Direct observation of polar tweed in LaAlO3

Polar tweed was discovered in mechanically stressed LaAlO3. Local patches of strained material (diameter ca. 5 μm) form interwoven patterns seen in birefringence images, Piezo-Force Microscopy (PFM) and Resonant Piezoelectric Spectroscopy (RPS). PFM and RPS observations prove unequivocally that electrical polarity exists inside the tweed patterns of LaAlO3. The local piezoelectric effect varies greatly within the tweed patterns and reaches magnitudes similar to quartz. The patterns were mapped by the shift of the Eg soft-mode frequency by Raman spectroscopy.

. The main obstacle to the discovery of tweed is the high mobility of tweed patterns, which remain invisible optically or by transmission electron microscopy. Nevertheless, diffraction evidence was found both in alloys and ceramics 23 . A prime candidate for tweed is LaAlO 3 , which is ferroelastic 39 and contains a high density of mobile twin walls 40 . Wall polarity was never seen in LaAlO 3 in contrast to CaTiO 3 and SrTiO 3 10, 14 where the local dipoles are related to the off-centering of Ti inside an octahedral oxygen cage. LaAlO 3 has no known ferroelectric instability and wall polarity was hereto unknown for perovskites structures with Al in octahedral position. Nevertheless, very weak piezoelectricity was previously suspected in some samples 39 (but never confirmed by diffraction based symmetry analysis). In this paper, we report a significant piezoelectricity in tweeded LaAlO 3 samples with low defect concentrations.

Results
Weak electric fields applied at frequencies between 100 kHz and 10 MHz excite strong piezoelectric vibrations in LaAlO 3 with a tweed structure but not in uniform samples. Amongst the large number of resonance peaks we selected the one with the lowest peak overlap (Fig. 2). This RPS signal is comparable with that of randomized quartz in agate 42 but is weaker than in tetragonal BaTiO 3 24 . The observation of RPS signals already proves unequivocally that samples with tweed structures are piezoelectric. Considering the diffraction based point group symmetry 3 m of LaAlO 3 we find that this piezoelectric point group symmetry is also polar.
The Piezoelectric Resonance Spectroscopy, RPS, method is described in more detail under 'experimental methods' . We now discuss some details of the RPS observations. The validity of the RPS observation is guaranteed because the peak frequency and its temperature evolution are identical to those of purely mechanical resonances shown in Fig. 3. The temperature evolution of the resonance frequency is unusual, however, as it shows a significant softening on cooling below room temperature. This softening is identical in samples with and without tweed and was already reported in 43 . A first tentative explanation related the softening to a Debye-like dissipation peak, which occurs near 250 K (activation energy 43 ± 6 kJ mol −1 ). The mechanism for this activation process is associated with the modulus C 44 . The physical origin of the process in not known. The softening in the temperature interval between 220 K and 70 K is similar to those observed in incipient ferroelastics or ferroelectrics. The softening interval ends with a further dissipation peak at < 40 K, its origin was discussed in 27 in terms of freezing of atomic motions of La and/or Al. LaAlO 3 thus shows evidence for an incipient structural instability at low temperatures which is potentially analogous to SrTiO 3 18 . The softening is the same in crystals with and without the tweed structure 27 and is hence not be related to tweed on a micron-scale. It is possible, however, that tweed on a much finer, submicroscopic scale may exist in most samples 27 . The dynamic excitations in tweed 26,27 are typically low energy phason modes, which strongly reduce the mechanical shear resonance frequencies. Their appearance could explain the observed temperature dependence of LaAlO 3 . The peak at < 40 K would then be due to 'domain' freezing of the tweed structure. The damping at low temperatures is below 5 10 −4 . It shows the excellent quality of the LaAlO 3 sample. No Snoek-type relaxations occur. Domain boundary movements may exist but their energy loss is equally extremely small.
The discovery of polarity by RPS was confirmed by PFM (Fig. 4). The pattern in Fig. 4b,c shows patches of polarity in the (100) plane. The diameters of these patches are around 5 μ m. They occur only in part of the sample where tweed was found by optical microscopy (Fig. 4a-c). An un-twinned region of the crystal without microscopically visible tweed showed only background PFM noise ( Fig. 4d-f), which corresponds to an effective piezoelectric coefficient of about 1 pm/V while the tweeded sample shows patches of higher and lower signals. The low signal is only 20-30% higher than the background noise while the corresponding effective piezoelectric coefficient in the high signal regions can be as high as (2.6+ /− 0.2) pm/V. The local piezoelectric coefficient is hence similar to quartz, in agreement with RPS results.
The tweed is observable by Raman spectroscopy using the spatial distribution of peak shifts in a sample with optically visible tweed 39,44 (Fig. 5). The lowest-lying E g soft mode showed a frequency shift of ca. 0.1 cm −1 . The peak shift of 0.1 cm −1 is correlated with the dominant structural change during the phase transition, namely    reflection mode and emphasize the surface effect. In contrast, the optical image in Fig. 1 was measured in transmission mode and superimposes tweed of several parts of the sample.

