n the United States, nearly 68% of the primary energy produced each year is wasted as heat 1 . For example, it is projected that a single next-generation exascale supercomputer will consume 5-10% of the total power output from the average coal-fired power plant and turn virtually all of that energy into heat 2 . Therefore, considerable efforts are underway to harvest some of this waste heat. The majority of research in this regard has focused on thermoelectrics (materials that convert a temperature gradient into electrical energy via the Seebeck effect) 3 . For low-grade waste-heat (< 100 °C) thermoelectrics are inherently limited by their low ZT, a dimensionless figure of merit (FoM) that requires high electrical and low thermal conductivity; a combination that is difficult to achieve 4 . For example, the widely studied Bi 2 Te 3 -based thermoelectrics have ZT ≈ 1, which corresponds to ~17% scaled efficiency (the ratio of the absolute to the Carnot efficiency) for low-grade heat scavenging 5 . Despite some commercial success with thermoelectrics, researchers continue to explore alternative technologies for waste-heat energy conversion, including approaches that take advantage of phenomena such as thermo-osmotic and -galvanic effects 6,7 . Here we demonstrate the potential of an approach based on pyroelectric materials.
The pyroelectric effect describes the temperature-dependent evolution of spontaneous polarization P (resulting in changes in the surface charge density of the material) and is parameterized by the pyroelectric coefficient, π = ∂ ∂ ( ) P T . In contrast to the steadystate operation of thermoelectrics, pyroelectric energy conversion requires thermodynamic cycles that make use of a temporally varying thermal profile to extract electrical work from the pyroelectric. Such cycles mimic gas-phase cycles and a number of different thermal-electrical cycles for pyroelectric energy conversion have been proposed, including, for example, Stirling-like cycles with two isothermal and two isodisplacement processes 8,9 , Carnot cycles with two isothermal and two adiabatic processes 10 , and an adaptation of the Ericsson cycle, an Olsen cycle 11 , which includes two isothermal and two isoelectric processes [11][12][13][14][15][16] . Early work in the exploration of these cycles revealed that these adapted Ericsson cycles can extract the maximum potential work from a pyroelectric out of all of the thermodynamic cycles studied to date 17 . In turn, much of the work in this field since this time has employed these adapted Ericsson cycles for pyroelectric energy conversion 12,13 and these approaches have produced maximum energy density, power density and scaled efficiency values of ~1 J cm -3 (ref. 14 ), ~30 W cm -3 (ref. 16 ) and 5.4% (ref. 15 ), respectively. On the basis of these thermal-electrical cycles, researchers have also established that a high-performance pyroelectric energy conversion material should have a high π and low relative permittivity (ε r ), a trade-off parameterized by the FoM for pyroelectric energy conversion (FoM PEC ), which is π 2 /ε 0 ε r (ε 0 is the permittivity of free space) 18 . In turn, optimization of pyroelectric performance requires independently enhancing π and suppressing ε r , which is difficult in conventional materials where dielectric and pyroelectric susceptibilities are generally enhanced by the same generic features (that is, proximity to phase transitions driven by chemistry, temperature, strain and so on) 19,20 .
Such phase transitions are a hallmark of relaxor ferroelectrics such as (1-x)Pb(Mg 1/3 Nb 2/3 )O 3 -xPbTiO 3 (PMN-xPT) where changing the ferroelectric PbTiO 3 content results in a change in the lattice symmetry from rhombohedral, R (x ≤ 0.31), to tetragonal, T (x ≥ 0.35), via a bridging low-symmetry monoclinic, M (0.31 < x < 0.35), phase constituting the morphotropic phase boundary 21,22 . In proximity to the morphotropic phase boundary, different ferroelectric phases are nearly energetically degenerate, resulting in facile rotation of
Shishir Pandya 1 , Joshua Wilbur 2 , Jieun Kim 1 , Ran Gao 1 , Arvind Dasgupta 1 , Chris Dames 2,3 and Lane W. Martin 1,3 *
The need for efficient energy utilization is driving research into ways to harvest ubiquitous waste heat. Here, we explore pyroelectric energy conversion from low-grade thermal sources that exploits strong field-and temperature-induced polarization susceptibilities in the relaxor ferroelectric 0.68Pb(Mg 1/3 Nb 2/3 )O 3 -0.32PbTiO 3 . Electric-field-driven enhancement of the pyroelectric response (as large as -550 μC m -2 K -1 ) and suppression of the dielectric response (by 72%) yield substantial figures of merit for pyroelectric energy conversion. Field-and temperature-dependent pyroelectric measurements highlight the role of polarization rotation and field-induced polarization in mediating these effects. Solid-state, thin-film devices that convert lowgrade heat into electrical energy are demonstrated using pyroelectric Ericsson cycles, and optimized to yield maximum energy density, power density and efficiency of 1.06 J cm -3 , 526 W cm -3 and 19% of Carnot, respectively; the highest values reported to date and equivalent to the performance of a thermoelectric with an effective ZT ≈ 1.16 for a temperature change of 10 K. Our findings suggest that pyroelectric devices may be competitive with thermoelectric devices for low-grade thermal harvesting.
