit strains (um) and out-of-plane stresses. With the increasing of the out-of-plane stress, both the magnitudes of ΔSeC and ΔTeC increase. Figure 4c, d show the contributions of volume change and polarization change to ΔSeC and ΔTeC, respectively. We choose a compressive stress of −1.28 GPa as an example, two contributions to ΔSeC can be identified as follows. The ordering of the dipoles by the application of external stress under isothermal conditions leads to a reduction or increase in the dipole configurational entropy (ΔSP), which is associated with the phase transitions. The other contribution is the volume change induced entropy change (ΔSV) given by \(\frac{{\beta _l}}{\rho }\left( {\sigma _1 + \sigma _2 + \sigma _3} \right)\), where the thermal expansion coefficient βl and the mass density ρ, have both been evaluated in the previous paper16. For [MDABCO](NH4)I3 film, these two parts compete with each other when compressive stress is applied but the ΔSV dominates the total entropy due to its characteristic of low Young’s modulus, which is only one percent of the Young’s modulus for typical ferroelectric oxides. The low Young’s modulus prompts the high thermal expansion coefficient and thus results in the big entropy reduction when applying the compressive stress (see Fig. 4a, c).

Fig. 4: Contributions of the eC performance of the [MDABCO](NH4)I3 thin film.
figure 4

a The eC entropy change ΔSeC and b the eC temperature change ΔTeC for [MDABCO](NH4)I3 thin film versus with misfit strain (um) under different external stresses. The contributions of polarization change and volume change under a compressive stress of 1.28 GPa for c the eC entropy change and d the eC temperature change ΔTeC. The gray, white, and yellow regions mark different phases. The pink dash lines mark the maximum eC ΔSeC and ΔTeC at a stress of −1.28 GPa.

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Calculations of elastocaloric effect for inorganic oxide ferroelectrics

Moreover, the impact of physical properties in materials on the eC strength is investigated, by calculating some common (111)-oriented ferroelectric oxide films using the same method. Material parameters are taken from existing publications for BaTiO3 (BTO)40, PbTiO3 (PTO)41, PbZr0.52Ti0.48O3 (PZT-0.52)42, PbZr0.8Ti0.2O3 (PZT-0.8)42, K0.5Na0.5NbO3 (KNN)43,44, and KNbO3 (KNO)44 thin films, respectively. Figure 5a, b show the comparison of isothermal entropy change ΔSeC and adiabatic temperature change ΔTeC between [MDABCO](NH4)I3 and other typical ferroelectric materials. The predicted eC strengths, isothermal ΔSeC/Δσ and adiabatic ΔTeC/Δσ, for [MDABCO](NH4)I3 are −60.0 J K−1 kg−1 GPa−1 and 17.9 K GPa−1, respectively, more than one order of magnitude higher than the largest value for oxide ferroelectric films. For example, the PTO film has the highest ΔTeC = −24.70 K, but measured under a considerably high stress Δσ of 4.55 GPa. The calculated eC strength for PTO agrees well with the previous study by first principle calculation, in which the eC temperature change ΔTeC is ~7 K under a stress Δσ of 1.4 GPa18. Moreover, the calculated eC strength |ΔTeC/Δσ| of 0.76 K GPa−1 for BaTiO3 film is consistent with Liu et al.1. Other ferroelectric oxides such as KNbO3 and K0.5Nb0.5O3 thin films also show high ΔTeC values under remarkably high compressive stress Δσ. In comparison, the [MDABCO](NH4)I3 thin film exhibits a high value of ΔSeC (−76.85 J K−1 kg−1) and ΔTeC (22.9 K) under a lower Δσ of 1.28 GPa. The outstanding eC strength of [MDABCO](NH4)I3 film can be understood by separating the contributions from two parts. For the polarization change induced eC temperature change (|ΔTP/Δσ|), the value of [MDABCO](NH4)I3 is in the same order of magnitude as the value of the oxide perovskites. But for the volume change induced eC temperature change (|ΔTV/Δσ|), due to the high compressibility of [MDABCO](NH4)I3, it is one order of magnitude higher than the highest value of the other ferroelectric films. The specific value for the eC properties of the above ferroelectric films could be found in Supplementary Table 4 and Supplementary Figs. 5,6.

