Technical CommentsAPPLIED SCIENCES AND ENGINEERING

Comment on “Giant electromechanical coupling of relaxor ferroelectrics controlled by polar nanoregion vibrations”

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Science Advances  22 Mar 2019:
Vol. 5, no. 3, eaar5066
DOI: 10.1126/sciadv.aar5066

Abstract

Manley et al. (Science Advances, 16 September 2016, p. e1501814) report the splitting of a transverse acoustic phonon branch below TC in the relaxor ferroelectric Pb[(Mg1/3Nb2/3)1−xTix]O3 with x = 0.30 using neutron scattering methods. Manley et al. argue that this splitting occurs because these phonons hybridize with local, harmonic lattice vibrations associated with polar nanoregions. We show that splitting is absent when the measurement is made using a different neutron wavelength, and we suggest an alternative interpretation.

Manley et al. (1) report neutron time-of-flight scattering measurements of the low-frequency lattice dynamics in the relaxor ferroelectric Pb[(Mg1/3Nb2/3)1−xTix]O3 (PMN-xPT) with Ti content x = 0.30. Above the Curie temperature TC (~405 K), their data are consistent with a single transverse acoustic (TA) phonon branch measured at wave vectors Q = (2 + H, H − 2, 0) for 0.0 rlu (reciprocal lattice units) < H < 0.4 rlu. Below TC, they observed a narrow dip in intensity located near the peak of the TA phonon line shape for H = 0.25 rlu. This was interpreted as evidence that the TA phonon branch had split into two branches that exhibit anticrossing behavior.

We measured the neutron inelastic scattering from a 10-cm3 single crystal of PMN-xPT with nominally identical composition (x = 0.29) below TC for H = 0.25 rlu, i.e., at a constant wave vector Q = (2.25, −1.75, 0). These data were obtained using the National Institute of Standards and Technology (NIST) BT7 triple-axis spectrometer, which selects the incident and final neutron energies via Bragg diffraction rather than time of flight, but instead of collecting data with a fixed incident neutron energy of Ei = 25 meV as performed in (1), we used a commonly used fixed final neutron energy Ef = 14.7 meV. Our data, as shown in Fig. 1 (top), show no evidence of this splitting. A least-squares fit to a single damped harmonic oscillator describes the TA phonon extremely well.

Fig. 1 TA mode in (22¯0) Brillouin zone.

(Top) Energy scan at Q = (2.25, −1.75, 0) showing an unsplit TA phonon line shape in PMN-xPT with x = 0.29. The solid line is a fit to a single damped harmonic oscillator. Data were measured with Ef = 14.7 meV. Errors bars represent ±√N, where N is the total number of counts. (Bottom) Energy scans from Manley et al. (1) for Q = (2 + H, H − 2, 0) using Ei = 25 meV. The ghoston energy is indicated by a red arrow for each value of H.

This result raises the question of why the TA phonon splitting is seen in the configuration used by Manley et al. (1) (Ei = 25 meV) but not in the one used by us (Ef = 14.7 meV). We can explain why quantitatively via a double scattering process involving a phonon and a Bragg peak. Spurions generated in this manner were termed “ghostons” by Rønnow et al. (2) and used successfully to explain unexpected features observed in the neutron inelastic scattering from CuGeO3. In Fig. 1 (bottom), we have replotted data published by Manley et al. (1) using the same energy scale to facilitate comparison between our datasets. Note that our data are plotted on a linear intensity scale, whereas those of Manley et al. (1) are plotted on a log scale. We calculated ghoston energies for the case when Ei = 25 meV using only the measured cubic lattice constant of 4.02 Å. The energies of three ghostons (red arrow) coincide precisely with the anomalous intensity dip seen in the data for H = 0.25 rlu (purple open circles), and each follows the dip to higher energy as H decreases. These are generated via scattering from phonons located at Q − τ = (0.25, −1.75, −2), (0.25, −1.75, 2), and (−1.75, −1.75, 0), respectively, followed by Bragg scattering from the reciprocal lattice vectors τ = (2, 0, 2), (2, 0, −2), and (4, 0, 0). Only the first two ghostons will contribute substantially because the last involves a longitudinal acoustic phonon at much higher energy. Ghostons can add or subtract intensity from a given location in reciprocal space; the magnitude and sign of the excess intensity depends on the sample and scattering geometries (3). In this case, the “Bragg-last” ghostons reduce the intensity at this energy, thereby producing a dip in the TA phonon line shape. It is important to note that this dip is less apparent below and above H = 0.25 rlu. Our model captures this behavior because these ghostons and the TA phonon disperse in opposite directions. That is, the TA phonon splitting seems weaker (or absent) at lower/higher H because the ghostons overlap less with the TA phonon.