polarization under applied stimuli (that is, temperature 22 , stress 23 and electric fields 24 ). While electric-field-induced polarization rotation has been shown to result in giant electromechanical response 25,26 , such field-coupling to pyroelectricity is poorly studied. The limited work in this regard has shown the possibility for enhancement of π under applied bias 27,28 ; however, the mechanism for such effects remains unclear, with arguments ranging from the importance of a diffuse first-order-like phase transition between the ferroelectric and relaxor phases 29 , to contributions from the secondary pyroelectric effect via field-induced piezoelectricity 30,31 . Understanding such electric field/temperature susceptibility of polarization in relaxor ferroelectrics is crucial to establishing these materials as promising candidates for pyroelectric energy conversion.
We report robust pyroelectric energy conversion that takes advantage of previously understudied strong field-and temperature-induced polarization susceptibilities in the relaxor ferroelectric 0.68Pb(Mg 1/3 Nb 2/3 )O 3 -0.32PbTiO 3 (PMN-0.32PT). Electric-fielddriven enhancement of the pyroelectric response to values as large as -550 μ C m -2 K -1 and suppression of the dielectric response (by 72%) yield unprecedented FoM PEC . Using field-and temperaturedependent pyroelectric measurements, the role of polarization rotation and field-induced polarization in mediating these large effects is explained. In turn, solid-state, thin-film devices that convert waste heat into electrical energy are demonstrated using pyroelectric Ericsson cycles yielding energy density, power density and scaled efficiency of 1.06 J cm -3 , 526 W cm -3 and 19%, respectively; the highest values reported to date and equivalent to the performance of a thermoelectric with an effective ZT ≈ 1.16 for Δ T = 10 K.
We focus on 150 nm PMN-0.32PT/20 nm Ba 0.5 Sr 0.5 RuO 3 /NdScO 3 (110) heterostructures grown via pulsed-laser deposition (Methods). X-ray diffraction line scans (Supplementary Fig. 1a) and reciprocal space maps (Supplementary Fig. 1b) reveal that the heterostructures are epitaxial with (001)-orientation, single-phase and coherently strained (compressive strain of -0.5%) (Methods). Pyroelectric devices were fabricated using established approaches (Methods) 32 . Briefly, these devices enable simultaneous direct measurement of dielectric, ferroelectric and pyroelectric responses and implementation of solid-state electro-thermal cycles such as pyroelectric Ericsson cycles. The technique utilizes a microfabricated heater/ sensor line that localizes high-frequency periodic heating to the ferroelectric under test, allowing simultaneous direct measurements of both pyroelectric currents and temperature change and thus providing a direct quantification of π in symmetric capacitor structures in epitaxial thin films (Fig. 1a). Polarization-electric field hysteresis loops, measured from such devices, reveal high polarizability and behaviour characteristic of relaxor ferroelectrics 33 (Fig. 1b). Additional features of relaxor behaviour are evident in temperature-dependent ε r that shows frequency dispersion below its maximum (T max = 150 °C) (Supplementary Fig. 2a) and deviation from Curie-Weiss behaviour below the Burns temperature (T b = 259 °C, above which the short-range-ordered domains or polar nanoregions dissolve and PMN-0.32PT is a nonpolar paraelectric) 34 (Supplementary Fig. 2b).
