Polar precursor ordering in BaTiO 3 detected by resonant piezoelectric spectroscopy

An experimental method, Resonant Piezoelectric Spectroscopy (RPS), is introduced for the detection of polar precursor effects in ferroelectric and multiferroic materials. RPS is based on the excitation of elastic waves through the piezoelectric effect in a sample. As the intensity of these waves is significantly amplified through mechanical resonances, RPS is very sensitive to the development of polar nanostructures. Using RPS, we identify polar nanostructures in BaTiO3 as a precursor in the cubic phase. Results are compatible with polar tweed structures which persist up to 613 K. This temperature is much higher than previously reported.

The development of novel multiferroic device materials is limited by the insensitivity of experimental tools to discover weak ferroelectricity or ferromagnetism.2][3][4][5][6] Such limitations occur when the material is optimized but the local multiferroic regions are small.This is the case when functionalities are related to interfaces, twin boundaries, and grain boundaries. 7,8Optimizing such systems is done in domain boundary engineering. 9,10 key requirement for research into multiferroic materials is improved experimental techniques to identify polar regions with high sensitivity.The most successful attempts are based on piezoresponse force microscopy (PFM). 11,12FM is useful when the polarity is spatially fixed but fails when the microstructure is dynamic, as in the case of multiferroic tweed structures and mobile twin boundaries.The only alternative method is based on the second harmonic generation (SHG), which is limited to optically transparent samples. 135][16] We will show here that SHG in BaTiO 3 underestimates the temperature range where precursor polarity can be observed. 2o investigate weak precursor polarity in BaTiO 3 , we use an experimental method we have labeled as Resonant Piezoelectric Spectroscopy, RPS.RPS is surprisingly simple to implement.The experimental arrangement is based on the excitation of elastic waves via piezoelectric coupling inherent to the sample.A small AC voltage (1-20 V) is applied across the sample, 17 which is balanced across its corners or parallel faces between the ends of two alumina rods, as shown in Fig. 1.The driving voltage leads to the excitation of local distortions that, when collective, lead to macroscopic resonant elastic waves.][20] The difference between RPS and RUS concerns the excitation of the waves: RPS uses the sample itself as an emitter while in RUS the waves are excited mechanically by an emitter transducer.In Fig. 1, this emitter transducer would be attached to the end of the upper alumina rod far from the sample.Switching from RPS to RUS is achieved simply by applying the AC voltage across the emitter transducer rather than across the sample.For heating experiments, a high temperature furnace is slid over the rods (but the transducers sit outside the furnace), as illustrated elsewhere. 21PS can also be used for low temperature measurements using an experimental arrangement similar to that described for RUS in Ref. 22.
RPS signals are strong in the ferroelectric phase of BaTiO 3 .In the cubic phase, polarized microstructures such as polar nanoregions (PNRs) and tweed structures become visible through the resonance condition: even small strain fields can lead to resonances and standing elastic waves. 23he energy scale for the wave is not the vibrational energy but the friction loss of the wave.Friction losses are well understood in multiferroics and have been evaluated by computer simulations. 24In defect free samples, friction is usually small if the frequency of the excited wave is high enough.We use frequencies of >10 5 Hz, depending on the size of the sample, and have found that friction is indeed small enough to allow the observation of tiny precursor effects in BaTiO 3 .
