Ferroelectric Domain Wall Engineering Enables Thermal Modulation in PMN–PT Single Crystals

Acting like thermal resistances, ferroelectric domain walls can be manipulated to realize dynamic modulation of thermal conductivity (k), which is essential for developing novel phononic circuits. Despite the interest, little attention has been paid to achieving room‐temperature thermal modulation in bulk materials due to challenges in obtaining a high thermal conductivity switching ratio (khigh/klow), particularly in commercially viable materials. Here, room‐temperature thermal modulation in 2.5 mm‐thick Pb(Mg1/3Nb2/3)O3–xPbTiO3 (PMN–xPT) single crystals is demonstrated. With the use of advanced poling conditions, assisted by the systematic study on composition and orientation dependence of PMN–xPT, a range of thermal conductivity switching ratios with a maximum of ≈1.27 is observed. Simultaneous measurements of piezoelectric coefficient (d33) to characterize the poling state, domain wall density using polarized light microscopy (PLM), and birefringence change using quantitative PLM reveal that compared to the unpoled state, the domain wall density at intermediate poling states (0< d33


Introduction
In recent years, domain wall (DW) engineering in ferroelectric materials has been at the forefront of leading advancements in nanoelectronics, optics, and photovoltaics, often considered as a promising approach to achieve modulation of electrical, magnetic, optical, and thermal properties. [1][2][3] DWs are interfaces separating regions of different polarization orientations in fer roelectric materials. The structural or polarization discontinuity other studies have shown conflicting results, suggesting an inverse relationship between domain size and piezoelectric properties. [20] Qiu et al. showed that the enhancement in [001] ACpoled PMN-PT is due to the reduction of 71° DWs. [21] Similar results were also obtained in other studies, [22] including other relaxorferroelectrics such as PIN-PMN-PT. [23] Part of the reason for the conflicting results observed in the literature lies in the limitations of DW density characteri zation methods. Typical experimental methods used to char acterize domains can be classified into electromechanical (piezoresponse force microscopy (PFM)), [11] optical (polarized light microscopy (PLM), [21] and diffractionbased (Xray diffrac tion (XRD)) [24] ) methods. PFM only scans the surface features (depth < 10 nm) and typically over a small region (≈10-50 µm). This localized measurement makes it highly susceptible to skin effects and artifacts in relaxorferroelectrics, [25] meaning that the PFM might not reflect the bulk domain structure in crystals. Although PLM does scan the bulk of the crystal, it is only suitable for observing DW density along a certain direc tion, otherwise, the overlap of domain walls makes it difficult to interpret the PLM data. [26] XRD works well to assess the bulk domain structure but is limited by the selection of refinements, particularly for inhomogeneous domain sizes, which leads to inconsistency in analyzing the XRD data. [27][28][29] Thus, although localized DW density can be obtained using such characteri zations, measurement of bulk domain structures (typically for thicker samples) can involve some uncertainty due to inhomo geneity in the DW distribution. In addition, use of simula tion methods such as phase field [21] and firstprinciples [30] can help identify the mesoscale or atomistic scale origin of piezo electricity, but does not account for potential inhomogeneity in bulk scale. This challenge highlights the need for a bulk characterization method to assess the overall domain structure in relaxorferroelectrics and to understand the influence of DW density on electromechanical property enhancement.
Interestingly, DW engineering has also been applied in the field of thermal science, to modulate thermal conductivity (k) for achieving better control of solidstate heat transfer. [31][32][33][34][35][36][37][38][39] Thermal conductivity decreases by introducing DWs that act as thermal resistances inhibiting thermal transport. [31][32][33][34][35][36][37][38][39] The ease in manipulating ferroelectric DW density by electrical input has opened novel possibilities in thermal transport engi neering, which led to developments in ferroelectric thermal switches to enable dynamic control over heat flux in a mate rial. Thermal switches modulate thermal conductivity between two states (k high and k low ), where the high thermal conductivity state (k high ) is a result of lower ferroelectric DW density and vice versa. Several ferroelectric DWbased thermal switches have been reported, attempting to achieve maximum contrast in DW density to obtain a high thermal conductivity switching ratio (k high / k low ). [31][32][33][34][35][36][37][38][39] Thus, utilizing this wellestablished relation between thermal conductivity and DW density, thermal conduc tivity characterization can serve as an alternative approach to assess the bulk DW density in relaxorferroelectrics.