Pyroelectric measurements were conducted by periodically oscillating the temperature of the heterostructure by applying a sinusoidal heating current of 19 mA (r.m.s.) at a frequency of 1 kHz on the microfabricated heater line (Fig. 1a andMethods). This heating current perturbs the temperature of the heterostructure by an amplitude θ FE = 10 K at a frequency of 2 kHz and is measured using the 3ω method (Methods and Supplementary Fig. 3) 32 . The resulting pyroelectric current (i P ) was measured as a function of d.c. electric field (Fig. 1c) and π is extracted from the relationship
(red data, Fig. 1d). Under zero bias, π ≈ -100 μ C m -2 K -1 ; however, under application of a d.c. electric field, i P (Fig. 1c) and π (Fig. 1d) are found to be dramatically enhanced such that |π| > 550 μ C m -2 K -1 , far surpassing the field-induced enhancement of π in a classic ferroelectric (for example, data for a (001)-oriented PbZr 0.2 Ti 0.8 O 3 thin film are provided for comparison; blue curve, Fig. 1d). We further measured the tunability of ε r with d.c. electric field and found that ε r is dramatically suppressed (by ~72%) with field (red open circles, Fig. 1e) due to the suppression of the extrinsic polarization contribution from the presence of polar nano-regions and consistent with prior observations in relaxor ferroelectrics 35 . In addition, the loss tangent due to charge leakage within the capacitor is also suppressed with increasing d.c. electric field (red filled squares, Fig. 1e). From a practical standpoint, strongly suppressed ε r (and loss tangent) in conjunction with significantly enhanced π results in an enhancement of the FoM PEC (red data, Fig. 1f) by ~5 times in comparison to commonly used materials (for example, LiNbO 3 (ref. 20 ) (black data, Fig. 1f) and PbZr 0.2 Ti 0.8 O 3 (ref. 32 ) (blue data, Fig. 1f)). The question, then, is: what is the role of the d.c. electric field in enhancing π to such an extent?
To probe the effect of electric field on this strongly field-and temperature-coupled relaxor ferroelectric, a series of field-and temperature-dependent pyroelectric measurements were conducted (Methods). For all studies, the heterostructures were first heated to above the T b to 300 °C before being cooled to room temperature in zero applied field. Once at room temperature, pyroelectric measurements were conducted as a function of d.c. electric field (0, 13.3, 26.7 and 40 kV cm -1 ) with increasing sample temperature using an oscillating a.c. temperature with amplitude θ FE = 2.5 K. The magnitude of oscillation was deliberately chosen to be small to capture any temperature-dependent changes in the pyroelectric susceptibility as the background temperature was varied. Under zero field, two distinct anomalies in π are observed (Fig. 2a). We attribute the first anomaly at 82 °C to a M (specifically M C wherein the polarization is confined to the {010}) to T phase transition 36 .
The second anomaly at 216 °C probably corresponds to a T to cubic phase transition. Single-crystal PMN-0.32PT shows such a transition at < 150 °C (ref. 36 ); however, in the compressively strained (-0.5%) films used here, the transition temperature could easily be shifted higher. For brevity and because we are primarily interested in the room-temperature enhancement of π, we focus further analysis on the 25-120 °C window (through the M C to T phase transition; the full temperature range from 25 to 250 °C is provided as well; Supplementary Fig. 4a). Upon probing the same pyroelectric response for heterostructures under applied d.c. electric fields of 13.3, 26.7 and 40 kV cm -1 , we observe field-induced enhancement of π at all temperatures (Fig. 2b). The first anomaly in π, corresponding to the M C to T phase transition, progressively shifts to lower temperatures (as extracted from the derivative of the temperature-dependent data; Supplementary Fig. 4b) with increasing field, indicating a field-induced rotation of polarization 24,37 that could contribute to the enhancement of π. At the same time, since the same electric field can also enhance the average magnitude of the polarization of the material either by aligning the polarization within the domains or re-alignment/growth of the domains 38,39 , the question arises as to whether the enhancement of π comes primarily from field-induced polarization rotation, field-induced enhancement of the average polarization or a combination thereof?