Discussion
Polar tweed is expected to require some additional structural instability which, at first glance, seem not to exist in LaAlO 3 20 . Nevertheless, some anomalies have been reported which may point to a 'hidden' instability. Let us start with the traditional interpretation of the Pm3 m/R3c phase transition in LaAlO 3 at T c = 813 K which is traditionally approximated by the rotation of centro-symmetric AlO 6 octahedra around of the pseudocubic [111] axes. The maximum rotation angle at absolute zero temperature is 5.6°3 9 . No evidence by x-ray or neutron diffraction was found previously that the R3c symmetry is lowered to a non-centrosymmetric space group. Nevertheless, several aspects of the phase transition are incompletely described by this octahedra-rotation model. The order parameter of the transition involves a large deformation of the AlO 6 octahedron and, possibly, additional deformations of the 12-fold coordinated La site. Only the full thermodynamic order parameter shows a second-order Landau transition near T c . According to Howard et al. 45 AlO 6 octahedra in LaAlO 3 suffer a slight compression between triangular faces aligned perpendicular to [111] of the cubic parent structure and a slight expansion in the plane perpendicular to this. The following observations indicate structural instabilities beyond the octahedral tilt model: (1) The rhombohedral spontaneous strain and the local rotation angle for LaAlO 3 do not extrapolate to the same transition temperature and show different temperature dependences. The spontaneous strain disappears at 830 K while the rotation angle shows additional anomalies near 730 K 39 . (2) The temperature evolutions of the two soft mode frequencies (A 1g and E g ) are not proportional to each other at T < 730 K, and the spontaneous strain is not proportional to the square of the AlO 6 rotation angle. These anomalies are formally consistent with biquadratic coupling between the primary order parameter of the transition 39 and a second, unknown process. From dielectric measurements, which indicate a smooth but rapid increase in conductivity in the temperature range 500-800 K, this second process may be related to hopping of intrinsic oxygen vacancies and possible local lattice distortions. Furthermore, twin domains are mobile above 730 K but are frozen below 730 K 46 , which may also be related to defects including oxygen vacancies. The measured specific heat anomaly peaks at 813 K 39 , which is below the extrapolated T c of the octahedral deformation at 830 K. (3) The decrease of c 44 under cooling below room temperature is not mirrored by an increase of the dielectric response, which excludes any mechanism involving an incipient ferroelectric transition 39,43 . In the equivalent situation of the incipient ferroelectric transition in KTaO 3 47 a steep increase of the dielectric susceptibility indicates the potential nucleation of a ferroelectric phase at low temperatures. Similarly results were found for SrTiO 3 48 . The elastic softening of LaAlO 3 cannot be related to such an incipient ferroelectric phase but to an incipient ferroelastic transition 43 . Its intrinsic lattice instability is unknown and may play a major role in the formation of the tweed pattern. A space group C2/m was discussed in 43 . (4) The order parameter saturation in the quantum regime 49 is different for the octahedral rotation and the octahedral deformation. The octahedral rotation saturates at 260 K while the octahedral distortion saturates at 150 K. The split of these two saturation temperatures is highly unusual in perovskite structures and suggests non-linear rotation-translation coupling. The low temperature structure is characterized by increasing octahedral distortions while their rotation angles remain almost constant under cooling. (5) Dipolar pattern formation was anticipated from dielectric resonator measurements of the loss tangent tanδ and relative permittivity ε r at low temperatures and 4-12 GHz 50 . A variety of single crystals grown by different techniques were investigated. The loss tangent tanδ is largely sample independent and shows a linear frequency dependence and monotonous temperature variation from 8 × 10 −6 at 300 K to 2.5 × 10 −6 at 150 K and 4.1 GHz at T > 150 K. The loss tangent below 150 K is characterised by a peak at ca. 70 K. The height of this peak is frequency and sample dependent. The peak was explained by defect dipole relaxations. The activation energy of the relaxation process is 31 meV. This low value was taken as evidence that the defect dipoles are associated with interstitials, possibly impurities in interstitial positions 50 . This model can be reconciled with our polar tweed patterns if local strain is sufficient to generate defects or correlate defects to follow the strain deformation. (6) The entropy of the Pm3 m-R3c phase transition is larger than normal for an octahedra-tilt transition. The 'a' coefficient of the Landau potential of the cubic ↔ tetragonal transition in SrTiO 3 is 0.65 J mol −1 51,52 giving a total excess entropy at order parameter Q = 1 of ~0.33 J mol −1 K −1 . For LaAlO 3 'a' is 3.9 J mol −1 K −1 and the equivalent total excess entropy is ~1.95 J mol −1 K −1 . This large value suggests some contribution from configurational effects such as the displacement of Al and La, which could lead to polarity of the AlO 6 and LaO 12 groups. (7) Sathe and Dubey 53 claim a weak additional peak in Raman spectra which displayed increasing intensity below ~240 K. They associated this peak with other weak anomalies at higher temperatures and considered the possibility that the local symmetry could be R3c or R3, again due to displacements of La and Al from their high symmetry positions in the R3c structure.
These seven arguments show that the structural state of LaAlO 3 below T c is not simply defined by the octahedral tilt and that other atomic movements exist. If these movements are strain related we would expect that the maximum strain contrast in the tweed is equivalent to ca. 1 K-temperature variation in the structural state in 39 . This strain contrast is 2.4 × 10 −6 for e 1 and 3 × 10 −6 for e 4 . The spatial gradient extends over some microns so that a simple flexoelectric effect may be too small to explain the observed polarity of the tweed pattern 54 . Structural instabilities related to the polar off-centering of Al and possibly La can explain the effect. A similar situation was found in tweeded BaTiO 3 where Ti at T ≫ T c is dynamically disordered over off-centered octahedral sites on fast time scales 55,56 .
We finally mention that polarity in thin films of LaAlO 3 have been reported in the pioneering paper by Sharma et al. 57 . These authors describe the switchable hysteretic electro-mechanical behaviour of crystalline epitaxial LaAlO 3 thin films associated with polarization induced by electrical and mechanical fields. They suggest that the ferroelectric-like response of the thin films is mediated by the field-induced ion migration in the bulk of the film, which could indeed also play a role in surface near regions in bulk samples.

