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Hyper-Raman and Raman scattering from the polar modes of PbMg1/3Nb2/3O3

This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 J. Phys.: Condens. Matter 26 015401 (http://iopscience.iop.org/0953-8984/26/1/015401) View the table of contents for this issue, or go to the journal homepage for more

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Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 26 (2014) 015401 (6pp)

doi:10.1088/0953-8984/26/1/015401

Hyper-Raman and Raman scattering from the polar modes of PbMg1/3Nb2/3O3 B Hehlen1 , A Amouri1,2 , A Al-Zein3 and H Khemakhem2 1

Laboratoire Charles Coulomb, UMR 5221, CNRS and Université Montpellier II, F-34095 Montpellier, France 2 Laboratoire de Physique Mathématiques et Applications—Unité des Matériaux Ferroélectriques, Faculté des Sciences de Sfax, BP 1171, 3000 Sfax, Tunisia 3 European Synchrotron Radiation Facility, BP 220, F-38043 Grenoble Cedex 9, France E-mail: [email protected], [email protected], [email protected] and [email protected] Received 30 September 2013, in final form 25 October 2013 Published 29 November 2013 Abstract

Microhyper-Raman spectroscopy of PbMg1/3 Nb2/3 O3 (PMN) single crystal is performed at room temperature. The use of an optical microscope working in backscattering geometry significantly reduces the LO signal, highlighting thereby the weak contributions underneath. We clearly identify the highest frequency transverse optic mode (TO3) in addition to the previously observed soft TO-doublet at low frequency and TO2 at intermediate frequency. TO3 exhibits strong inhomogeneous broadening but perfectly fulfils the hyper-Raman cubic selection rules. The analysis shows that hyper-Raman spectroscopy is sensitive to all the ¯ symmetry group of PMN, the three polar F1u - and the vibrations of the average cubic Pm3m silent F2u -symmetry modes. All these vibrations can be identified in the Raman spectra alongside other vibrational bands likely arising from symmetry breaking in polar nanoregions. (Some figures may appear in colour only in the online journal)

1. Introduction

index [7], the thermal strain [8] and the dielectric constant [9, 10], as well as the observation of a peak in the acoustic emission [11], defines the Burns temperature Td (∼620 K in PMN) where the nanopolar regions start to grow. It also corresponds to the temperature range at which the vibrational character of the soft mode (underdamped regime) at high temperature transforms into a relaxational one (overdamped regime) at low temperature, thereby defining the relaxor’s state from the point of view of the vibrations [5]. Despite multiple inelastic investigations the vibrational properties of PMN are not yet well understood, even at the stage of mode assignment. For example, the Raman spectrum of PMN is very rich, although first order scattering from the triply degenerated 3F1u + 1F2u symmetry vibrations expected ¯ in the Pm3m-symmetry group is forbidden. The scattering could eventually originate from second or higher order scattering processes, as for many ferroelectric compounds. However, it is also very likely that for such strongly disordered local structures, momentum conservation does not apply anymore. Hence, the Raman spectra could also contain a

Lead based mixed perovskite systems are well known for their relaxor ferroelectric properties characterized by a broad and frequency-dependent dielectric maximum in their dielectric response [1]. Within this family, lead magnesium niobate, PbMg1/3 Nb2/3 O3 (PMN), has been extensively investigated because of its high dielectric permittivity, piezoelectric coefficients, and large electro-optic response suitable for technological applications [2]. It exhibits a cubic average ¯ structure of symmetry Pm3m, but the random distribution of the cations Mg2+ and Nb5+ occupying the B site and the off-centering of the A and B cations give rise to polar nanoregions (PNRs), lowering the symmetry at the local scale. In addition, the absence of charge compensation between Mg2+ and Nb5+ leads to the appearance of very strong local electric fields which probably prevent a long range order [3]. Deviation from the average symmetry is already observed at high temperature where several modes are split [4–6]. On cooling, the deviation from linear behavior of the refractive 0953-8984/14/015401+06$33.00

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J. Phys.: Condens. Matter 26 (2014) 015401