The following three questions remain: (i) Why does this feature vanish above TC? (ii) Why is it observed in the (11¯0) Brillouin zone? (iii) Why is it affected by an external electric field? The answers are (i) primary extinction (4), (ii) ghostons exist in all zones (2), and (iii) electric fields strongly affect PMN-xPT Bragg intensities (5). In the cubic perovskite structure, Bragg reflections having all even Miller indices (hkl) have the largest structure factor. Therefore, they (and all related ghostons) suffer the greatest extinction on heating above TC (4). This effect is large: The (200) Bragg intensity in our crystal decreases by a factor of six between 300 and 500 K. In the (11¯0) zone, several ghostons have energies close to those in the (22¯0) zone for Ei = 25 meV, including the Bragg-first ghostons generated by τ = (1, 3, ±1). Moreover, as shown in Fig. 2, we observed no TA splitting at Q = (1.25, 0.75, 0), when Ef = 13.7 meV (another common configuration). Thus, the splitting in this zone is also wavelength dependent. Last, applied electric fields are known to affect Bragg intensities (5); for this reason, they necessarily affect any associated ghoston intensities.

Fig. 2 TA mode in (110) Brillouin zone.

Energy scan at Q = (1.25, 0.75, 0) in PMN-xPT with x = 0.29. The solid line is a fit to a single damped harmonic oscillator line shape. These data were measured on the NIST BT4 triple-axis spectrometer with Ef = 13.7 meV. Errors bars represent ±√N, where N is the total number of counts.

Elastic-inelastic double scattering processes are generally extremely weak, but Rønnow et al. (2) note that even 1-cm3 crystals can produce ghostons. As the PMN-xPT crystal used by Manley et al. (1) has a volume of order of 20 cm3, these effects should be expected. Scattering studies of large single crystals of relaxors are particularly problematic: The unusually broad phonon energy widths greatly enhance the chances of observing ghostons because the strict constraint imposed by energy conservation is much easier to satisfy (6).

We have shown that the purported TA phonon splitting depends on the choice of neutron energy. We can account for this anomaly quantitatively using an inelastic double-scattering model. Thus, we believe that the TA phonon splitting reported by Manley et al. (1) is spurious.

MATERIALS AND METHODS

We studied an 80-g single crystal of PMN-xPT with nominal Ti content x = 0.29. The crystal was cut with {100} faces and dimensions of 17.8 mm by 23 mm by 24.3 mm. The crystal was loaded into an aluminum sample can in the (HK0) scattering plane with [100] parallel to the 17.8-mm dimension and mounted inside a closed-cycle 4He refrigerator. Data on the NIST BT7 triple-axis spectrometer were measured at constant wave vector Q by varying the incident neutron energy while holding the final neutron energy Ef fixed at 14.7 meV. Horizontal beam collimations of 120′-80′-80′-120′ were used. A neutron velocity selector located before the monochromator eliminated higher-order neutrons from the incident beam; a highly oriented pyrolytic graphite filter was placed in the scattered beam. Similar measurements were carried out on the NIST BT4 triple-axis spectrometer using a fixed final neutron energy of 13.7 meV and no velocity selector. We calibrated the BT7 and BT4 wavelengths and scattering angles using an alumina standard and aligned the analyzers using vanadium, which is an incoherent scatterer.

This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial license, which permits use, distribution, and reproduction in any medium, so long as the resultant use is not for commercial advantage and provided the original work is properly cited.

REFERENCES AND NOTES

Acknowledgments: P.M.G. acknowledges useful communications with Michael E. Manley. Funding: The authors acknowledge that they received no funding in support of this work. Author contributions: P.M.G. conceived experiments. P.M.G., C.S., and G.X. performed neutron scattering measurements on BT4. P.M.G., Z.X., and D.P. performed those on BT7. P.M.G. analyzed all scattering data. P.M.G., L.H., and C.A.G. performed ghoston model calculations. X.L. and H.L. grew the single crystals. P.M.G. wrote the manuscript with input from all authors. Competing interests: The authors declare that they have no competing interests. Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper. Additional data related to this Technical Comment may be requested from the corresponding author.
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