Conclusion
We have proven that polar tweed structures exist. Similar observations in ferroelectric materials in their paraelectric phase may simply be related to some local short range order. However, as LaAlO 3 is not ferroelectric and has no incipient ferroelectric instability we have shown that polar tweed exist even in purely ferroelastic materials. This result may possibly be generalized: (almost) all ferroelastic perovskite materials may be polar in their tweed state. If this hypothesis is true, we may ask why has such polar tweed not been observed before? As we show in this paper, the amplitude of polarity is very small in LaAlO 3 and the effect may simply have been missed in other materials. Furthermore, not all perovskites form tweed easily and it may take a specific effort to generate tweed. Nevertheless, once the existence of polar tweed in non-polar LaAlO 3 is known, it may open avenues to the discovery of polar tweed structures in other materials.
Our findings may be important also for LaAlO 3 substrates. We cannot exclude that such substrates contain polar tweed in their surface layers when mechanically worked (e.g. by cutting). These substrates will then interact with deposited thin films not only by shear deformations but also by polar interactions which may dominate when the thin film is ferroelectric. In particular ultrathin ferroelectric films may reflect the polarity of the underlying substrate and show, equally, tweed like features.

Experimental Methods
Resonant Piezoelectric Spectroscopy, RPS, shows the polarity of the structures. 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, which is balanced across its corners or parallel faces between the ends of two piezoelectric transducers. The driving voltage leads to the excitation of local distortions that, when collective, lead to macroscopic resonant elastic waves. Great care is taken to disallow cross-talk between the applied field and the mechanical detectors. Additionally, each experiment was performed with uniform and tweed samples. The uniform samples never showed an RPS signal but all tweed samples did. The sample size for the final experiment was 5 × 5 × 1 mm. Any mechanical resonance is transmitted from the sample to the receiver transducer attached to the sample inside a He-cryostat, similar to Resonant Ultrasound Spectroscopy (RUS) [58][59][60] .
The difference between RPS and Resonant Ultrasonic Spectroscopy, RUS, relates to 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. Switching from RPS to RUS is achieved by applying the AC voltage across the emitter transducer rather than across the sample 24 .
AFM studies were performed using a commercial AFM XE-100, Park Systems working in contact mode. Piezo-response and vertical and lateral piezoresponse force microscopy (PFM) images were routinely obtained with an AC voltage of 5 Vrms at 22.5 kHz applied to a Pt coated silicon cantilever with a spring constant of 2.8 N/m (NSC14, μ Masch). Local piezoelectric coefficient has been estimated from the slope of the PFM signal versus the ac excitation signal and by comparing the slopes obtained using the same cantilever for the investigated LaAlO 3 samples, a PZT 20/80 epitaxial film and a x-cut quartz crystal.
Raman spectra were collected with a Renishaw in Via Reflex Raman Microscope using an excitation wavelength of 633 nm with a spectral cut-off at 10 cm −1 and a spectral resolution of 0.4 cm −1 . Measurements were performed in micro-Raman mode with an objective with numerical aperture 0.75 providing a theoretical laser spot size of 1 μ m. Mapping experiments were conducted with a step size of 0.8 μ m. The sample was in a thermally stable environment, the time for a complete measurement was 48 hours.