B Hehlen et al

collection of local or quasi-local excitations whose activity is weighted by specific coupling-to-light coefficients eventually related to the symmetry of the local structures, similarly to the case of structural glasses [12, 13]. Recently, the TO and LO components of the three F1u -symmetry modes have been derived from the infrared (IR) reflectivity spectra of PMN, within a model assuming an anisotropy of the dielectric constant [14]. The results for the LO components nicely match hyper-Raman data obtained soon after [15]. The latter spectroscopy then appeared to provide a powerful tool for mode assignment in relaxors. Since then, hyper-Raman scattering (HRS) has been performed in great detail in PMN and PMT, another cubic relaxor, allowing a clear observation of the three F1u (LO) [16] and the F2u -silent non-polar [17] vibrations. Due to the very good resolution and contrast of hyper-Raman as compared to neutron scattering, it was also possible to follow the temperature dependence of the primary soft mode of PMN [5] and to unambiguously confirm its doublet structure, a situation promoted long ago by Vakhrushev and co-workers [18]. In this paper, HRS is performed under an optical microscope (micro HRS or µHRS) in three different samples and for a large set of scattering geometries. The use of a microscope strongly reduces the LO signal, therefore revealing the weak contributions. These include the two high frequency TO modes but also additional excitations ¯ group. The HRS that cannot be accounted for in the Pm3m results are compared to Raman data providing a more accurate picture of the vibrations in PMN.

grating diffractometer. The vibrational spectra at frequencies close to the second harmonic signal (532 nm) are obtained either by a 600 groove mm−1 or by an 1800 groove mm−1 grating, defining a high luminosity (low resolution) and high resolution operation mode, respectively. Polarization analysis of the scattered light is carried out using a broadband half-wave plate followed by a Glan–Thomson polarizer. The setup ensures polarization measurement with more than few per cent precision over the whole frequency range explored. We used the same commercially available PMN single crystals as in [17], grown at the Shanghai Institute of Ceramics. Three platelets of thickness ∼1 mm were used, with crystallographic orientation (001), (110), and (111) normal to the surface and therefore parallel to the scattering wavevector q. Twelve spectra were collected under different scattering geometries. Special attention was given to the measurement of relative intensities. The spectra are labeled using the usual Porto notation a(bc)d, where a and d stand for the directions of the incident and scattered photons, and b and c for their polarization directions. The crystalline axes are denoted as ¯ follows: x k [100], y k [010], z k [001], x0 k [110], y0 k [110], ¯ and z00 k [111]. According to [21] the hyper-Raman x00 k [112], intensity is related to the scattering geometry by X δ L L 2 IHRS ∝ R2 = |eSi βijk ej ek | , (1) δ

where eL and eS are the polarization vectors of the incident (laser) and scattered photon, δ = x, y, or z distinguishes independent eigenvectors in the case of degenerated modes, δ stands for the element of the HRS tensor of third and βijk rank β associated to a given phonon. In the usual case of an incident field of energy far from the electronic transitions, β is fully symmetric in i, j, k, and the only non-vanishing elements x = a (diagonal for the polar F1u -symmetry modes become β111 x x element) and β122 = β133 = b (off-diagonal element) for the y y y mode polarized along [100], β222 = a and β211 = β233 = z b for the mode polarized along [010], and β333 = a and z z β311 = β322 = b for the mode polarized along [001]. The HRS tensor symmetry is the same for TO and LO modes, but the values of the tensor elements (a, b) are different owing to a usually strong electro-optic contribution in the case of LO excitations. Using equation (1), it is possible to calculate the HRS efficiency for every scattering geometry. For simplification the intensity factors R2 will be given as a function of η = a/b, the ratio between the diagonal and off-diagonal components, and in units of b2 /12 [17].