To separate these effects, π was measured while heating under a d.c. electric field of 40 kV cm -1 (field heating, FH) through the M C to T phase transition to 125 °C (red data, Fig. 2c) and on cooling to room temperature under application of the same field (field cooling, FC) (blue data, Fig. 2c). In this situation, the transition back to the M C phase is quenched by the applied electric field and the
sample remains in the T phase (in effect, contributions to π from polarization rotation would be 'turned off '). To confirm that it is indeed 'locked' in the T phase, π was measured again while heating (FH) after the initial FH and FC cycle and, in this case, the M C to T phase transition is not observed, confirming that the sample remained in the T phase (Supplementary Fig. 5). By comparing the difference between the FH (red) and FC (blue) curves, the contribution to π due to polarization rotation (orange data, Fig. 2c) can be quantified at any temperature. For example, polarization rotation contributes a maximum of ~16% of the total π near the phase transition. Repeating the same experiment at a higher d.c. electric field (67 kV cm -1 ) yielded the same fractional contribution from polarization rotation (Supplementary Fig. 6). In turn, this implies that the majority of the large response under bias arises from field-induced enhancement of the average polarization. Ultimately, the combined temperature-and field-induced changes in polarization magnitude and direction yield large pyroelectric response that makes this material promising for pyroelectric energy conversion.
Having understood the mechanism behind the large electricfield enhancement of π, we proceed to demonstrate the potential of directly converting heat into electrical energy via pyroelectric Ericsson (or Olsen) cycles. The ideal cycle begins with an isothermal (T low ) change of electric field (E low → E high ; 1 → 2, Fig. 3a) that polarizes the system. This is followed by an isoelectric (E high )
Nature Materials absorption of heat (T low → T high ; 2 → 3, Fig. 3a). Next, the electric field is isothermally (T high ) reduced (E high → E low ; 3 → 4, Fig. 3a). Finally, the heat is expelled isoelectrically (E low ) (T high → T low ; 4 → 1, Fig. 3a). In our devices, this cycle is implemented by applying carefully chosen time-dependent, spatially uniform temperatures and electric fields to the relaxor ferroelectric. Akin to the pyroelectric measurements above, applying a sinusoidally varying current at 1ω that locally heats the heterostructure via Joule heating (red curve, Fig. 3b) results in the temperature of the heterostructure varying sinusoidally at 2ω with an amplitude that depends on the magnitude of the heating current (for example, Δ T = 70 K; blue curve, Fig. 3b). A synchronized periodic electric field E(t) is applied across
the heterostructure in a nearly square-wave fashion (Fig. 3c). In our devices, isothermal polarization and depolarization is achieved by switching the electric field exactly where the temperature achieves its extrema, thereby approximating steps 1 → 2 and 3 → 4 of the ideal Ericsson cycle (Fig. 3a). In other words, the electric field changes from high to low or vice versa while the temperature goes through a maximum or a minimum with less than 5% change in the temperature. This small, but finite, 5% temperature-change window was chosen so as not to change the electric field using a step function that results in a very large capacitive current saturating our current-to-voltage amplifier. In response to the periodically varying temperature and electric field, the resulting current shows two features, respectively: a background pyroelectric current; and dielectric current spikes (blue curve, Fig. 3d). The total current can then be integrated (Methods) to extract the change in polarization Δ P(t) (orange curve, Fig. 3d). Using this approach, plots of Δ P(t) versus E(t) yield a familiar representation of the pyroelectric Ericsson cycle such as, for example, how the response changes for various magnitudes of Δ T = 10-90 K (maintaining T low = 25 °C, Δ E = 267 kV cm -1 , and cycle frequency f = 40 Hz; Fig. 3e). Data at higher cycling frequencies are also provided (Supplementary Fig. 7). Examination of these data reveals that on increasing the magnitude of Δ T, the area of the cycle in P-E space increases as more heat is converted into electrical work (∮ ⋅ E P d ).