However, most thermal switches proposed so far focuses on thin films, [34][35][36][37][38][39] and less attention has been paid to achieving thermal conductivity modulation in bulk crystals [31][32][33] despite their practical feasibility. Further, the length scale and orien tation of domains in thin films are primarily restricted by the film thickness aside from other factors such as strain, residual stress, and boundary conditions. Thus, achieving a high thermal conductivity modulation (by enhancing contrast in DW density) is challenging. The only solution is to somehow reduce the domain size to sizes comparable to the length scale of heat carriers (phonon mean free path), taking advantage of boundary scattering. But achieving domain size reduction to such scales (usually < 100 nm) requires specific film prepara tion and high electric field, which has limited the maximum thermal conductivity contrast. [34][35][36][37][38][39] It poses the question of whether bulkscale thermal modulation can offer a comparable or even higher thermal contrast, considering the domain size restrictions on bulk samples are less severe. Additionally, while several studies have used a constant voltage bias (i.e., DCP) to manipulate ferroelectric domain walls, there has been little exploration of other electrical poling methods, such as ACP, which may improve the thermal conductivity contrast.
In this regard, we demonstrate thermal conductivity modu lation in leadbased relaxorferroelectric [001]oriented (100−x) Pb(Mg 1/3 Nb 2/3 )O 3 -xPbTiO 3 (PMN-xPT), (27<x< 33) single crystals (2.5 mmthick). The primary reason to choose PMN-PT single crystals is their substantial enhancement in piezo electric coefficient (d 33 > 2000 pC N −1 ) using DW engineering near morphotropic phase boundary (MPB: 27<x< 32) com pared to other ferroelectrics. In addition, DW engineering of PMN-PT SCs using ACP has been readily conducted and well documented in the literature. [10][11][12][13][14][15][16] The purpose of this work is twofold: 1) First, to demonstrate thermal conductivity modula tion (or DW density contrast) with DW engineering of PMN-PT SCs using DCP and ACP, which is supported by the DW density measurements using PLM and quantitative PLM (QPLM) based birefringence measurement; 2) Second, to measure the piezoelectric coefficient (d 33 ) for the same set of samples to understand the effect of DW density on the d 33 enhancement.

Thermal Conductivity Modulation for ACP PMN-(≈30-33) PT SCs Poled Along the [001] Direction
Probing the bulk thermal properties of ferroelectric DWs in PMN-PT single crystals is challenging for several reasons. First, the probing depth (thermal penetration depth) in two of the most accurate thermal characterization methods, namely time domain thermoreflectance (TDTR) [40][41][42] and frequency domain thermoreflectance (FDTR), [43] is only a few microns. Considering an average domain size of 1 µm in PMN-PT SCs, these methods can only capture a few domains near the surface that do not reflect the real domain structure inside the material. Another common approach to measure thermal conduc tivity, the 3ω method, [44] does not apply in this case. The 3ω method requires the deposition of a metal thermometer on top of the sample. This requirement is typically accomplished through lithography, which necessitates baking samples at temperatures greater than 150 °C, higher than the depoling temperature (when the aligned domains begin to reorient) of PMN-PT SCs (≈130-170 °C). [45] Other methods, such as Laser Flash Analysis and HotDisk, have strict requirements on sample shape and size, requiring large sample sizes and thicknesses that have a limited frequency range for their transducer applica tions. [46] Thus, given the need to probe bulk thermal transport in PMN-PT SCs, this work uses a steadystate infrared radiation (IR) camera measurement to obtain the temperature difference across the single crystals (along the [001] direction). Figure 1a shows the schematic of the steadystate IR camera method for temperature difference (the details are described in the "Thermal Characterization" part of the Experimental Section). The steadystate IR camera method was calibrated using standard BK7 glass (k ≈ 1.0 W m −1 K −1 ) and fused quartz (k ≈1.4 W m −1 K −1 ) samples. These standard samples were selected to ensure that the method is sensitive to small changes in thermal conductivity (thermal conductivity contrast of 40%). Based on the data from previous thermal conductivity studies (refer Section S2, Supporting Information, for more details), the anticipated thermal conductivity contrast is between ≈10%-60%. Further details regarding calibration are provided in Section S3, Supporting Information.