Fig. 5: Comparisons of the eC performance between [MDABCO](NH4)I3 and other ferroelectric thin films from thermodynamic calculations.
figure 5

a The eC entropy change |ΔSeC|, b the eC temperature change |ΔTeC|, c the eC strength |ΔSeC/Δσ|, and d the eC strength |ΔTeC/Δσ|.

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Discussion

Following the previous results, we further identify several intrinsic physical properties, namely the elastic compliance sij, thermal expansion coefficient βl on the eC effects of the metal-free ferroelectrics, hoping to find design principles for high eC materials. The calculated eC temperature changes ΔTeC is plotted in Fig. 6 and Supplementary Fig. 6, by varying the values of the above-mentioned material properties. Figure 6a shows a two-dimensional plot of the temperature change ΔTeC as a function of both elastic compliance and thermal expansion. It is indicated that generally, eC decreases with increasing of elastic compliance, while increases with increasing thermal expansion coefficient. A relatively stronger dependency on βl can be observed. For instance, ΔTeC shows a dramatic increase to ~100 K with increasing of the βl to five times of [MDABCO](NH4)I3 with fixing of the elastic compliance (Supplementary Fig. 6).

Fig. 6: Design space for high eC materials with respect to the linear thermal expansion and elastic compliance.
figure 6

a Two-dimensional plot of the evaluated eC temperature change ΔTeC for [MDABCO](NH4)I3 based metal-free ferroelectrics as a function of βl and sij. The red star represents the [MDABCO](NH4)I3 and the dashed arrow points out the direction for the design of organic ferroelectrics with high eC properties. b The thermal expansion coefficient βl and elastic compliance sij for different ferroelectrics. The compressive stress and the misfit strain are fixed at 1.28 GPa and 0.01, respectively.

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Note that the elastic compliance and thermal expansion coefficient are not independent physical parameters for a certain material. We map out the elastic compliance and thermal expansion coefficients of several oxide ferroelectrics, PVDF, and [MDABCO](NH4)I3 in Fig. 6b. The thermal expansion coefficient increases along with the increases of elastic compliance for almost all ferroelectric materials. Compared to oxide ferroelectric films, metal-free ferroelectric [MDABCO](NH4)I3 film has higher elastic compliance that will surpress the eC effect, but the higher thermal expansion coefficient has a higher influence on the eC performance, resulting in one order of magnitude higher in eC strength. Furthermore, modifying the cation [MDABCO]2+ and anion I− in the [MDABCO](NH4)I3 crystal could change the physical properties including the thermal expansion coefficient and elastic compliance25,45. Thus, theoretically, by rational design of the composition of the [MDABCO](NH4)I3 film, the eC performance in ferroelectrics can be further improved by enhancing the thermal expansion coefficient of the organic ferroelectrics.

In summary, we have developed a thermodynamic description for (111)-oriented organic ferroelectric [MDABCO](NH4)I3 thin film and investigated its phase transition behavior and eC properties under different misfit strains and applied external stresses. We found that there are two contributions to the eC strength, namely the polarization changes induced entropy change (ΔSP) and the volume change induced entropy change (ΔSV), which competes with each other under compressive stress. For organic ferroelectric materials which are relatively soft, the entropy change ΔSV dominates, which is an order of magnitude higher than traditional ferroelectric oxides. It is demonstrated that an eC entropy change of −65.4 J kg−1 K−1 and an adiabatic eC temperature change of 22.9 K are achieved for [MDABCO](NH4)I3 under a compressive stress of 1.28 GPa at a misfit strain of 0.01. This can be attributed to the low Young’s modulus of [MDABCO](NH4)I3, which is only one percent of Young’s modulus of conventional oxides. By analyzing the relationship of eC with thermal expansion coefficient and elastic compliance, we further discovered that the thermal expansion coefficient has a dominant role in determining the eC. Based on our theoretical analysis, we predict that it is possible to further improve the eC properties by enhancing the thermal expansion coefficient through chemical modification of the [MDABCO](NH4)I3. We envision this work will attract broad interest from the community of solid eC materials.