The thin-film geometry of our devices also enables application of both larger electric fields and faster temperature oscillations as compared to bulk ceramics or single crystals, allowing us to explore the pyroelectric energy conversion potential across a range of experimental conditions (Δ T = 10-110 K, Δ E = 33-400 kV cm -1 , and cycle frequency f = 10-2,000 Hz). Following an initial optimization within these parameter ranges, the PMN-0.32PT thin films are shown to provide record-breaking pyroelectric energy conversion, including: first, the largest energy density of 1.06 J cm -3 (at Δ T = 90 K, Δ E = 267 kV cm -1 and f = 40 Hz; Fig. 4a), which is made possible because of the large field-induced value of π and the ability to apply large electric fields maximizing the electrical work (∮ ⋅ E P d ). Second, the largest power density of 526 Wcm -3 (at Δ T = 56 K, Δ E = 267 kV cm -1 and f = 1,000 Hz; Fig. 4b) that is realized because the power density scales directly with cycling frequency, which can be increased because the thermal time constant of the thin-film geometry is small. Third, the largest scaled efficiency of 19% is the calculated heat input to the active material with a temperature-dependent volumetric heat capacity C(T) 40 (at Δ T = 10 K, Δ E = 267 kVcm -1 and f = 40 Hz; Fig. 4c), a significant improvement over the highest reported value of ~5.4% for the same Δ T (ref. 15 ). It should be noted that for the current work, C(T) is assumed to change only with temperature 41,42 and is assumed to be constant with electric field 43 over the range studied herein.
For comparison, the energy outputs from the current work are compared to a number of experimentally investigated energy and power densities extracted from previous studies of pyroelectric energy conversion (Fig. 4d). These works employed a variety of thermal cycling methods, from pumping hot/cold fluids to immersing the pyroelectric material alternately in hot and cold thermal baths, to study bulk-ceramic (Pb 1-x La x (Zr 0.65 Ti 0.35 ) 1-x/4 O 3 (ref. 14 )), single-crystal (Pb 0.99 Nb 0.02 (Zr 0.68 Sn 0.25 Ti 0.07 ) 0.98 O 3 (ref. 17 ), Pb(Zn 1/3 Nb 2/3 ) 0.955 Ti 0.045 O 3 (refs 44,45 ) and Pb(Mg 1/3 Nb 2/3 ) 0.68 Ti 0.32 O 3 (ref. 46 )) and thin-film (P(VDF-TrFE) (refs [47][48][49] ) and BaTiO 3 (ref. 16 )) samples. As compared to the current work, the ultimate performance of these prior studies was limited by aspects related to the materials themselves (that is, they had intrinsically low pyroelectric coefficients) and/or to the functional form of the material (that is, inability to apply large electric fields and slow thermal cycling). In the current work, we have created a fieldtuned, intrinsically large pyroelectric coefficient in conjunction with a thin-film device geometry. This thin-film geometry allows a number of important advantages over work in bulk materials, including: significantly larger sweeps of electric field (achieved with much lower voltage (V) in comparison to bulk materials), thus maximizing fieldinduced polarization changes and work; high-frequency, high-temperature-amplitude cycling to increase power and work, respectively; and significantly less heat input (Q in ) is required to increase the temperature of the lattice (since it scales with volume (V) as
) while still driving the same changes in the surface charge density with the applied voltage (V), which is equivalent to the electrical work done (which scales with area (A) as
d since electric field is simply due to the applied voltage). Thus, said another way, the advantage of performing pyroelectric energy conversion with thin films is that the effects scale with just the area of the device, not the volume. Ultimately, this places pyroelectric thin films (here corresponding to an effective ZT = 1.16) as a very promising candidate for low-quality waste-heat energy harvesting, on par with thermoelectrics.