First, we measured the thermal conductivity modulation in ACP ([001] poled) PMN-(≈30-33)PT SCs. All the crystals were initially depoled using the method delineated in the "Sample Description and Poling Conditions" part of the Experimental Section, resulting in an unpoled (UP) state, which corresponds to a d 33 ≈ 0 pC N −1 . We varied the poling conditions in ACP to obtain a range of poling states (marked by distinct d 33 values). The poling conditions and measured d 33 are shown in the "Poling Conditions and Piezoelectric Coeffi cient" part of the Experiental Section and Table 1. The reported thermal conductivity enhancement (or contrast) is measured with reference to the thermal conductivity of the UP state. We anticipated a monotonous thermal conductivity contrast with an increasing d 33 , under the assumption that the DW density (or domain size) change is primarily responsible for the con trast in d 33 . [17][18][19][20] Figure 1c shows the normalized temperature difference   We also measured thermal conductivity of the same set of single crystals using the photothermal radiometry (PTR) method (the schematic of the PTR method is in Figure 1b and the description can be found in the "Thermal Characteri zation" part of the Experimental Section). Figure 1d presents the normalized thermal conductivity (k [100] /k [100],UP ) along the [100] direction as a function of d 33 . Thermal conductivity is comparable in both UP and the optimized ACP states, with a maximum value at the intermediate poling state (ACP1, d 33 ≈ 1480 pC N −1 ). This finding is consistent with the results obtained from the steadystate IR camera method. The maximum thermal conductivity enhancement measured using PTR is ≈11%, which is lower than the contrast measured using steadystate IR measurement (≈21%). This discrepancy can be attributed to the fact that PTR measures the inplane thermal conductivity (along the [100] direction), while steadystate IR measurement is along the crossplane direction ([001]). Furthermore, our anisotropic temperature difference measure ments (shown in Figure 2 and described in Section 2.2) show that the maximum contrast occurs along the poling direction ([001]), due to different domain structures, which explains the lower thermal conductivity enhancement in PTR compared to the steadystate IR measurement.
Using the inverse dependence of thermal conductivity on DW density, the observations indicate that the DW density decreases with AC poling until ACP1 and then increases upon further poling. The reduction in DW density for intermediate poling states is consistent with the phase field simulation of Qiu et al. at intermediate Efield (equivalent to intermediate poling state in our case) under ACP that shows an enlargement of domains due to the elimination of 71° DWs. [21] The interme diate poling states offer finer control over thermal conductivity and heat transfer, as opposed to binary k high and k low states in conventional thermal switches. At optimized poling, the domain enlargement behavior is not fully replicated, potentially because of increasing inhomogeneity in the material, where some regions grew smaller while others grew larger, resulting in an overall increase in DW density. The inhomogeneity in the optimized ACP sample is further highlighted in Figure 3 and discussed in Section 2.3.
