Dual‐Channel Dielectric Tunability in Highly Textured BaTi0.99Fe0.01O3−δ Ceramics With Micro‐Twin Boundary

Dielectric tunability is widely used in numerous electronic devices, including wavelet filters, lens antennae, and varactors. However, a dielectric device often has only one tunable dielectric constant range, confining the integration of a multi‐frequency electronic circuit. Herein, a new kind of dielectric tunable textured BaTi0.99Fe0.01O3−δ ceramics with micro‐twin boundaries is proposed for the dual‐channel controllable dielectric constants. The relative tunability with the acceptable figure of merit is as large as 76% in the crossover channel, which is superior to that of the most state‐of‐the‐art BaxSr1 −xTiO3 counterparts. This new design strategy offers the possibility of dual‐channel filters in one dielectric device controlled by external electric fields. The required external electric field is moderate with the help of reversible micro twins, which is confirmed by first‐principles studies. The static magnetic field interference on the dielectric constant is also evaluated, showing the frequency stability of dielectric tunability in a range between 5k and 1 m Hz.


Introduction
Tunable dielectric materials are increasingly being investigated and widely used in electronic devices in integrated circuits. [1] The realized applications, such as wavelet filters and lens antennae, have been demonstrated in microwave devices, triggering new designs and electronic devices for tunable dielectric materials. The screening or filtering ability of tunable dielectric materials is evaluated by their figure of merit (FOM) k = [ε(0)−ε(E)]/ [ε(0)·tan δ], where ε(0), ε(E), and tan δ are the dielectric constant at zero electric field, the dielectric constant at electric field E, and the loss tangent, respectively. Toward an efficient tunable dielectric material, the dielectric tunability should be as large as possible, and its dielectric loss should be minimized. In practice, the change of dielectric constant and loss tangent is contradictory, making the improvement of k a challenge. Ferroelectric thin films, thick films, single crystals, ceramics, and composites in the paraelectric phase above the Curie temperature (T C ) are considered the ideal candidate for tunable microwave devices due to their large tunability, fast response time, and excellent power consumption. [2] For example, the Ba 0.5 Sr 0.5 TiO 3 thin film has a large tunability of 87% and a good quality factor Q of 161. [3] The tunability of the KTa 0.6 Nb 0.4 O 3 single crystal could reach 77% at 20 kV cm −1 . [4] A good tunability of 56% and low tangent angle of 0.003 is achieved in the BaTi 0.85 Sn 0.15 O 3 ceramic at a very small field of 7.6 kV cm −1 . [5] However, these typical applications ignore the anisotropy superiority of a ferroelectric that one crystal orientation is at the polar state while another orientation is at the non-polar state, and two states can be switched under an external electric field.
In recent years, textured ferroelectric ceramics such as (Ba, Ca)(Ti, Zr)O 3 , (K, Na)NbO 3 , and Pb(Mg 1/3 Nb 2/3 )O 3 -PbTiO 3 have drawn lots of interest due to their optimized performance for applications in the field of functional electronic devices. [6] The anisotropy of polar states in textured ferroelectric ceramics is similar to that in single crystals. However, for a typical tetragonal ferroelectric crystal, the switching between the polar and non-polar states on different crystal orientations is blocked because the large micro strain is not symmetrycompatible with the spontaneous polarization in ferroelectric domain microstructures. [7] Compared to the single crystal, the introduced microstructures such as the twin boundary or Dielectric tunability is widely used in numerous electronic devices, including wavelet filters, lens antennae, and varactors. However, a dielectric device often has only one tunable dielectric constant range, confining the integration of a multi-frequency electronic circuit. Herein, a new kind of dielectric tunable textured BaTi 0.99 Fe 0.01 O 3−δ ceramics with micro-twin boundaries is proposed for the dual-channel controllable dielectric constants. The relative tunability with the acceptable figure of merit is as large as 76% in the crossover channel, which is superior to that of the most state-of-the-art Ba x Sr 1 −x TiO 3 counterparts. This new design strategy offers the possibility of dual-channel filters in one dielectric device controlled by external electric fields. The required external electric field is moderate with the help of reversible micro twins, which is confirmed by first-principles studies. The static magnetic field interference on the dielectric constant is also evaluated, showing the frequency stability of dielectric tunability in a range between 5k and 1 m Hz.