Large |π| > 550 μ C m -2 K -1 under an application of d.c. electric field is obtained in PMN-0.32PT thin films owing to a strong fieldinduced enhancement of the average polarization and polarization rotation. The same electric field also suppresses ε r by > 70%, which, in turn, enhances the FoM PEC by ~5 times in comparison to zero-field values and standard pyroelectric materials. Ultimately, implementation of solid-state pyroelectric Ericsson cycles yields a maximum energy density, power density and scaled efficiency of 1.06 J cm -3 per cycle, 526 W cm -3 per cycle and 19%, respectively; these are the highest values reported to date for pyroelectrics. The implications of this work are multi-fold. First, these results suggest that there could be novel routes to enhance the pyroelectric response in materials. Much as field-induced polarization enhancement and rotation were used herein to augment the response, other field-induced routes to large effects should also be considered (for example, field-induced domain and phase structure evolution, field-induced defect reorientation and motion and so on). This could, in turn, greatly expand the number of candidate materials for pyroelectric energy conversion. Second, this work reveals the importance of expanding the study of pyroelectric energy conversion in thin-film versions of materials since this process scales inherently with material area, not volume. At the same time, thin films permit operation at both high electric fields and thermal oscillation frequencies that can further enhance energy and power outputs. Finally, this work suggests that pyroelectric energy conversion can potentially compete with thermoelectrics, in particular, for energy harvesting from low-grade waste heat.
Methods, including statements of data availability and any associated accession codes and references, are available at https://doi. org/10.1038/s41563-018-0059-8.
Thin-film growth. This work focuses on 150 nm 0.68Pb(Mg 1/3 Nb 2/3 )O 3 -0.32PbTiO 3 (PMN-PT)/20 Ba 0.5 Sr 0.5 RuO 3 heterostructures grown on (110)-oriented, singlecrystalline NdScO 3 substrates by pulsed-laser deposition using a KrF excimer laser (248 nm, LPX 300, Coherent), in an on-axis geometry with a 60 mm target-tosubstrate spacing. PMN-PT growth was carried out at a deposition temperature of 600 °C in a dynamic oxygen pressure of 200 mtorr using a laser fluence of 1.8 J cm -2 and a laser repetition rate of 2 Hz. The Ba 0.5 Sr 0.5 RuO 3 bottom electrode layer was grown at a temperature of 750 °C in a dynamic oxygen pressure of 20 mtorr by ablating a Ba 0.5 Sr 0.5 RuO 3 target (Praxair) at a laser fluence of 1.85 J cm -2 and a laser repetition rate of 3 Hz. Following growth, the heterostructures were cooled to room temperature in a static oxygen pressure of 760 torr at 10 °C min -1 .
Device fabrication. Following the growth of 150 nm 0.68Pb(Mg 1/3 Nb 2/3 ) O 3 -0.32PbTiO 3 (PMN-PT)/20 nm Ba 0.5 Sr 0.5 RuO 3 /NdScO 3 (110) substrates, the electrothermal characterization devices are produced via a multistep, microfabrication process, according to ref. 32 , some of which is reproduced here for completeness. Briefly, the relaxor-ferroelectric heterostructure is lithographically patterned and ion-milled to define the bottom electrode and the relaxorferroelectric 'active' layer (Fig. 1a of ref. 32 ). After this step, the bottom electrode (Ba 0.5 Sr 0.5 RuO 3 ) is removed from everywhere except under the active layer and the bottom electrode probe pad. To define the top electrode, 90 nm SrRuO 3 is selectively deposited using an inverse MgO hard-mask process. This establishes a rectangular ferroelectric capacitor geometry (300 μ m × 20 μ m). The SrRuO 3 deposited over the active-layer mesa does not contact the SrRuO 3 deposited on the ion-milled region of the substrate, but a small gap is left in between. This is done purposefully to ensure that deposition on the sidewall of the ferroelectric layer does not electrically short to the bottom electrode. Next, a 200-nm-thick blanket layer of SiN x is deposited on the symmetric ferroelectric capacitor structure using plasma-enhanced chemical vapour deposition (SiH 4 + NH 3 based) at 350 °C. This nitride layer is selectively patterned and etched using reactive ion etching in a SF 6 plasma, resulting in an electrically insulating film on top of the ferroelectric capacitor. Finally, a 100-nm-thick platinum thin-film resistance heater is sputtered in the shape of a thin strip with four probe pads (two outer and two inner pads; see the geometry in Fig. 1a of ref. 32 ) to define the thermal circuit (Fig. 1b of ref. 32 ). The top and the bottom electrode contact pads are also defined in this step. The top electrode platinum contact pad runs over the SiN x and contacts the top SrRuO 3 (see the highlighted region in Fig. 1b of ref. 32 ) while the bottom electrode platinum contact connects to the bottom Ba 0.5 Sr 0.5 RuO 3 after the device gets wire bonded.