2. Experimental details

Hyper-Raman scattering is a three photon process where two incident photons of frequency ωI scatter one photon at frequency ωS after interaction with an excitation in the medium (ω) [19]. The energy conservation is written as ωS = 2ωI ± ω. The purely elastic part at ω = 0 defines the hyper-Rayleigh signal or the generation of a second harmonic (in fact the so-called ‘second harmonic generation’ corresponds in general to a measure in the forward direction of the integrated intensity close to 2ωI ). One main interest of HRS is its selection rules which are different from those of Raman scattering and infrared absorption. For example, all polar modes are active in HRS whatever the crystalline symmetry. In the case of PMN, this ensures first order scattering from the three F1u modes but also from the F2u ¯ cubic group. silent vibration, active in HRS in the Pm3m Hyper-Raman scattering is excited by a pulsed YAG laser emitting at λ = 1064 nm, with ∼30 ns pulse width and a repetition rate of typically 5 kHz. Experiments have been performed at room temperature with an incident peak power of about 2 kW, slightly below the damage threshold of the sample. An optical microscope is used for both focusing the incident beam and collecting the backscattered photons [20]. Two objectives are used, a ×20 and a ×50, providing scattering volumes of ∼15 µm and a few microns at the beam waist, respectively. After passing through a confocal device, the scattered light is imaged into the entrance slit of a single

3. Results and discussion 3.1. Main LO modes

Experiments were first performed with the ×20 objective in the (001) sample without polarization analysis. The spectra displayed in figure 1(a) have been taken at different depths in the sample. They are normalized on top of the non-polar F2u -mode contributing at 247 cm−1 , whose intensity is constant whatever the position of the scattering volume inside the sample. Although forbidden by symmetry, the LO modes 2


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dominate the HRS spectra. Their activity arises from a forward scattering process induced by the reflection of the incident beam on the back face of the sample [16]. This contribution strongly decreases when focusing closer to the front face owing to the divergence of the incident radiation (figure 1(a)). This is also the reason why working under an optical microscope reduces this parasitic signal much more efficiently than by performing HRS in macro-mode. Forward scattering by LO modes should be even weaker when using an objective of shorter focal length. A spectrum obtained at 190 µm depth from the front face with the ×50 objective is compared to one obtained at the same depth using the ×20 objective (figure 1(a)). The spectra overlap, except for LO3 around 700 cm−1 whose intensity continues to decrease when focusing more tightly. Despite being weak, LO1 and LO2 are still active while forbidden by symmetry for this scattering geometry. The fact that their spectral responses overlap with the two objectives shows that the activity does not originate from the wide angular aperture of the collected light. This residual contribution is therefore intrinsic, as probably is the very weak LO3 observed with the ×50 objective. As LO modes couple to the macroscopic electric field through the electro-optic contribution, the lifting of the HRS selection rules could eventually originate from the strong random field arising from the charge disorder [3] and/or from the random orientation of the polar nanoregions. Since the activity of LO modes depends on the focusing depth only, it is possible to reconstruct the HRS LO spectra of the three main LO bands. This is done in figure 1(b) where a spectrum obtained by focusing close to the front face (weak LOs) is subtracted from one obtained by focusing deep inside the sample (strong LOs). The recording time has been optimized to improve the statistics. In this view, the contribution of the main LOs is highlighted, preventing us from observing additional weak underlying contributions. The result emphasizes the asymmetry of LO1, the splitting of LO2, and the quasi-Lorentzian shape of LO3. It also ¯ shows that the three LO components of the Pm3m-symmetry structure largely dominate the LO spectra over possible other LO modes arising, for example, from vibrations in the polar nanoregions.

Figure 1. (a) µHRS spectra obtained with q k [001], without

polarization analysis, and collected using the ×20 objective focusing at different depths in the sample (190–700 µm away from the front face). The spectra are normalized on top of the F2u mode at 247 cm−1 . The dashed spectrum is obtained at 190 µm with the ×50 objective. The inset shows the integrated intensity of the peak at 490 cm−1 , marked by an arrow: ×20 objective (•) and ×50 objective (◦) results. (b) HRS spectra of the main LO modes of PMN.

