Lattice dynamics reveals a local symmetry breaking in the emergent dipole phase of PbTe

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Lattice dynamics reveals a local symmetry breaking in the emergent dipole phase of PbTe

Kirsten M. Ø. Jensen, Emil S. Božin, Christos D. Malliakas, Matthew B. Stone, Mark D. Lumsden, Mercouri G. Kanatzidis, Stephen M. Shapiro, and Simon J. L. Billinge

Phys. Rev. B 86, 085313 – Published 20 August 2012

Abstract

Local symmetry breaking in complex materials is emerging as an important contributor to materials properties but is inherently difficult to study. Here we follow up an earlier structural observation of such a local symmetry broken phase in the technologically important compound PbTe with a study of the lattice dynamics using inelastic neutron scattering (INS). We show that the lattice dynamics are responsive to the local symmetry broken phase, giving key insights in the behavior of PbTe, but also revealing INS as a powerful tool for studying local structure. The new result is the observation of the unexpected appearance upon warming of a new zone center phonon branch in PbTe. In a harmonic solid the number of phonon branches is strictly determined by the contents and symmetry of the unit cell. The appearance of the new mode indicates a crossover to a dynamic lower symmetry structure with increasing temperature. No structural transition is seen crystallographically, but the appearance of the new mode in inelastic neutron scattering coincides with the observation of local Pb off-centering dipoles observed in the local structure. The observation resembles relaxor ferroelectricity, but since there are no inhomogeneous dopants in pure PbTe this anomalous behavior is an intrinsic response of the system. We call such an appearance of dipoles out of a nondipolar ground-state “emphanisis” meaning the appearance out of nothing. It cannot be explained within the framework of conventional phase transition theories such as soft-mode theory and challenges our basic understanding of the physics of materials.

Received 14 May 2012

DOI:https://doi.org/10.1103/PhysRevB.86.085313

Authors & Affiliations

Kirsten M. Ø. Jensen¹, Emil S. Božin², Christos D. Malliakas³, Matthew B. Stone⁴, Mark D. Lumsden⁴, Mercouri G. Kanatzidis^3,5, Stephen M. Shapiro², and Simon J. L. Billinge^2,6

¹Center for Materials Crystallography, Department of Chemistry and iNano, Aarhus University, Denmark
²Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA
³Department of Chemistry, Northwestern University, Evanston, Illinois 60208, USA
⁴Quantum Condensed Matter Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
⁵Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
⁶Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027, USA

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Vol. 86, Iss. 8 — 15 August 2012

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Images

Figure 1
INS spectra of a PbTe single crystal at 288 K at different $\vec{Q}$ points in reciprocal space: (a) (0 3 3) zone edge, (b) (2.5 2.5 2.5) zone edge, and (c) (1 3 3) zone center. The red dashed lines indicate the phonon energies measured by Cochran et al. (Ref. 3) for comparison. The inset in (c) is a schematic of the plane of reciprocal space that the triple axis spectrometer was set to work in. The grey dots are the reciprocal lattice points, and the lines are Brillouin zone boundaries. The red, pink, and blue dots are the $\vec{Q}$ points for the data shown in (a) ( $K$ point), (b) ( $L$ point), and (c) ( $Γ$ point), respectively. (d)–(f) show false color plots of the intensity (color axis) vs energy transfer, $Δ E = ℏ ω$ , and temperature of the same modes shown in the panels above. (g)–(i) show representative fits of Lorentzian peaks (in red) to the TO mode at the [133] zone center spectra: (g) 2 K, (h) 134 K, and (i) 231 K. The vertical dashed lines are the extracted mode energies $ω$ . (j) $ω^{2}$ vs $T$ for all the temperatures fit in the temperature range below 300 K with a straight line fit to the data shown in red.Reuse & Permissions
Figure 2
Plots of the INS spectrum at $\vec{Q} = (133)$ . From the bottom (pale blue) the temperatures shown are 28, 99, 203, 299, 410, 486, and 601 K (topmost curve). Datasets are offset with respect to each other by 75 intensity units for clarity. The two arrows are guides to the eye, indicating the positions of the TO and the new mode at the highest temperature. Both modes soften upon cooling.Reuse & Permissions
Figure 3
(a)–(f) Dynamic susceptibility obtained from the measured INS spectra (symbols) at representative temperatures with fits to the data shown as a pink line. There are two damped harmonic oscillator components, one for the TO mode (red) and one for the new mode (green). A Gaussian function was added to fit the intensity from the tail of the Bragg peak (orange). The horizontal blue line is a constant background component. (a) 2 K, (b) 98 K, (c) 203 K, (d) 299 K, (e) 482 K, and (f) 601 K. (g) shows the temperature dependence of the integrated weight in the new mode from the fits (black symbols). The inset shows the Pb off-centering displacement measured from the PDF measurement on PbTe reported in Ref. 1.Reuse & Permissions
Figure 4
Neutron scattering intensity vs energy transfer from single crystal PbTe measured on the ARCS spectrometer. Curves in each panel are cuts along $[h 11]$ for 5 (zone center) $< h < 5.2$ showing the dispersion of the modes. (a) 100 K, (b) 200 K, (c) 300 K, (d) 400 K, (e) 500 K, and (f) 600 K. At high temperature the intensity is almost exclusively coming from the new mode which is seen clearly dispersing to higher energy with increasing $h$ .Reuse & Permissions
Figure 5
Elastic diffuse scattering around the [h00],[0kk] plane of reciprocal space measured using the Triple axis spectrometer: (a) 16 K, (b) 482 K, (c) difference between the scans in (b) and (a): $I (482) - I (16)$ . (d) and (e). As (a) and (b) but the intensities have been corrected to account for the change in phonon occupation of the acoustic modes that are within the energy resolution of the measurement.(f) The difference between the scans in (e) and (d).Reuse & Permissions

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