Wide-angle θ-2θ X-ray diffraction patterns (Supplementary Fig. 1a) and asymmetric reciprocal space maps (Supplementary Fig. 1b) were obtained with a Panalytical X'Pert Pro X-ray Diffraction machine with a Cu source.
Ferroelectric and dielectric properties were measured for six devices on the heterostructure. Polarization-electric field hysteresis loops were measured using a Precision Multiferroic Tester (Radiant Technologies) (Fig. 1b) that uses a virtual-ground method to measure ferroelectric hysteresis loops. Temperatureand electric-field-dependent low-field permittivity was measured using an E4990A Impedance Analyzer (Agilent Technologies) using an a.c. excitation voltage of 10 mV at various frequencies (Supplementary Fig. 2a). Burns temperature, below which short-range-ordered polar nano-regions begin to form, is calculated by measuring the deviation from the Curie-Weiss behaviour (Supplementary Fig. 2b).
Pyroelectric measurements. Average heater temperature amplitude (3ω measurement). Current supplied to the metal heater line (using a Keithley 6221 a.c. current source) results in power dissipation (Joule heating) as P = I 2 R. Thus, a sinusoidal input current, ω = I I t cos( ) 0 , results in power dissipation at d.c. and 2ω and, therefore, a temperature rise of the line also at d.c. and 2ω, Using an SRS SR830 lock-in amplifier, we measure the third harmonic of the voltage signal and thus determine the average heater temperature amplitude as 50 , where R 0 is the zero-current resistance at some reference temperature, is the driving force behind the resistance thermometry used to determine the average temperature of the heater line. This TCR must be calibrated for each device since it is dependent on the deposition parameters and can also vary significantly from bulk values, leading to variations by up to a factor of ~2 from handbook values in practice.
The sample is first heated to a desired temperature using a heating stage with a thermal mass much larger than the sample. Then the voltage is measured for a series of increasing current inputs and the resistance at each current is determined via Ohm's law. The resulting data are plotted as = R V I as a function of power P = IV, and a linear fit is used to determine R 0 from the zero-power limit (that is, the y intercept) for the given temperature. This process is then repeated for several more temperatures over a predetermined range (~10 K here). Finally, the resulting R 0 (T) is plotted against temperature and a linear fit is used to determine R 0 at 0 °C and R Average ferroelectric temperature amplitude (validity of one-dimensional approximation). To be rigorous in the estimate of π, we also account for lateral heat spreading in the films since the effective area of the relaxor ferroelectric heated via the oscillating temperature on the top heater line with area 2b heater L is not necessarily the same as the electrode area 2b electrode L used to collect the pyroelectric current (Supplementary Fig. 8a). Therefore, an effective current-collecting area is defined as 2b eff L, where b eff is the effective half-width of the heater line. A numerical finite element analysis (FEA) package was employed to evaluate the appropriate geometric correction to π (Supplementary Fig. 8b).
The temperature amplitude of the ferroelectric film does not vary by more than a few per cent through the ferroelectric film's thickness (the z direction of Supplementary Fig. 8a) but the temperature profile does vary significantly along the x direction. For a one-dimensional non-uniform profile such as this, the total measured pyrocurrent is rigorously defined as Note that θ FE is determined from θ heater and is therefore an estimate of the average temperature amplitude of the ferroelectric only out to b heater , whereas i p is collected via the electrode with a larger half-width (b electrode > b heater ) necessitating a correction. The goal of using FEA is to determine an effective half-width, b eff , that properly combines the disparate b electrode and b heater in such a way as to return the rigorous definition of the pyrocurrent, i p . Mathematically, this requirement corresponds to The above equation shows that b eff is simply the heater half-width, b heater , multiplied by the ratio of two integrals. Appropriately employing FEA can give θ(x) at any height in the stack and can therefore be used to solve for the numerical factor (the ratio of the two integrals) in b eff .