It is essential to clarify that even though Figure 1 and   Table 2, and 3. The data is presented in the form of mean ± standard deviation. c) The schematics of DW orientation under ACP and DCP along the [001] direction. ACP results in laminar domains formed by 109° DWs when viewed along the (100) plane. The majority of 71° DWs are eliminated during ACP leading to a smaller DW density in ACP compared to DCP. The average domain size in the ACP is thus larger than in the DCP. When viewed along the (001) plane for the ACP sample, the overlapping 109° DW makes the domain size smaller. d 33 , these two parameters are not directly related. Both para meters are related to the DW density, but correlating thermal conductivity and d 33 is not within the purview of this work. Additionally, we would like to point out that piezoelectric coeffi cient and thermal conductivity characterization are two separate measurements on the same set of samples. The piezoelectric coefficient serves as a quantifiable parameter to characterize different poling states. The figures are intended to assess the variation in thermal conductivity contrast at different poling states (marked by distinct d 33 values). Moreover, given the inverse dependence of thermal conductivity on DW density, the figures are also used to highlight the relationship between d 33 and DW density for PMN-PT single crystals used in this study.
We note that in the current study, the thermal conductivity in PMN-PT single crystals is primarily due to phonons (i.e., lattice vibration) with a negligible electronic contribution. In some ferroelectrics, the formation of charged domain walls can result in metalliclike electrical conductivity, [47][48][49] which may lead to significant electronic contribution with increasing DW density. However, as described in Section S6, Supporting Information, the poling conditions employed in this study make it unlikely to form such strongly charged domain walls.
Furthermore, even if the enhanced electrical conductivity of charged domain walls is considered, the estimated electronic contribution is still negligible compared to the thermal conduc tivity contrast observed in the study. Moreover, to deconvolute the effect of potential structural changes incurred during ACP on thermal conductivity, we conducted XRD measurements on PMN-(≈30-33)PT single crystals. Section S7, Supporting Information, shows the XRD results of UP, ACP1, and ACP2 samples. The peak positions for all the poling states are con sistent within the XRD measurement uncertainty, indicating that the effect of any strain on thermal conductivity is similar in all the cases. This suggests that the observed thermal con ductivity contrast in the current study is primarily due to the change in DW density with poling.

Anisotropic Thermal Conductivity Modulation in PMN-PT SCs
To determine the direction that offers the maximum thermal conductivity contrast, we conducted the steadystate tem perature difference measurement along all three directions Adv. Mater. 2023, 35,2211286 (Figure 2a), the DW density increases on poling, contrary to the highPT compositions (Figure 2b), where the DW density decreases in comparison to the UP state. This dissimilarity in thermal conductivity can potentially be explained by the comparatively higher presence of polar nano regions (PNRs) in lowPT SCs. PNRs serve as regions of phase instability in relaxorferroelectrics, which leads to softening of transverse acoustic phonon modes. [50] This explains the lower thermal conductivity of the UP lowPT SC in comparison to highPT as measured by PTR (k UP,lowPT ≈ 1.38 W m −1 K −1 com pared to k UP,highPT ≈ 1.43 W m −1 K −1 ). Thus, in lowPT, the thermal conductivity reduction caused by PNRs can outweigh the thermal conductivity increase caused by DW reduction. The inconsistent behavior in the three directions for the lowPT is indicative of asymmetry in lattice dynamics induced by aniso tropic PNR structure. [50][51][52] However, further study is needed to understand this effect. As this study primarily concerns high thermal conductivity contrast, we stick to highPT crystals for further discussion. Figure 2b shows the normalized temperature difference along the three directions for DCP and ACP highPT SCs. The maximum thermal conductivity contrast (≈21%) occurs in the poling direction ([001]). Additionally, the contrast observed in the [010] and [100] directions, which is equivalent in a rhombohedral [001] poled PMN-PT, is similar within the experimental uncertainty. The maximum contrast along these two directions is ≈12%, which is consistent with the PTR measurements shown in Figure 1d. The thermal conductivity of samples increases to a maximum upon poling and then decreases. The trend is particularly evident in [001], where the maximum contrast is higher, but can also be observed along  (Figure 4) and in other studies. [21,53] The same sample shows reduced overall domain size when observed along [100] or [010] directions caused by overlapping 71° and 109° DWs. As shown in Figure 2c, the domain size is maximized along the [001] direction, resulting in the highest thermal conductivity contrast in comparison to other directions.