the morphotropic phase boundary that break the local symmetry in tetragonal textured ceramics have the opportunity to tailor both the polar and non-polar states. The ferroelectric bulk ceramics with these microstructures can therefore be used to design dual-channel dielectric devices as shown in Scheme 1a,b. In this design, the polar state is regulated by alternant external electric fields from two orthogonal directions instead of applying a scalar reversible electric field. The introduction of dual-channel regulation makes it possible to build novel functional devices. For example, a prototype dualchannel active low pass filter (DLPF) based on the textured ferroelectric ceramic is proposed as sketched in Scheme 1c. A DLPF differs from a typical LPF in three characteristics: i) the textured ceramic is used to displace the simple capacitor; ii) the textured ceramic has two work directions parallel and perpendicular to the texture direction. The capacitance in the parallel direction C para is different from the perpendicular one C prep . The work direction is changed by a modulation switch; iii) a DLPF has at least two cut-off frequencies. In each work direction, the capacitance of the textured ceramic C t is regulated by the input voltage. Thus, the cut-off frequency f c = 1/(2πRC t ) of a DLPF is tuned from f c1 = 1/(2πRC para ) to f c2 = 1/(2πRC prep ) and could be further tuned by the applied voltage. Compared with the present tunable LPF using the potentiometer, the DLPF has two channels, a simpler structure, and a faster response time.
Here, we report a highly [00l] textured Fe-doped BaTiO 3based ferroelectric ceramic (BaTi 0.99 Fe 0.01 O 3−δ , BTF) with the inherent micro-twin boundary to meet the design requirement of a DLPF. The BTF ceramic shows 40% anisotropic dielectric constants in parallel and perpendicular to the texture direction. The dielectric tunability of the dual-channel is 76% with a poling electric field of 20 kV cm −1 . The introduction of slight Fe doping in the textured structure plays an important role that lows down the switching barrier between the polar state along the c-axis orientation and the non-polar state along the a-axis orientation, respectively. The present strategy inspires the novel dual-channel dielectric tunability using textured ferroelectric ceramics, opening a new avenue to design new concept applications.

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grains is perpendicular to the surface. Figure 1c,d shows XRD patterns of textured BTF ceramics measured from different directions, and the angles between the diffraction plane and the nominal (00l) are 0° (parallel), 45°, and 90° (perpendicular), respectively. All patterns possess a tetragonal structure. Lattice parameters c, a, and the relevant c/a ratio are calculated as 4.0301 Å, 3.9985 Å, and 1.0078, respectively.
The (00l)/(l00) texture degree is evaluated to be 94% using the Lotgering factor F (00l) from the 0° pattern. [8] March parameter r (00l) is also calculated as 0.21 when reference reflections are selected as (002) and (101). [9] Unlike single crystals; although textured ceramics synthesized by TGG technique are considered quasi-single oriented along the texture orientation, they are randomly oriented in the perpendicular direction. Thus, the 90° pattern is similar to the profile of standard BaTiO 3 powders. We note that the intensity of the (l00) reflection in the 0° pattern is comparable with that of the (00l) reflection, which means the sample is not totally (00l) oriented. This phenomenon is widely observed in textured tetragonal ceramics synthesized by TGG technique. [10] Further, the intensity of (002) reflection is higher than that of (200) reflection in the 90° pattern, which is opposite in the 0° pattern. Figure 1b illustrates the actual grain orientation distribution according to the above patterns. Each blue cuboid represents one BTF grain. Gray and colorful arrows represent the laboratory and crystallographic coordinate system, respectively. The distribution of (00l) and (l00) orientations is similar, either parallel to the texture direction or randomly distributed in the plane perpendicular to the texture direction. In this distribution, any (00l) and (l00) reflections would not be observed in other directions, as demonstrated by the 45° pattern. The (l00) and (00l) reflections disappear in the 45° pattern, and all other reflections are emergent. With this taking into account of the limited distribution of grains in the textured BTF ceramic, it is very usual for adjacent grains to be connected by (00l) and (l00) crystallographic planes, leading to the intergrain strain of up to 0.8% based on the c/a ratio. To minimize the intergrain strain, the self-organized microstructure, such as domains or twin boundaries, is expected to take place in the textured BTF ceramic.