vibration in pure (x = 1) PbTiO3 [16]. In PbTiO3 , the latter arises from a degeneracy of an F1u cubic vibration into E + A1 components in the P4mm (C4v ) tetragonal (polar) phase. The above considerations therefore suggest that whatever the degeneracy channel, either from F2g to E or from F1u to E, the mode at 490 cm−1 is likely polar and originates from a lifting of degeneracy in polar nanoregions. The polar character is further confirmed by the dependence of its area on the focusing depth which varies by a factor of ∼2.5 when going from the front to the back face, as shown in the inset of figure 1. The effect is significant but much less than for the main LOs, whose intensities decrease by a factor of 6–7 for the same depth range. Owing to the very local origin of the 490 cm−1 vibration one also expects a very weak polar character of the mode and accordingly a very weak TO–LO splitting. It is therefore likely that both TO and LO components contribute to the signal at 490 cm−1 . The broad feature around 580 cm−1 is at the same frequency as TO3 extracted from IR reflectivity [14] and we therefore assign it to the third TO mode of the average cubic structure of PMN. It was embedded underneath the strong LO3 in macro HRS but appears clearly in µHRS, allowing an accurate selection rule analysis. Figure 2 displays a series of spectra obtained with different scattering geometries and different values of R2 . The data have been subtracted by a sloping background locally accounting for the broad

3.2. F1u (TO3) vibration

One advantage of lowering the LO intensity by working under a microscope is to reveal the weak underlying features. For example, one observes in figure 1 a mode at 490 cm−1 and a broad and asymmetric feature centered near 580 cm−1 . The weak HRS response at 490 cm−1 (marked by an arrow in figure 1(a)) deserves attention as it also appears in the Raman spectra and it is subject to different interpretations. It could be one of the two F2g -symmetry modes of the ¯ Fm3m-symmetry group, as already proposed for PMN and related materials [22]. These modes are normally inactive in HRS but transform into E + A polar vibrations (HRS active) in polar clusters. Interestingly, the band becomes prominent in the (1−x)PMN–xPbTiO3 system for the highest x values [23], and occurs at the same frequency as the harder E-symmetry 3


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Figure 2. HRS spectra for TO3 for different scattering geometries.

Spectra with the same HRS efficiency overlap, defining four groups labeled from 1 to 4. For clarity, groups 2–4 have been translated vertically by 7, 12 and 10, respectively.

Figure 3. Fit of TO3 and surrounding modes for three spectra taken

quasi-elastic contribution in the HRS spectra. The intensities are in relative units and for clarity the three upper groups of spectra have been translated vertically. Looking at table I of [17], one clearly observes that spectra of identical values of R2 overlap. This is the case for the two spectra of group 1 corresponding to the z00 (y0 x00 )z¯00 and z00 (x00 y0 )z¯00 scattering geometries where TO3 is almost inactive. It is also valid for the three spectra of group 2 with the scattering geometries z(xy)¯z, x0 (zy0 )x¯0 and x0 (y0 z)x¯0 , as well as for the two spectra of group 4 corresponding to z(xx)¯z and x0 (zz)x¯0 . This result strongly supports an assignment of this feature as the F1u -symmetry TO3-mode. To go further we fitted TO3 and its surrounding spectral responses. The results are shown in figure 3 for a given spectrum of the group 2–4 in figure 2. Two Gaussian functions were used to account for the bimodal structure of TO3. An iterative fitting procedure was carried out, in order to finally constrain all the fitting parameters of TO3 except one single intensity factor. We find the peak maxima at frequencies 579 cm−1 and 636.5 cm−1 , and half widths at half maximum of 50 cm−1 and 23.5 cm−1 , respectively. The fitting agreement in figure 3 remains very good for the three spectra, revealing that the shape of TO3 is identical whatever the scattering geometry. In addition, its LO companion (LO3) at 716 cm−1 is well reproduced by one single spectral response with quasi-Lorentzian shape. It is worth noting that the highest ¯ symmetry frequency F1u (TO3–LO3) vibration in the Pm3m group only involves motions of the oxygen atoms, as for the F2u silent mode at 247 cm−1 . Similarly to TO3, the spectral shape of F2u is asymmetric and evolves as a single entity with scattering geometry and also with temperature [17]. Therefore, the broadening is inhomogeneous in both cases and likely accounts for a random disorder on the oxygen site rather than a splitting of the modes due to local symmetry breaking. This contrasts with the behavior of the soft F1u (TO1) mode