The maximum thermal conductivity enhancement in ACP samples (≈21%) is higher compared to DCP samples (≈18%), as also shown in Figure S8, Supporting Information. The inter mediate poling states (DCP1 and ACP1) display the highest enhancement for both poling conditions. The higher contrast in ACP highlights its effectiveness in eliminating the 71° DWs. Additionally, the thermal conductivity contrast between DCP1 and DCP2 is significantly lower than ACP samples, which implies that the enhanced inhomogeneity in ACP2 is related to the switching of electric field direction.

Domain Wall Density Measured by PLM
To investigate the effect of DW density on piezoelectric enhancement and to further reinforce the thermal conductivity measurement results, we did PLM measurements on PMN-(≈30-33)PT crystals. Figure 3 shows the PLM response of the UP and the ACP samples. Referring to Figure 1c, the inter mediate poled state (d 33 ≈ 1480 pC N −1 ) is called ACP1, and the optimized poled state (d 33 ≈ 2530 pC N −1 ) is ACP2.
Aligning the principal optical axis of single crystals with either that of polarizer or analyzer results in complete extinc tion. [54] Figure 3a shows extinction at P/A (angle between polar izer and analyzer) = 45° (along {110} directions), which indicates the dominant presence of rhombohedral phase (Rphase). [54] The UP single crystal is expected to be Rphase dominant con sidering the composition of crystal within the MPB at room temperature. Figure 3b shows that the majority of the regions in ACP1 are Rphase with small indications of other phases, similar to other studies. [10,55] Figure 3c indicates that ACP2 is also predominantly Rphase, which implies that the poling con ditions do not lead to a significant phase change. Figure 3d shows a typical domain orientation under ACP of PMN-PT singe crystals, consisting primarily of 109° DWs with a few 71° DWs. The former DWs are birefringent, meaning that light passing through the sample will be retarded depending on the differences in the refractive indices between the fast and slow axis. The retardation of white light results in an inter ference pattern, as shown in Figure 3a-c at P/A:0°, which is observed using PLM. Higher density of birefringent DWs will result in higherorder interference colors. ACP1 shows a uniform interference throughout the sample surface, indicating a homogenous domain wall distribution. In contrast, ACP2 exhibits a mix of higher and lowerorder interference colors. This suggests that some domains grew larger while others shrank, resulting in an inhomogeneous DW distribution in ACP2, similar to results reported in ref. [56].
Such inhomogeneity in an optimized poling state occurs at a bulk scale (≈mm), which is challenging to observe with local ized DW characterization methods. This potentially explains the conflicting results in the studies on domain observation in ACP PMN-PT single crystals. We believe that the continuous polarization reversal during ACP causes inhomogeneous electric field distribution within the material. The ACP1 underwent ≈1-2 cycles of polarization switching, while ACP2 underwent 40 cycles under the same electric field. Additionally, as discussed in Section S8, Supporting Information, ACP2 is more inhomogeneous than DCP2, indicating inhomogeneity in polarization reversal. Similar inhomogeneity in electric field distribution has been observed in studies involving other ferro electrics. [57][58][59] The inherently disordered PMN-PT structure coupled with the large volume of single crystals employed in this study further facilitates the inhomogeneity in polarization reversal. [60,61] Determining the exact cause of inhomogeneity would require a dedicated study involving in situ structural characterizations, which could be an interesting area for future research.
Next, we calculated the DW density distribution for the UP, ACP1, and ACP2 samples. Figure 3d shows that ACP along the [001] direction leads to dominant 109° DWs forming laminar domains. As these 109° DWs are nonoverlapping when observed along the (100) plane, the thickness of these laminar domains is a fair estimate for the variation in the domain size with the AC poling. The procedure for calculating the domain size and DW density is described in Section S5, Supporting Information. Figure 4 shows examples of the domain size distribution for the samples measured using PLM under crossed polars (P/A: 90°).