Using a commercial FEA package, COMSOL Multiphysics, the twodimensional time-periodic heat diffusion problem is solved and the temperature amplitude θ(x,z) with appropriate boundary conditions (that is, uniform periodic heat flux from the heater and adiabatic boundaries elsewhere) is used to evaluate the integrals. The FEA solution was verified against the analytical solution for the average heater temperature amplitude, θ heater (ref. 50 ). The magnitudes of the © 2018 Macmillan Publishers Limited, part of Springer Nature. All rights reserved. 10) are found and their ratio determined for the given system with properties specified in Supplementary Table 1 and for many frequencies, as can be seen in Supplementary Fig. 9. of pyroelectric current, i P . With the measured average temperature oscillation in the ferroelectric, measurement of i P permits the extraction of π. As described in ref. 32 , the current i total is measured via the bottom electrode using a lock-in amplifier (Stanford Research, SR830) (Fig. 1a). The top electrode is deliberately held at ground potential to shield capacitive coupling between the thermal and ferroelectric measurement circuits. i P is extracted from i total by taking the component of i total that leads the temperature change by 90°. Ultimately, π is
, where A is the area equal to 2b eff L. Pyroelectric Ericsson cycle. The ideal pyroelectric Ericsson cycle begins with an isothermal (T low ) change of electric field (E low → E high ; 1 → 2, Fig. 3a) that polarizes the system. This is followed by an isoelectric (E high ) absorption of heat (T low → T high ; 2 → 3, Fig. 3a). Next, the electric field is isothermally (T high ) reduced (E high → E low ; 3 → 4, Fig. 3a). Finally, the heat is expelled isoelectrically (E low ) (T high → T low ; 4 → 1, Fig. 3a). In our solid-state device, this is implemented by applying a carefully chosen time-dependent temperature and applied electric field across the relaxor ferroelectric. By applying a sinusoidally varying current i h (t) at 1ω (red curve, Fig. 3b) that locally heats the heterostructure via Joule heating, the temperature of the heterostructure is sinusoidally varied with a variable amplitude at a desired frequency 2ω (blue curve, Fig. 3b). A synchronized periodic electric field E(t) is applied across the heterostructure in a nearly square-wave fashion (Fig. 3c). The heating current and the electric field are offset by a phase ϕ to account for the thermal phase lag using the measured phase lag from the 3ω method (Supplementary 3). In device, isothermal polarization and depolarization is achieved by switching the electric field exactly where the temperature achieves its extrema. In other words, the electric field changes from high to low or vice versa while the temperature goes through a maximum or a minimum with less than 5% change in the temperature. This small but finite 5% temperature-change window was chosen so as not to change the electric field using a step function that results in a very large capacitive current saturating our current-to-voltage amplifier. The total current in response to this periodically varying temperature and electric field is measured using a variable-gain low-noise current amplifier (DLPCA-200, Femto). All three signals (heating current, electric field and measured total current) are measured using a digital oscilloscope (InfiniiVision DSO-X-4024A, Agilent Technologies). The measured total current can then be numerically integrated to calculate the change in polarization, Δ P(t). However, it should be noted that the electrode area for collecting the dielectric current (A electrode ) is larger than the area getting heated or the effective area for collecting the pyroelectric current (A heater ); therefore, the net change in polarization is calculated by separately integrating the current using the respective areas as To separate the current contribution from the change in capacitance (dielectric current i d (t)) versus the pyroelectric current (i p (t)), the heating is turned off (i h (t) = 0) to measure just the dielectric current alone. Since the dielectric current does not change dramatically as a function of temperature under large applied field (due to quenched dielectric permittivity), this dielectric current is subtracted from the total measured current to get the pyroelectric current. Using equation ( 13), Δ P(t) is calculated and further plotting Δ P(t) versus E(t) gives the pyroelectric Ericsson cycle with the cyclic loop (Fig. 3e).
Work done per cycle per volume (equivalently energy density per cycle) was calculated by numerically extracting the area of the loop (∮ . is the Carnot efficiency and C(T) is the temperature-dependent volumetric heat capacity of the ferroelectric film. In our calculations, C(T) is extracted by fitting the experimental data from ref. 41 .
© 2018 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.NAtuRe MAteRIALS | www.nature.com/naturematerials