Methods

Thermodynamic calculations of ferroelectric thin films

Based on the Landau-Devonshire theory, there are mainly four contributions in the total thermodynamic free energy density:

  1. (1)

    Polarization energy \(G_{{{{\mathrm{polarization}}}}} = \alpha _iP_i + \alpha _{ij}P_iP_j + \alpha _{ijk}P_iP_jP_k + \alpha _{ijkl}P_iP_jP_kP_l + \alpha _{ijklm}P_iP_jP_kP_lP_m + \alpha _{ijklmn}P_iP_jP_kP_lP_mP_n,\)

(2) thermal energy \(G_{{{{\mathrm{thermal}}}}} = - c_pT\ln \frac{T}{{T_0}} + c_p\left( {T - T_0} \right),\)

(3) mechanical energy \(G_{{{{\mathrm{Mechanic}}}}} = \frac{1}{2}C_{ijkl}( {\varepsilon _{ij} - \varepsilon ^ \circ _{ij}} )( {\varepsilon _{kl} - \varepsilon ^ \circ _{kl}} )\)

And (4) electric energy \(G_{{{{\mathrm{electric}}}}} = - E_iP_i - \frac{1}{2}K_{ij}\varepsilon _0E_iE_j\).

Where αi, αij, αijk, αijkl, αijklm, and αijklmn are the Landau coefficients, and cp, Cijkl, Kij, ε0, and Ei represent the heat capacity, elastic modulus tensor, background dielectric constants, permittivity of vacuum, and electric fields. Pi, T, and T0 are the polarization components, temperature, and romm temperature, respectively. The eigen strain is defined as \(\varepsilon ^ \circ _{ij} = Q_{ijkl}P_kP_l + R_{ijklm}P_kP_lP_m + \beta _l(T - T_0)\)

Here Qijkl and Rijklm are the electromechanical strictive tensors. βl is the linear thermal expansion coefficient. Consider a paraelectric-ferroelectric phase transition from high symmetry cubic phase (with space group P432) to rhombohedral phase (space group R3), expanding the polynomials to eighth order, neglecting all the symmetry forbidden terms, one can rewrite:

$$\begin{array}{lll} {\Delta}{{{\mathrm{G}}}}\, = \,\alpha _{1}\left( {P_1^{2} + P_{2}^{2} + P_{3}^{2}} \right) + \alpha _{{11}}\left( {P_{1}^{4} + P_{2}^{4} + P_{3}^{4}} \right) + \alpha _{{12}}\left( {P_{1}^{2}P_{2}^{2} + P_{1}^{2}P_{3}^{2} + P_{2}^{2}P_{3}^{2}} \right) + \alpha _{{111}}\left( {P_{1}^6 + P_{2}^6 + P_{3}^6} \right) \\ \qquad\quad + \,\alpha _{{112}}\left[ {P_{1}^{2}\left( {P_{2}^{4} + P_{3}^{4}} \right) + P_{2}^{2}\left( {P_{1}^{4} + P_{3}^{4}} \right) + P_{3}^{2}\left( {P_{1}^{4} + P_{2}^{4}} \right)} \right] + \alpha _{{123}}P_{1}^{2}P_{2}^{2}P_{3}^{2} + \alpha _{{1111}}\left( {P_{1}^8 + P_{2}^8 + P_{3}^8} \right) + \alpha _{{1122}}\left( {P_{1}^{4}P_{2}^{4} + P_{2}^{4}P_{3}^{4} + P_{1}^{4}P_{3}^{4}} \right) \\ \qquad\quad + \,\alpha _{{1112}}\left[ {P_{1}^6\left( {P_{2}^{2} + P_{3}^{2}} \right) + P_{2}^6\left( {P_{1}^{2} + P_{3}^{2}} \right) + P_{3}^6\left( {P_{1}^{2} + P_{2}^{2}} \right)} \right] + \alpha _{{1123}}\left( {P_{1}^{4}P_{2}^{2}P_{3}^{2} + P_{2}^{4}P_{1}^{2}P_{3}^{2} + P_{3}^{4}P_{1}^{2}P_{2}^{2}} \right) \\ \qquad\quad - \,\frac{{1}}{{2}}s_{{11}}\left( {\sigma _{1}^{2} + \sigma _{2}^{2} + \sigma _{3}^{2}} \right) - s_{{12}}\left( {\sigma _{1}\sigma _{2} + \sigma _{1}\sigma _{3} + \sigma _{2}\sigma _{3}} \right) - \frac{{1}}{{2}}s_{{44}}\left( {\sigma _{4}^{2} + \sigma _{5}^{2} + \sigma _{6}^{2}} \right) - Q_{{11}}\left( {\sigma _{1}{{{\mathrm{P}}}}_1^{2} + \sigma _2{{{\mathrm{P}}}}_2^{2} + \sigma _3{{{\mathrm{P}}}}_3^2} \right) \\ \qquad\quad - \,Q_{{12}}\left[ {\sigma _{1}\left( {P_{2}^{2} + P_{3}^{2}} \right) + \sigma _{3}\left( {P_{1}^{2} + P_{2}^{2}} \right) + \sigma _{2}\left( {P_{1}^{2} + P_3^{2}} \right)} \right] - Q_{{44}}\left( {P_2P_3\sigma _{4} + P_1P_3\sigma _5 + P_1P_2\sigma _6} \right) \\ \qquad\quad - \,\beta _l\left( {\sigma _1 + \sigma _2 + \sigma _3} \right)\left( {T - T_0} \right) \\ \qquad\quad - \,\lambda _{eff}\left[ {\sigma _6\left( {P_{1}^{2} - P_2^{2}} \right)P_{3} + \sigma _5\left( {P_{3}^{2} - P_1^{2}} \right)P_2 + \sigma _4\left( {P_2^2 - P_3^2} \right){{{\mathrm{P}}}}_1} \right] \\ \qquad\quad - \,E_1P_1 - E_2P_2 - E_3P_3 - \frac{{1}}{{2}}\varepsilon _{0}\left( K_{{11}}E_1^2 + K_{{22}}E_2^2 + K_{{33}}E_3^2\right.\\ \qquad\quad \left. + K_{{12}}E_1E_2 + K_{{13}}E_1E_3 + K_{{23}}E_2E_3 \right).\\ \end{array}$$
(1)