The calculated domain wall density for UP, ACP1, and ACP2 samples are (2.48 ± 0.10) ×10 3 , (1.73 ± 0.08) ×10 3 , and (2.70 ± 0.25) ×10 3 µm −1 , respectively. The DW density agrees with the thermal modulation trend in Figure 1c. The UP and ACP2 sample show similar thermal conductivity and hence a similar DW density. Similarly, ACP1 shows enhanced thermal conductivity owing to a reduced ferroelectric DW density. Also, the standard deviation in DW density for ACP2 is much larger than the ACP1 samples, which again reflects the increased inhomogeneity in domain size distribution. It is important to note that the DW density calculated from PLM for the UP sample only indicates the birefringent DW density, and the actual DW density can be slightly higher than the one calcu lated here. This also explains the slightly lower UP DW density compared to ACP2 even though their thermal conductivity is similar.

Apparent Birefringence Measurement using QPLM
The inhomogeneity observed in ACP2 (Figure 3c) emphasizes the need for bulk DW density characterization. Localized meas urements may lead to smaller or higher DW density values that can lead to incorrect conclusions. To further validate our PLM measurements in the last section, we turn to bulk apparent birefringence measurement of the UP and ACP PMN-(≈30-33) PT samples using the QPLM experimental setup. More information regarding the QPLM is provided in Section S9, Supporting Information. We compared the apparent birefrin gence of the UP, ACP1, and ACP2 samples. Theoretically, birefringence is the measurement of optical retardation in a crystal. The change in birefringence is influenced by the DW density and orientation. [21,53] Figure 5 shows the retardation maps and corresponding histograms for the UP, ACP1, and ACP2 samples. The average retardation (ϕ) is calculated over a 600 µm × 600 µm area for five different locations in the samples, which is sufficient to scan the bulk of the SC of size 2500 × 2500 µm. Based on ϕ, the apparent birefringence was calculated using Equation (1) in the "Quantitative Polarized Light Microscopy for Birefrin gence Characterization" part of the Experimental Section. The average apparent birefringence (Δn) is calculated to be 0.00069 for UP, 0.00057 for ACP1, and 0.00062 for ACP2 samples, respectively. In the case of the UP sample, the orientation of DW is random, as also illustrated in Figure 5b,e, where the retardation map shows no specific orientation preference. The net retardation is thus expected to be the highest as compared to the ACP samples. For ACP, the presence of birefringent 109° DW primarily dictates the retardation observed in the samples. Naturally, a higher density of 109° DW will result in higher birefringence. This is exactly what we observed in our QPLM measurements, which indicates that the DW density in the case of ACP2 is higher than ACP1. This observation further rein forces the DW density contrast as observed by thermal conduc tivity modulation and PLM measurements.
We note that the birefringence reported in the QPLM is not the actual birefringence of the material. We measured the apparent birefringence of the samples, which is sensitive to small changes in birefringence between two samples. As the domain wall density changes by around 58% between ACP1 and ACP2, leading to an enhancement in thermal conductivity  of 21%, the change in birefringence is also expected to be 58% or even lower. Therefore, QPLM was selected specifically because it is sensitive enough to detect such small changes in birefringence.

Ex Situ Cyclic Poling-Unpoling Test
Heat loss determination is vital for steadystate measurements to ensure repeatability. In the current setup, the total heat input is divided into four pathways: diffusion in the PMN-PT single crystals, conduction loss into the insulation, convection loss to the ambience, and radiation loss. The total heat loss is calculated by subtracting the heat input from the heat diffused into the PMN-PT samples. The heat input is computed based on resistive heating. The diffused heat is evaluated by taking the thermal conductivity of the PMN-PT sample as measured by PTR and the temperature difference measured by the IR camera.