at low temperature since the latter exhibits a double peak structure, each peak having very different HRS selection rules and temperature dependences [5]. The soft mode involves motions of A and B atoms in addition to the oxygen ones. The vibrational observations confirm that it is the anisotropic ¯ cubic off-centering of the A and/or B atoms from the Pm3m symmetry which gives rise to a local structure different from the average one, and suggest that the isotropic (random) disorder of the oxygen sites plays a less significant role in the structural properties of the PNRs. Normalization of the F1u (TO3) intensity factor to 12 for the z(xy)¯z spectrum leads to values of 43.9 ± 4 and 95.8 ± 8 for the z(x0 y0 )¯z and x0 (zz)x¯0 spectra, respectively. These numbers are in very good agreement with the HRS efficiencies 2 ¯ group, R2 predicted in the Pm3m z(xy)¯z = 12, Rz(x0 y0 )¯z = 3(1 − 2 2 2 η) , R 0 ¯0 = 12η , with the value of η = a/b = −2.8 ± 0.2. x (zz)x This number also accounts for the almost null TO3 activity of the two spectra of group 1 in figure 3 corresponding to R2 = 3(1 + η/3)2 , demonstrating thereby that TO3 at 580 cm−1 ¯ perfectly fulfils the Pm3m-symmetry selection rules. Finally, it seems that the bands at 490 and 580 cm−1 merge into one broad component at high temperature [23], suggesting that they could be two components of the same parent vibrational response. Accordingly, the former could correspond to a partial degeneracy of the latter in the polar nanoregions.

from groups 2–4 of figure 2. The dashed line shows the contribution of the asymmetric TO3 band.

3.3. Comparison to Raman

¯ group, none of the three F1u or the silent Within the Pm3m F2u vibrations should be active in Raman, but despite this one observes a large number of vibrational bands [24, 23]. ¯ They originate either from a lifting of the cubic (Pm3m) selection rules due to local disorder, from local modes 4


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nanoregions. The mode at 340 cm−1 (B–B) also originates from a local order, and corresponds mostly to the antiparallel vibrations of neighboring B-site cations [26]. It is polar and IR-active [14], but apparently very weak in Raman. The region 200–300 cm−1 is more complex. It is composed of three hyper-Raman bands at 217, 247, and 270 cm−1 . These three bands are well isolated in the spectra obtained with scattering geometries x0 (y0 z)x¯0 (dashed line), z00 (x00 y0 )z¯00 (full line), and z(xx)¯z (dotted line) shown in the inset of figure 4. The present µHRS spectroscopy confirms the previous conclusions of [17] that the first two fully satisfy ¯ the hyper-Raman cubic (Pm3m) selection rules for F1u and F2u vibrations, respectively. The origin of the third vibrational response at 270 cm−1 is still unclear, hence its labeling ‘U’ as ‘unknown’. These three modes mix in the Raman spectra to form the broad feature centered around 250 cm−1 . It seems that the three modes participate in the polarized Raman spectra while the U-mode dominates the depolarized spectra with, however, a shoulder likely associated with TO2 on its low frequency side. The present HRS data enabled us to refine the value of η found in [17] for F1u (TO2) at 217 cm−1 . We find η ∼ 1/2 which can be obtained, for example, from the spectra z00 (x00 x00 )z¯00 and z(xy)¯z for which R2 = 27(1 + η/3)2 and 12, respectively. Below 100 cm−1 , the soft mode doublet F1u (TO1), whose lowest component is highly overdamped at room temperature (not shown), complements the set of ¯ vibrations expected in the Pm3m-symmetry group [5]. Finally, it is worth noting that second or higher order scattering processes contribute very weakly in hyper-Raman, and to the best of our knowledge they have never been observed experimentally. The HRS activity of the vibrations marked by a full circle in figure 4 cannot be accounted for ¯ by the Pm3m-symmetry group and all are therefore likely associated with a local symmetry breaking in PNRs. The correspondence between hyper-Raman and Raman spectral responses shows that the latter originate from first order scattering processes and that higher order processes can be neglected. Interestingly, signatures from local excitations (•) dominate the depolarized (VH) Raman spectra.