Where the α-terms are the simplified Landau coefficients, s11, s12, and s44 are the elastic compliance, \(\sigma _i(i = 1,6)\) are the stresses, λeff is the high-order electrostrictive term. Ei are the applied electric fields, Kij are the relative dielectric constants.

We then transfer the polarization and stresses from the local coordinate system x to the global coordinate system x′ by using the transformation matrix tij:

$$t_{ij} = \left( {\begin{array}{*{20}{c}} {\frac{1}{{\sqrt 2 }}} & { - \frac{1}{{\sqrt 2 }}} & 0 \\ {\frac{1}{{\sqrt 6 }}} & {\frac{1}{{\sqrt 6 }}} & { - \frac{2}{{\sqrt 6 }}} \\ {\frac{1}{{\sqrt 3 }}} & {\frac{1}{{\sqrt 3 }}} & {\frac{1}{{\sqrt 3 }}} \end{array}} \right).$$
(2)

For the epitaxial thin film with the in-plane misfit strains of \(\varepsilon _1^\prime\) and \(\varepsilon _2^\prime\) (the strain in global coordinate), the free energy ΔG′ can be derived using the Legendre transformation

$${\Delta}G^\prime = {\Delta}G + \varepsilon _1^\prime \sigma _1^\prime + \varepsilon _2^\prime \sigma _2^\prime = {\Delta}G + u_{{{\mathrm{m}}}}\left( {\sigma _1^\prime + \sigma _2^\prime } \right).$$
(3)

In Eq. 3, the misfit strains \(\varepsilon _1^\prime\) and \(\varepsilon _2^\prime\) are the same for a cubic substrate.

For the epitaxial film under typical in-plane biaxial misfit strains and out-plane stress in a global coordinate system, it is subjected to a mixed mechanical boundary condition with

$$\partial G^\prime /\partial \sigma _i^\prime = - \varepsilon _i^\prime ,\varepsilon _1^\prime = \varepsilon _2^\prime = u_m,\;\varepsilon _6^\prime = 0,\,\sigma _3^\prime = \sigma _{{{{\mathrm{app}}}}},\;\sigma _4^\prime = \sigma _5^\prime = {{{\mathrm{0}}}}{{{\mathrm{.}}}}$$
(4)

in which the \(\varepsilon _1^\prime\) and \(\varepsilon _2^\prime\) are the in-plane strains, the \(\varepsilon _6^\prime\) is the shear strain, the \(\sigma _3^\prime\) is the out-plane stress along [111] direction, and the \(\sigma _4^\prime\) and \(\sigma _5^\prime\) are the in-plane stresses.