As we compared ΔT among different states (e.g., UP, ACP1, ACP2) in this study, it is vital to ensure that the heat loss is the same in all the measurements. The difference between the total heat loss for the UP (≈3.87 mW) and ACP1 (≈3.79 mW) is around 2.1%, which is much lower than the observed rise in ΔT (≈21%). Additionally, we conducted an ex situ repeatability test on PMN-(3033)PT single crystals to validate this claim. We measured the same crystals to eliminate any potential influence of varying compositions. Before the IR camera test, the crys tals were taken off the heater and thermally depoled for about two hours. Once completely depoled, the UP samples were reattached to the heater using silver paste and tested under the IR camera. The samples were then poled and tested in the same way. The poling conditions and measured piezoelectric coef ficient are shown in the "Poling Conditions and Piezoelectric Coefficient" part of the Experimental Section and Table 4. We conducted this test three times to ensure repeatability. Figure 6 demonstrates consistent thermal contrast for both ACP and DCP PMN-(30-33)PT SCs. The UP samples show a con sistent reduction in thermal conductivity, which indicates that the domains are completely reoriented. The maximum thermal contrast in one of the UP-ACP-UP cycles reaches 27%, and the average is 22% over the three cycles. In the UP-DCP-UP test, the maximum modulation is 25%, with an average of 20%. This test confirms that heat loss is similar throughout our measurements and highlights the reliability of the relaxor based ferroelectric thermal switch.

Conclusion
We have demonstrated the thermal conductivity modulation in bulk scale (millimeter thick) using ferroelectric PMN-PT SCs. We observed a maximum thermal conductivity enhance ment of ≈27% for the PMN-(30-33)PT and ≈12% for the PMN- (27)(28)(29)(30) PT SCs using AC poling. The anisotropic steadystate temperature difference measurements suggest that the poling direction exhibits the maximum thermal conductivity modu lation (maximum DW density contrast). The DW density measurement using PLM and apparent birefringence measure ment using QPLM validate the observed thermal conductivity contrast. The PLM also reveals the increased inhomogeneity in domain size distribution in the [001] ACpoled PMN- (30)(31)(32)(33) PT SCs under optimized poling conditions. Comparing the thermal conductivity measurement results with piezoelectric property (d 33 ) enhancement reveals that DW density reaches a minimum at intermediate poling states (characterized by an intermittent d 33 value: 0< d 33 <d 33,max ). Our observations also indicate that the increasing DW density leads to a higher domain size inhomogeneity, particularly for ACP single crys tals. At optimized poling (maximum d 33 ), the inhomogeneity dominates, which results in increased overall DW density com pared to intermediate poling states. This study highlights the relevance of thermal conductivity characterization as an alterna tive tool to understand the variation of domain walls in future ferroelectric studies. From the thermal conductivity modulation perspective, such relaxorbased ferroelectric thermal switches can offer remarkable control over thermal transport in a solid state device, not limited to only the bipolar ON and OFF states as in conventional switches, with the aid of AC poling. Consid ering a unit of single crystal produces around 20% reduction in heat transfer coupled with the ease of applying an electric field, an array of single crystals would lead to a considerable reduction in overall heat transfer, ideal for solidstate thermal management applications.

Experimental Section
Sample Description and Poling Conditions: The [001]-oriented PMN- (27)(28)(29)(30)PT (referred to as low-PT) and PMN- (30)(31)(32)(33)PT (referred to as high-PT) SCs, with 200 nm-thick Au electrodes on both surfaces were procured from CTS Corp., IL, USA. The sample dimensions for each test are listed in the "Poling Conditions and Piezoelectric Coefficient" part of the Experimental Section. The samples were heated to 200 °C for 30 min for a fullydepoled state (i.e., unpoled (UP) state) before each poling process. All poling procedures were performed using electric signals generated and amplified by a function generator (Agilent 33250A, Santa Clara, CA, USA) and a high-voltage amplifier (Trek, 609B, New York, NY, USA), respectively. Several electric DC-poling conditions were adopted adjusting the amplitude (0-5 kV cm −1 ) and duration  Figure 1a). The temperature from the top and bottom of the PMN-PT sample surface was measured