To investigate the textured structure at the microscale, the high angle annular dark field (HAADF) image is conducted as shown in Figure 2a. Elemental mappings across several micrometers show the spatially uniform distribution of three elements: Ba, Ti, and Fe. The typical microstructure is interweaving 90°-twin boundaries, as displayed in Figure 2b. Highresolution transmission electron microscope (HRTEM) images collected at the micro-twin boundary in Figure 2c show the polarization configuration of micro twins. The phase projections of Ba and Ti atomic columns have different contrasts and various pixel positions. Their relative pixel positions verify that the polarization directions of twins A and B are perpendicular, making a tail-to-tail polarization configuration. The corresponding selected area diffraction pattern and the schematic diagram of the micro-twin boundary are presented in Figure S1, Supporting Information. The mesoscale morphology is observed using the scanning electron microscope (SEM) as

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shown in Figure 2d. In chemically etched textured ceramic, 90° domains extend along the texture direction between multiple grains, meaning the relatively small intergrain strain. The domain configuration is straightforward, including protuberant stripes and concave slopes, where most stripes are parallel or perpendicular to the texture direction, and concave slopes tilt along ≈45°. We attribute the unusual mesoscale domain configuration to micro twins, which can reduce the strain between (l00) and (l00) orientations. Non-90° domains that are less effective for decreasing the strain are rare in this cross-section. Only a couple of typical 180° domains, signed by an orange arrow in the inset, are found at the junction of stripe 90° domains.
The dielectric tunability of the textured BTF ceramic based on the dual-channel regulation is characterized as shown in Figure 3. Dielectric anisotropy of the unpoled textured BTF ceramic at room temperature is characterized by the frequencydependent dielectric constant and loss tangent as displayed in Figure 3a. The dielectric constant perpendicular to nominal [00l] (1513, 100 kHz) is ≈40% larger than the parallel one (1077, 100 kHz) over the whole frequency range measured, rendering strong anisotropy. In addition, the relatively small frequency dispersion means the weak space charge in the textured ceramic, while a slight increase at the high frequency can be attributed to oxygen vacancies and electron hopping between Fe 2+ and Fe 3+ . [11] To elaborate the anisotropy of the dielectric tunability, the sample is poled along two directions in turn as shown in Figure 3b. In the schematic illustration, the experimental procedure is sketched. An unpoled sample was poled sequentially along parallel, perpendicular, and then parallel directions with an electrical field of 20 kV cm −1 . As the dielectric tunability of the textured BTF ceramic is non-volatile, dielectric constants were measured along both parallel and perpendicular directions after each poling process. The first poling process along the parallel direction increased the dielectric anisotropy from 40% to 76% at 100k Hz as shown in Figure 3c. The FOM was 61 for the crossover channel. Dielectric constants along the parallel and perpendicular direction decreased and increased by 15% and 19%, respectively. The second poling process along the perpendicular direction made the dielectric anisotropy recover from 76% to 17% at 100k Hz, which was also much smaller than the value of 40% in the initial state. Then, the third poling process along the parallel direction once again increased the dielectric anisotropy to 68% at 100k Hz, which means the large dielectric anisotropy was repeatable. Figure 3d plots the temperature evolution of the anisotropic dielectric constant at 1 M Hz. Sharp peaks, which correspond to ferroelectric-paraelectric transition, are observed around T C ≈ 96 °C in both curves. The T C of the textured sample is slightly lower than that of the random sample (shown in Figure S2, Supporting Information). We attribute the decrease of T C to the reduced strain with the micro-twin boundary, as the result of the Monte Carlo simulation suggests (see Figure S3, Supporting Information). Normally, the dielectric constants are the same for all orientations in the cubic-symmetry ceramic above T C . In our sample, the anisotropy of the dielectric constant is kept at a very high temperature until 400 °C. The dielectric measurement of a random sample (seen in Figure S2, Supporting

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Information) shows no anisotropy during the whole temperature range, which excludes the potential influence of pores and other macro structures of dielectric anisotropy. The dielectric anisotropy above T C in the textured BTF ceramic may originate from another microstructure evolved from the micro-twin boundary. The temperature versus dielectric constant behavior obeys the modified Curie-Weiss law, [12] which is given by 1/ε r −1/ε rm = (T−T m ) γ /C, where ε rm is the maximum dielectric constant at temperature T m , γ is the dispersion coefficient, and C is the Curie-Weiss constant. The fitted results in Figure 3e show nearly the same γ of 1.17 and 1.16 for the perpendicular and the parallel curves, respectively. In contrast, the BaTiO 3 crystal has a dispersion coefficient of ≈1. [13] We attribute the enhanced dispersion behavior to the degeneration of micro twins in textured ceramics, which is analogous to another microstructure (i.e., polar nanoscale regions, PNR).