A stack of segments of RPS spectra is shown in Fig. 2(a).Resonance peaks are found at temperatures below 611 K, well above the transition point at 405 K.The equivalent RUS spectra are shown in Fig. 2(b) for comparison.In spectra obtained by both RPS and RUS, the frequencies of resonance peaks show a characteristic dip associated with the ferroelectric transition (405 K).This behavior is analyzed in detail elsewhere. 23The most notable difference between the spectra in Figs.2(a) and 2(b) is that the intensities of resonance peaks in RPS spectra slowly fade away as the temperature is increased.The decrease in peak intensities is illustrated in Fig. 2(c), where segments of spectra collected between 550 K and 615 K are displayed.As the temperature is increased, the amplitude of the resonance mode located at $230 kHz slowly decreases up to 611 K.At 613 K, the peak is not discernible from the background, which means that this elastic wave was not excited at T > 611 K.In Fig. 2(d), the temperature evolution of the squared frequencies x of two modes (at $260 kHz and $300 kHz) is presented. 17For comparison, RPS and RUS data are shown with red and blue symbols, respectively.Data obtained up to 750 K in RUS measurements are not shown in Fig. 2(d) but reproduce results reported in Ref. 23.According to Fig. 2(d), resonance frequencies obtained by RPS measurements are consistent with those measured by RUS.This agreement is expected since both techniques excite the same mechanical resonance modes of the sample, albeit electrically or mechanically.The mode at 300 kHz softens as temperature reduces towards 405 K, at which the ferroelectric cubic-tetragonal (Pm 3m À P4mm) transition occurs.The square of a resonance frequency gives the effective elastic modulus C eff associated with that mode. 23Thus, the observed softening upon cooling to the transition temperature indicates a reduction in the value of the effective elastic modulus, corresponding to some combination of bulk and shear moduli depending on the geometry of the standing wave. 18,25Similarly, the mode at 260 kHz shows softening as the temperature is decreased towards the structural transition from the tetragonal P4mm phase to the orthorhombic Amm2 phase.The damping coefficient is also presented in Fig. 2(d) in the form of inverse quality factor Q À1 which is calculated using the relationship Q À1 ¼ Dx=x; x is a resonance frequency and Dx is the full width at half maximum of the resonance peak.Some scatter of data points for Q À1 is evident in both RPS and RUS results, due to small values of the inverse quality factor FIG. 1. Experimental arrangement for resonant piezoelectric spectroscopy: A weak electrical signal (1-20 V) is applied to a sample, which sits lightly across its corners between the tips of alumina rods.The frequency of the electrical signal is scanned between 100 kHz and 10 MHz.When the frequency coincides with an elastic resonance of a standing wave, a standing wave will be induced even if the local piezoelectric coupling is weak.The characteristic energy for the electric input to overcome is the friction loss of the standing wave which is small for defect-free materials.The sample is shown as distorted (with gross exaggeration) to represent the excitation of a natural vibration.A piezoelectric detector glued at the end of the lower alumina rod is used to detect the mechanical resonance modes excited in the sample.($0.1%).The overall behavior of Q À1 is consistent for both techniques, however.Q À1 is small but increases slightly with decreasing temperature for T > T trans and peaks at temperatures slightly below the transition temperature T trans (405 K), characteristic of first order transitions.At T < T trans , Q À1 shows a slight decrease as the temperature is further decreased.
Resonance peaks contain information on the phase factor from the phase shift between their in-phase and outof-phase components (real and imaginary components).The Cole-Cole or Nyquist plot 23 of the real and imaginary parts forms circles if the Kramers-Kronig relationship is fulfilled. 19,26If the control parameters such as temperature are changed in RUS and RPS, the circle may rotate by a phase angle / around the origin.Trivial phase shifts occur when resonance peaks interact.Interestingly, dynamic microstructural changes also lead to a phase shift while stable microstructures will not. 24As a result, one can determine whether the microstructure is dynamic or static.Figs.3(a) and 3(b) show such phase shifts in RPS and RUS spectra collected every 3 K between 443 K and 500 K.
In Fig. 3(c), the phase shift relative to the phase angle at 443 K is plotted using both RPS and RUS spectra.Near 450 K, an overlap of the sample resonance with a peak representing a resonance of the alumina rod causes a first phase shift unrelated to microstructural changes.Above 452 K, there is no rod peak while the phase still changes as the temperature is increased.The relative phase change observed in RUS is larger than that in RPS.These phase changes clearly indicate the dynamic nature of the precursor microstructure.In order to test the field dependence of the phase angle, we performed RPS measurements at 490 K using different AC voltages between 4 V and 20 V.No such field dependence was found (Fig. 3(d)) so that it is concluded that the microstructural changes are intrinsic and not induced by electric fields.