using an IR camera. The samples were attached on top of a copper plate that was placed on top of a resistance heater using a thermal adhesive (k ≈ 2 W m −1 K −1 ). The heater was driven by a DC source. The sample assembly was insulated using silicone (k≈ 0.2 W m −1 K −1 ) and foam (k ≈ 0.05 W m −1 K −1 ) to avoid excessive heat loss to surroundings. The maximum temperature was kept within 60 °C to avoid sample depoling and minimize thermal radiation. Under the steady state, temperature difference (ΔT = T bottom − T top ) across the samples was inversely proportional to their thermal conductivity. Thus, the ratio of temperature difference, under the constant heat loss assumption (more details can be found in Section 2.5), should be the same as the thermal conductivity contrast (i.e., ΔT UP /ΔT ACP ≈ k ACP /k UP ). Further, to validate the thermal conductivity contrast obtained from steady-state measurements, the PTR method was used to measure the in-plane thermal conductivity (along the [100] direction) of the PMN-(≈30-33)PT SCs as shown in Figure 1b. PTR measures thermal diffusivity of the sample using an intensity-modulated CW laser pump beam and probing the resulting blackbody radiation-induced on the surface. A thin layer of graphite was applied on the sample surface to improve the surface emissivity. The graphite layer thickness was measured using profilometry (≈5 µm), which was insensitive to the fitted thermal diffusivity. Details of the measurement, data analysis, and validation can be found elsewhere. [62] Polarized Light Microscopy Characterization: The domain characterization was performed using the Eclipse LV100N POL polarized microscope. For the DW density characterization, an additional tint plate (1λ) was used to increase the domain contrast. The samples were polished down to a thickness of ≈0.2 mm for the measurements using diamond lapping films, with 30 µm grit size for coarse polishing and 1 µm for fine polishing.
Quantitative Polarized Light Microscopy for Birefringence Characterization: The quantitative polarized light microscopy (QPLM) setup for the apparent birefringence measurements of the PMN-PT SCs was based on the work of references. [63][64][65] The specimen was illuminated with a monochromatic green LED light source that was first filtered with a narrow band (10±2 nm) wavelength filter centered at 546.1±2 nm (10MLF10-546, Newport). Linear polarizers for the wavelength range of 480-550 nm, (LPVISA050, ThorLabs) and quarter waveplates (QWP) designed for 546 nm (WPQ05M-546, ThorLabs) were used to generate and analyze polarized light entering and exiting the sample. A high-speed camera (Photron FASTCAM SA-X2) with a 25 mm macro lens (Laowa 25 mm f/2.8 2.5-5X Ultra Macro Lens) was used to record the intensity images at a rate of 250 frames per second. The first QWP was rotated at a constant speed of 105 RPM by a high-speed servo motor (Kollmorgen AKM11B), controlled using a Kollmorgen AKD-T00306 drive with its built-in PID speed control system. All QWP alignment angles were set with respect to the horizontal direction. The method described here [63] was used for calibration of the QWPs. The samples were fixed to a poly(methyl methacrylate) (PMMA) sheet with cut out square holes for the polarized light to travel through. The PMMA was only used as a fixture for the samples and had no effect on the results of the measurements. A harmonic image analysis [63] for images collected over 180° of QWP rotation was used to calculate the alignment and retardation values of each pixel in the sample. The apparent birefringence (Δn) was then calculated using Equation (1), 2 φλ π ∆ = n t (1) where φ is the retardation in radians, λ is the wavelength of the light propagating through the specimen (546 nm), and t is the thickness of the sample in nm.
Poling Conditions and Piezoelectric Coefficient: Here the sample sizes, poling conditions, and properties at different poled states are described. Three samples were poled for each condition and the average data is presented in the tables. The sample sizes were 10 mm × 5 mm × 2.5 mm for the PTR thermal conductivity and steady-state IR measurements (Figure 1c,d). For the rest of the measurements (Figure 2 and Figure 6), the sample sizes were 2.5 mm × 2.5 mm × 2.5 mm. The samples were poled along the thickness (2.  Figure 4d-f were fitted with a normal distribution in the software Origin. The mean value of the normal distribution was presented in the plots. The data for DW density was presented in the form of mean ± standard deviation (n = 9).

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