As the dual-channel tunability of the textured BTF ceramic is caused by its crystallographic anisotropy and dielectric anisotropy under the external electric field, the ultrahigh dual-channel tunability can be expected in materials with the most considerable anisotropy such as BaTiO 3 single crystals. However, there have been no relevant applications based on single crystals as the strain to reverse the crystallographic orientation in BaTiO 3 single crystals is giant. We note that, with the help of the microtwin boundary, the reversal of strain or crystallographic orientation in the textured BTF ceramic can be easy. Figure 4a shows the polarization versus applied electric field (P−E) loops of textured BTF ceramics measured in parallel and perpendicular directions. In the parallel direction, the remanent polarization P r and the saturated polarization P sat are 12.0 and 35.6 µC cm −2 under 100 kV cm −1 , respectively; showing that although almost all domains would be switched under the large electric field, a large part of the domains returns to the initial state when the electric field is removed. On the other hand, the P−E loops are isotropic in the textured BTF ceramic. The P sat of 34.3 µC cm −2 in the perpendicular direction is very close to that in the parallel direction, which means that the reversible domain switching behavior exists both in the parallel and perpendicular direction. The domain switching behavior of the BTF textured ceramic is more like that of the random ceramic (see Figure S4, Supporting Information) rather than the single crystal. In BaTiO 3 single crystals, the P r and P sat are almost equal, both ≈22−26 µC cm −2 under ≈2 kV cm −1 . [14] The random ceramic-like P−E loops have also been widely observed in other textured perovskite ceramics. [15] This phenomenon can be further discussed using an atomic level perspective below.  (Figure 4d). At room temperature around 300 K, the thermal fluctuation energy of 1D direction (i.e., the a-axis/[l00] direction or the c-axis/[00l] direction) k B T/3 ≈ 8.62 meV is sufficient to overcome the shallow double wells in the a-axis of the BTF ceramic and result in rapid polarization fluctuations perpendicular to the c-axis or [00l] direction. In the dielectric measurement, the relatively low electric field of ≈0.01 kV cm −1 hardly provides sufficient extra energy. The polarization could be reversed from the a-axis to the c-axis, but not the opposite. Different polarization fluctuations in two directions result in a larger dielectric constant along the a-axis, which is the same in both textured ceramic and single crystals.
The situation is different in the ferroelectric test. Polarization fluctuations along four equal crystallographic directions of the a-axis or [l00] direction would offset one another, which results in macroscopic nonpolar a-axis in single crystals. For the textured BTF ceramic without the external field, the polarization exists in both the parallel and perpendicular direction with the restriction of the micro-twin boundary. The small depth of a double well of BTF cannot prevent the polarization reversal between the c-axis and a-axis under a large electric field of around 100 kV cm −1 . Similar polarizations are reached parallel to and perpendicular to [00l] in the textured BTF ceramic.
Our DFT calculations suggest that the small c/a ratio by Fe doping and the puny energy difference between double wells in the c-axis and a-axis is responsible for the strong dielectric anisotropy and the dual-channel dielectric regulation. The microtwin boundary and the similar dual-channel dielectric tunability should also be observed in other textured perovskite systems with small c/a ratios. By contrast, dielectric anisotropy would be much smaller than that of BTF in other tetragonal ferroelectrics with large c/a ratios such as PbTiO 3 (c/a = 1.063). [16] Recent work for PbTiO 3 -based textured ceramics also shows a stronger ferroelectric anisotropy than that of the BTF textured ceramic. [17] To display the regulating effect of the electrical field to the micro-twin boundary, parallel XRD patterns of the textured BTF ceramic after poling at electric fields from 0 to 40 kV cm −1 are displayed in Figure 4e. Each poling process is held at the stated voltage for 15 min. For stability, the pattern is collected after 10 min. The intensity of the (00l) reflection increases with an increasing poling field, whereas the intensity of the (l00) reflection decreases continuously. To observe the evolution of the micro-twin boundary, (200)/(002) intensity ratios are calculated using the peak-to-peak method, as shown in Figure 4f. The evolution can be described as the following three stages. i) When the poling field is from 0 to 4 kV cm −1 (the average coercive field of P−E loop), the intensity ratio is almost unchanged, which indicates that the micro-twin boundary is stable, or domain switching is completely reversible. ii) For 4 kV cm −1 < the poling field ≤ 20 kV cm −1 , the intensity ratio decreases almost linearly from 2.02 to 1.07. Domain switching is partly irreversible in this stage. iii) For 20 kV cm −1 ≤ the poling field ≤ 40 kV cm −1 , the www.advelectronicmat.de intensity ratio gradually decreases from 1.07 to 0.82, which suggests that another stable state for micro twins is reached under the static electric field. The ratio of the (200) crystallographic plane is calculated using the formula P (200) = IR (200) /(IR (200) + 1), where P (200) is the ratio of the (200) crystallographic plane and IR (200) is the intensity ratio of (200)/(002). P (200) equals 0.69 and 0.44 under 0 −1 and 40 kV cm −1 , respectively. Therefore, the ratio of (l00) crystallographic planes switching to the nominal [00l] direction is 36% using the intensity ratio. The poling experiment indicates that domains in the textured BTF ceramic can be irreversibly switched under a static electric field, but the upper limit of reversible domains is restricted by the microtwin boundary. A recent first-principles study shows that the interaction of oxygen vacancies and charged twin boundaries may be another reason to restrain switching. [18] Unlike in single crystals, complete poling to the [00l] direction in the textured BaTi 0.99 Fe 0.01 O 3−δ ceramic is difficult even with an electric field that is ten times that of the coercive field.