Figure 4. VV (full line) and VH (dashed line) hyper-Raman

backscattering spectra of PMN with q k (001) and their corresponding Raman spectra. The inset shows HRS spectra obtained with different scattering geometries, emphasizing the presence of three modes in the region 200–300 cm−1 . The circles show the HRS modes whose selection rules cannot be accounted for ¯ in the Pm3m-symmetry group.

vibrating in a crystalline symmetry different from the average one, or from second or higher order Raman scattering processes. Figure 4 compares the polarized and depolarized hyper-Raman and Raman spectra obtained in the (001)-platelet (q k [001]). Despite different spectral shapes, one observes strong similarities in the positions of several peaks. It could eventually be argued that part of the HRS spectrum arises from a Raman scattering process arising from the second harmonic signal generated by the sample at the focus of the incident beam, similarly to what was observed in PZT [25]. However, the second harmonic signal is orders of magnitude less in PMN than in PZT. A calibration of the Raman and hyper-Raman relative intensities reveals that in our PMN samples, such a contamination should not exceed 0.2 cts/mn, which implies that it is negligible in the HRS spectra. This is further supported by the fact that the activity of most of the HRS modes is strongly scattering-geometry dependent, and by the behavior of TO2 and TO3 which perfectly fulfils the HRS selection rules. LO1 and LO2 are weak but visible in Raman, while LO3 is hidden underneath the strong Raman band near 780 cm−1 . The HRS response of F1u (TO3) around 580 cm−1 very nicely mimics the Raman feature appearing at about the same frequency. Despite slightly different spectral shapes in the two spectroscopies it is very tempting to associate this Raman band to TO3. Its scattering could easily be ¯ activated in Raman owing to the lifting of the Pm3m selection rules by local distortions. Following the discussion above, the peak around 490 cm−1 could be associated with a partial degeneracy of F1u (TO3) vibrations in the polar

4. Conclusions

HRS spectroscopy under an optical microscope provides several advantages for the investigation of the vibrations in relaxors as compared to macro HRS. The operational mode is much easier than in the macro-mode and the setup allows one to accurately define the focus in the lateral position and the depth into the sample down to micrometric sizes. The insertion of a confocal device with adjustable pinholes helps to reduce the background signal arising from any parasitic scattering outside the scattering volume, such as that from the front and back faces. Last but not least, in the case of relaxors it limits the scattering from an unexpected but very efficient forward scattering process of LO modes. This greatly improves the contrast for observing weak underlying features, such as TO modes, but also excitations not expected in the average cubic symmetry. 5


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In this work we clearly identified TO3 at ∼580 cm−1 as well as a signature of its partial degeneracy in nanopolar regions around 490 cm−1 . The spectroscopy shows that the ¯ selection rules, and suggests former perfectly fulfils the Pm3m that its asymmetric and bimodal shape originates from an inhomogeneous broadening rather than from a splitting of the mode due to a local symmetry breaking. As TO3 involves only oxygen atoms we conclude that the latter are randomly positioned out of their equilibrium position in the cubic cell but do not play a central role in the definition of the local structure of PMN. It was not possible to fully remove the signal from the main LOs, emphasizing an intrinsic scattering process likely arising from a lifting of the HRS selection rules due to the strong random field characteristics of the relaxor’s state [3]. Finally, the comparison between hyper-Raman and Raman provides a clear assignment of the three F1u (TO–LO)-modes and of the F2u ‘silent’ vibration in the latter spectroscopy. It is worth noting that almost all the hyper-Raman spectral responses above 100 cm−1 are reproduced in the Raman spectra. The analysis allows separation between local modes in polar nanoregions and those expected in the average cubic medium. Regarding the cubic 3F1u + F2u excitations, they are observed in HRS via a first order scattering process, while the origin of their Raman activity is more complex. This is the reason why a selection ¯ rule analysis in the Pm3m-symmetry group works in the first case and not in the second.

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