Assuming the film is pre-polarized in the electric field, the polarization (Pi) under given misfit strains and out-plane applied stress at room temperature can be obtained by minimizing the thermodynamic free energy density ΔG′ with respect to polarization Pi.

Establishment of phase diagrams

The phase evolutions under applied stress at different misfit strains for [MDABCO](NH4)I3 thin films are thoroughly investigated and exhibited in Fig. 2 after we obtained the magnitude of the polarization components. Here we also employ the thermodynamic method to explore the phase evolutions for common ferroelectrics including BaTiO3, PbTiO3, PbZr0.52Ti0.48O3, PbZr0.8Ti0.2O3, K0.5Na0.5NbO3, and KNbO3. The stress versus misfit strain phase diagrams for these ferroelectric films at room temperature are displayed in Supplementary Fig. 3.

Calculation of elastocaloric effect

The total isothermal eC entropy change per mass under an application of stress σapp at room temperature can be calculated by \({\Delta}S_{{{{\mathrm{eC}}}}} = - \frac{1}{\rho }\left( {\frac{{\partial {\Delta}G^\prime }}{{\partial T}}} \right)_{\sigma _{ij}}\) and it is derived from two parts:

(1) the polarization configuration change

$$\begin{array}{ll}\\ {\Delta}S^{{{\mathrm{P}}}}\, = \, {\Delta}S_{{\mathrm{dipole}}}\left( {{{{\mathrm{298}}}}\;{{{\mathrm{K}}}},\sigma = \sigma _{{\mathrm{app}}}} \right) - {\Delta}S_{{\mathrm{dipole}}}\left( {{{{\mathrm{298}}}}\;{{{\mathrm{K}}}},\sigma = 0} \right)\cr \\ \qquad \,\,\,= - \frac{1}{\rho }\left( {\frac{{d\alpha _1\left( T \right)}}{{dT}}\left( {P_i^2|_{\sigma = \sigma _{{\mathrm{app}}}} - P_i^2|_{\sigma = 0}} \right) + \frac{{d\alpha _{111}\left( T \right)}}{{dT}}\left( {P_i^6|_{\sigma = \sigma _{{\mathrm{app}}}} - P_i^6|_{\sigma = 0}} \right)} \right),\\ \end{array}$$
(5)

and (2) the stress-induced volume change

$${\Delta}S^{{{\mathrm{V}}}} = {\Delta}S_{{\mathrm{lattice}}}\left( {298\;{{{\mathrm{K,}}}}\sigma = \sigma _{{\mathrm{app}}}} \right) - {\Delta}S_{{\mathrm{lattice}}}\left( {298\;{{{\mathrm{K,}}}}\,\sigma = {{{\mathrm{0}}}}} \right) = \frac{{\beta _I}}{\rho }\left( {\sigma _1 + \sigma _2 + \sigma _3} \right).$$
(6)

Under the reversible adiabatic condition, the total entropy is conserved upon a stress change, thus we can obtain

$$\begin{array}{ll}{\Delta}T_{{{{\mathrm{eC}}}}} = \frac{T}{{c_p\rho }}\left( {\frac{{d\alpha _1\left( T \right)}}{{dT}}\left( {P_i^2|_{_{\sigma = \sigma _{{\mathrm{app}}}}} - P_i^2|_{\sigma = 0}} \right) + \frac{{d\alpha _{111}\left( T \right)}}{{dT}}\left( {P_i^6|_{\sigma = \sigma _{{\mathrm{app}}}} - P_i^6|_{_{\sigma = 0}}} \right)} \right)\\ \qquad\qquad- \frac{{T\beta _l}}{{c_p\rho }}\left( {\sigma _1 + \sigma _2 + \sigma _3} \right).\end{array}$$
(7)

All the physical parameters and all coefficients can be found in Supplementary Tables 1 and 2 in the Supporting Information.

The COP can be evaluated by the following equation:

$${{{\mathrm{COP}}}} = \frac{Q}{W}$$
(8)

in which Q represents the absorbed heat and W is the specific mechanical work in the eC cooling cycle. The absorbed heat Q is derived from ∫TdS, in which the T and S are the temperature and entropy, respectively. The specific mechanical work W is calculated by \(\frac{1}{\rho }{\int} {\sigma d\varepsilon }\), in which the ρ, σ, and ε are the mass density, stress, and strain, respectively.