Second-harmonic phonon spectroscopy of $\ensuremath{\alpha}$-quartz

Second-harmonic phonon spectroscopy of $α$ -quartz

Christopher J. Winta, Sandy Gewinner, Wieland Schöllkopf, Martin Wolf, and Alexander Paarmann

Phys. Rev. B 97, 094108 – Published 20 March 2018

Abstract

We demonstrate midinfrared second-harmonic generation as a highly sensitive phonon spectroscopy technique that we exemplify using $α$ -quartz ( ${SiO}_{2}$ ) as a model system. A midinfrared free-electron laser provides direct access to optical phonon resonances ranging from 350 to $1400 {cm}^{- 1}$ . While the extremely wide tunability and high peak fields of a free-electron laser promote nonlinear spectroscopic studies—complemented by simultaneous linear reflectivity measurements—azimuthal scans reveal crystallographic symmetry information of the sample. Additionally, temperature-dependent measurements show how damping rates increase, phonon modes shift spectrally and in certain cases disappear completely when approaching $T_{c} = 846 K$ where quartz undergoes a structural phase transition from trigonal $α$ -quartz to hexagonal $β$ -quartz, demonstrating the technique's potential for studies of phase transitions.

Received 6 October 2017

DOI:https://doi.org/10.1103/PhysRevB.97.094108

Physics Subject Headings (PhySH)

Anharmonic lattice dynamics Dielectric properties First order phase transitions Optical phonons

Dielectrics Noncentrosymmetric materials

Crystal structures Infrared spectroscopy Optical second-harmonic generation

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Christopher J. Winta, Sandy Gewinner, Wieland Schöllkopf, Martin Wolf, and Alexander Paarmann^*

Fritz-Haber-Institut der Max-Planck-Gesellschaft, Department of Physical Chemistry, Faradayweg 4-6, 14195 Berlin, Germany

^*alexander.paarmann@fhi-berlin.mpg.de

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Vol. 97, Iss. 9 — 1 March 2018

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Figure 1
(a) Schematic of the experimental setup and definition of the coordinate systems. Noncollinear two-beam excitation with the FEL generates two-pulse correlated SHG in reflection. Rotation of the sample about the $z$ axis provides the azimuthal behavior of the SHG signal. (b) Crystal structure of $α$ -quartz (view along the optic $c$ axis). Oxygen atoms (red) form tetrahedra around the silicon atoms (blue).
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Figure 2
(a) Experimental SHG spectrum of $α$ -quartz for SPP polarization conditions at an azimuthal angle $φ = 30^{\circ}$ . Strong SHG enhancements at TO phonon frequencies are observed. (b) Reflectivity spectrum for P-polarization measured at an angle of incidence $α^{i} = 60^{\circ}$ with respect to the surface normal, demonstrating the correlation between nonlinear and linear spectroscopy. Shaded orange boxes mark the phonon modes, ranging from the respective lower frequency TO phonons to the corresponding higher frequency LO phonons, indicating the formation of Reststrahlen regions. SHG peaks appear at spectral positions marked by blue arrows and are labeled $ω_{j}^{SHG}$ .
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Figure 3
Azimuthal behavior of the SHG at four exemplary TO phonon resonances for SPP and PPP polarization conditions. Solid lines represent model fits using Eqs. (6) and (7), respectively. While PPP measurements exhibit a clear sixfold symmetry, SPP measurements show a threefold symmetry due to the two uniquely contributing $χ^{(2)}$ elements, $χ_{a c b}^{(2)}$ and $χ_{a a a}^{(2)}$ .
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Figure 4
Temperature-dependent SHG and reflectivity spectra for temperatures ranging from room temperature up to $950 K$ . Due to the different azimuthal shapes of the SHG in SPP polarization, these data were taken at $φ = 30^{\circ}$ in the low-frequency range [(a) and (b)] and at $φ = 90^{\circ}$ in the high-frequency range [(c) and (d)]. The SHG resonances in (a) and (c) decrease and broaden, while spectral positions shift with higher temperatures. Note the logarithmic scale. The corresponding reflectivity spectra [(b) and (d)] were taken at an angle of incidence of $60^{\circ}$ and in P polarization. Spectral features in the reflectivity behave in accordance with their respective SHG peaks.
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Figure 5
Composition of the measured SHG spectrum: The highly dispersive $χ^{(2)}$ tensor elements (b), the Fresnel factors (c) as well as the inverse squared wave vector mismatch $1 / Δ k^{2}$ (d) enter the measured SHG signal (a). The latter also determines an effective escape depth $δ_{p}$ of the SHG light (d). Note the logarithmic scales in all four graphs.
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Figure 6
(a) Fitted peak positions (blue) and damping constants (orange) from the SHG spectrum (dots with error bars) compared to TO phonon frequencies and dampings, respectively, as measured by Gervais and Piriou [31] (diamonds and squares). Lines are a guide to the eye. The $α \to β$ phase transition of quartz presumably takes place in the temperature interval indicated by the gray shaded area. (b) Fitted SHG peak amplitudes at phonon resonances (black dots) with estimations of their temperature-dependent behavior of the SHG based on the respective oscillator strengths $S$ and damping constants $γ$ . For TO6 in (a) and (b), the closed and open dots correspond to the data taken at $φ = 30^{\circ}$ and $90^{\circ}$ in Figs. 4 and 4, respectively.
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Physical Review B

covering condensed matter and materials physics

Second-harmonic phonon spectroscopy of $α$ -quartz

Christopher J. Winta, Sandy Gewinner, Wieland Schöllkopf, Martin Wolf, and Alexander Paarmann

Phys. Rev. B 97, 094108 – Published 20 March 2018

Abstract

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Physical Review B

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Second-harmonic phonon spectroscopy of α-quartz

Christopher J. Winta, Sandy Gewinner, Wieland Schöllkopf, Martin Wolf, and Alexander Paarmann

Phys. Rev. B 97, 094108 – Published 20 March 2018

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Second-harmonic phonon spectroscopy of $α$ -quartz