Compared to the undoped BaTiO 3 ceramic, the Fe doping improves the dielectric tunability performance of the textured ceramic in several respects: i) it makes the reversal of the polarization easier by reducing the c/a ratio; ii) it also decreases the dielectric constant and the loss tangent, which would both increase the figure of merit k; iii) the breakdown strength of the ceramic is enhanced. However, the Fe dopant would also introduce the magnetism and magnetoelectric effect, which triggers the potential influence of the dielectric constant by the freespace electromagnetic field. Magnetic properties are therefore analyzed to evaluate the electromagnetic susceptibility (EMS) performance of the BTF ceramic. Figure 5a shows the magnetic moment versus magnetic field (M−H) loops of the textured BTF ceramic poled parallel and perpendicular to [00l]. The magnetic www.advelectronicmat.de field in each test is parallel to the poling direction of the sample. Different from the diamagnetism of undoped BaTiO 3 , the rearrangement of d orbital electrons caused by Fe doping introduces ferromagnetism or paramagnetism into BTF, which is verified by first-principle calculations and experiments. [19] The textured ceramic poled parallel to the [00l] direction shows a distinct non-linear M−H loop, which indicates weak ferromagnetism. Meanwhile, the M−H loop of the textured ceramic poled perpendicular to the [00l] direction is almost entirely paramagnetic. Distinct magnetic anisotropy is only observed in poled samples, and the unpoled sample is magnetic isotropy as shown in Figure 5b. The calculated magnetic susceptibilities χ of poled and unpoled BTF ceramics are smaller than 10 −3 , and the relative permeabilities µ = 1 + χ are approximately equal to 1, which indicates that the external magnetic field would not influence the electric properties. Figure 5c,d shows the direct influence of the large magnetic field on the dielectric constant of the textured BTF ceramic poled parallel to the [00l] direction. Dielectric constants remain stable at different frequencies from 1k Hz to 1 m Hz even under a 5 T magnetic field. The difference in the dielectric constant between 0 and 5 T is very close to zero at a broad frequency range as displayed in Figure 5e,f. Even at the resonant frequency, the maximum absolute difference is less than 6%. The stable EMS performance is beneficial to the application of BTF textured ceramics in a DLPF device and to other electron devices in the future.

Conclusion
In conclusion, highly [00l] textured BTF ceramics are developed for dual-channel dielectric tunability applications by introducing strong dielectric anisotropy in the ferroelectric state. Due to the intrinsic difference of the polarization between the [00l] direction and other directions, the unpoled BTF ceramic show 40% dielectric anisotropy in parallel and perpendicular texture directions. The dielectric anisotropy can be further tuned by the poling electrical field. The dual-channel dielectric tunability is regulated in a wide range from 17% to 76% through successive poling processes along orthogonal directions. The combination of DFT calculations and experimental analyses show that the shallow double well potential with polarization fluctuations in the a-axis is responsible for the tunable dielectric anisotropy of the textured BTF ceramic with a small c/a ratio. The dopant Fe introduced to improve the tunability performance brings the controlled ferromagnetism, which would not significantly decrease the EMS performance because of the weak permeability. Based on the novel dual-channel dielectric tunability of the textured BTF ceramic, it may develop a universal strategy to design dielectric tuning materials for new microwave applications in the future.