RPS has found polar precursor microstructures in BaTiO 3 at T > 405 K. Evidence of the microstructure remains visible up to temperatures below 613 K.This temperature is higher than any cut-off temperature seen in other experiments.In SHG, the highest temperature at which SHG signals were observed is 580 K. 27 In acoustic emission experiments, 28 the observation of acoustic avalanches was associated with a Burns temperature, where polarity starts near 553 K, and a coherency temperature, where the polar regions start to become coherent, 29 T* ¼ 500 K. RPS shows that all these temperatures are significantly underestimated.The polarity of the microstructure disappears in RPS near 613 K.This temperature can be associated with the Burnslike temperature if the microstructure consisted of polar nano regions as discussed in the relaxor literature.The onset of coherency is also not confirmed beyond the trivial case that changing microstructures lead to changing thermal expansion and elastic moduli.Singularities are seen 23 near 560 K related to thermal expansion which can also lead to acoustic emission signals. 28In our experiments, some coherency is required to obtain a RPS signal.Some (perhaps not complete) coherency must already exist at T Շ 613 K, i.e., when the first polar regions nucleate, because we observe RPS signals up to this temperature.
The change of the phase factor is significant because it shows that the precursor microstructure is not static.This observation is inconsistent with any idea that static PNRs nucleate near T B and exist inside a paraelectric matrix.The   standing elastic waves show that a local piezoelectric effect exists at T < 613 K; the resulting vibrations include the movement of microstructural features such as wave patterns and intersections of waves that are present inside the entire sample.Combining this with the origin of the polarity, namely, the off-centering of Ti inside the TiO 6 octahedra, leads to a picture of a much softer microstructure akin to tweed patterns rather than static PNRs.The coupling between the Ti-off-centering and the elastic distortion was analyzed in theoretical models 30 where it was shown that tweed patterns result as an intrinsic feature without the influence of defects or chemical heterogeneities.The second requirement for tweed is that the elastic system needs to be sufficiently anisotropic to avoid clustering. 31This is the case for BaTiO 3 .Our measurements show that tweed in BaTiO 3 is dynamic and leads to central peaks 23 and other dynamic excitations but not necessarily to static tweed which would occur as a result of defect pinning.The mechanism of precursor ordering in BaTiO 3 , as it emerges from our RPS measurements, contains piezoelectric regions inside the precursor structure.The piezoelectric effect in the tweed structures could be direct or flexoelectricity could generate the piezoelectric effect if the local structure is sheared. 8,32These regions condense from a disordered matrix at very high temperatures (around 613 K), a temperature which is much higher than any other onset temperature observed with SHG or AE experiments.This apparent disagreement is due to the higher sensitivity of RPS compared with these other observational techniques, so that weak piezoelectricity can be seen even if other methods fail.The transition between the disordered phase and the tweed phase is continuous.We do not see any indication of a glass-like transition. 33The tweed structure is dynamic as evidenced from the change of the phase angle with temperature.Near the cubic-tetragonal transition, we reproduce the recent findings of RUS where softening of the elastic moduli was observed.The temperature interval where this softening occurs is slightly smaller than the observed tweed interval, namely, between 405 K and 560 K. 23

FIG. 2 .
FIG.2.Temperature evolution of mechanical resonance peaks between room temperature and high temperatures.Stack of (a) RUS and (b) RPS spectra for a single crystal of BaTiO 3 collected during heating from 290 K to 750 K and 290 K to 620 K, respectively.Spectra were vertically translated in proportion to the temperature at which they were collected so that although the y axis represents the amplitude it is labeled as temperature.(c) Stack of RPS spectra showing the disappearance of the mechanical resonance peak located at $240 kHz.(d) Temperature evolution of the squared frequency (circles) and inverse quality factor (stars) of two resonance modes above and below the Curie temperature.Symbols corresponding to RUS data are shown in blue while those of RPS are red.

FIG. 3 .
FIG. 3. Change of the phase factor for a resonance mode due to dynamical microstructures (tweed structures) in the cubic phase of BaTiO 3 .(a) RPS and (b) RUS spectra taken between 443 K and 493 K showing the interaction of a resonance of the alumina rod with a resonance of the sample.(c) The relative phase shift vs temperature.(d) Cole-Cole plot of the peak located at $320 kHz obtained with AC voltages between 4 V and 20 V. 142902