Shift-current-induced strain waves in ${\mathrm{LiNbO}}_{3}$ mapped by femtosecond x-ray diffraction

Shift-current-induced strain waves in ${LiNbO}_{3}$ mapped by femtosecond x-ray diffraction

Marcel Holtz, Christoph Hauf, Antonio-Andres Hernández Salvador, Rene Costard, Michael Woerner, and Thomas Elsaesser

Phys. Rev. B 94, 104302 – Published 19 September 2016

Abstract

The response of the crystal lattice to an electric shift current induced via the two-photon bulk-photovoltaic effect in a lithium niobate ( ${LiNbO}_{3}$ ) crystal is directly mapped by femtosecond x-ray diffraction. Acoustic strain waves of large amplitude are generated by piezoelectric coupling to the current-related polarization while other mechanisms such as anharmonic phonon-phonon couplings and electron-phonon coupling through deformation potentials play a minor role. A striking variation of the strain wave speed occurs as a function of the relative orientation between the crystal's $c$ -axis, the direction of the current flow, and the polarization of the incident pump pulse. The observed behavior is relevant for a large class of ferroelectrics.

Received 14 June 2016
Revised 22 July 2016

DOI:https://doi.org/10.1103/PhysRevB.94.104302

Physics Subject Headings (PhySH)

Electron-phonon coupling Lattice dynamics Piezoelectricity Stress propagation

Piezoelectrics

Photoexcitation X-ray diffraction

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Marcel Holtz^*, Christoph Hauf, Antonio-Andres Hernández Salvador, Rene Costard, Michael Woerner^†, and Thomas Elsaesser

Max-Born-Institut für Nichtlineare Optik und Kurzzeitspektroskopie, 12489 Berlin, Germany

^*mholtz@mbi-berlin.de
^†woerner@mbi-berlin.de

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Vol. 94, Iss. 10 — 1 September 2016

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Figure 1
(a) Ball and stick representation of the crystal structure of ${LiNbO}_{3}$ with highlighted edge-sharing ${NbO}_{6}$ octahedra viewed along the $x$ direction, together with the definition of the rotation angle $ϕ$ . (b) Schematic drawing of the pump-probe geometry, together with the relevant components of the electric field of the pump light inside the single crystal. (c) Dependency of the three components of the electric field $E (ϕ, t) = E (ϕ) E (t)$ on the angle $ϕ$ .
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Figure 2
(a) Normalized x-ray reflectivity transients of the (110) Bragg reflection of ${LiNbO}_{3}$ for two angles $ϕ$ (red solid circles for $ϕ = 0^{\circ}$ ; blue solid circles for $ϕ = 45^{\circ}$ ). The measured change of diffracted x-ray intensity ${(Δ I / I)}_{n}$ is plotted as a function of pump-probe delay (symbols). Calculated reflectivity transients are represented as black and orange lines, respectively. The insets show calculated slowness surfaces for the corresponding phonon modes [29]. (b) Polar plot representation of the normalized x-ray reflectivity transients of the (110) Bragg reflection with varying angles $ϕ$ . The radial value indicates the percentage of the maximal ${(Δ I / I)}_{n}$ value of each transient reached at specific delay times, which are color-coded according to the legend on the right-hand side. The black line indicates the percentage reached after a delay time of $t = 90$ ps. On the left-hand side, the polarization of the strain wave for $ϕ = 0^{\circ}$ and $ϕ = 45^{\circ}$ is depicted schematically.
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Figure 3
(a) Contour plot of the x-ray reflectivity for the (110) Bragg reflection of ${LiNbO}_{3}$ calculated from a Darwin model in dependency of the delay time $t$ and the diffraction angle $θ$ for $ϕ = 45^{\circ}$ at a strain amplitude of $Δ d_{110} / d_{110} = 3.3 \times 10^{- 4}$ . (b) Rocking curves with the actual experimental angular resolution for $t = 800$ ps. Black and red solid dots represent the measured angular dependency of the number of detected photons for an unstrained and a partially strained sample, respectively. The solid orange and blue lines represent calculated Gaussian line-shape functions of the data. (c) The calculated change of the normalized diffracted x-ray intensity ${(Δ I / I)}_{n}$ (solid black line) as well as the calculated shift of the center of gravity of the rocking curves (solid blue line) are plotted as a function of pump-probe delay. Center of gravity shifts determined experimentally at different delay times are shown as blue solid circles.
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Figure 4
The eight unique components of the fourth-order conductivity tensor $J_{i} = σ_{i j k l m} E_{j} E_{k} E_{l} E_{m}$ are shown. Red contours denote contributions to a polarization (shift current) in the $x$ direction, blue contours denote contributions in the $y$ direction, and green contours denote contributions in the $z$ direction.
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Physical Review B

covering condensed matter and materials physics

Shift-current-induced strain waves in ${LiNbO}_{3}$ mapped by femtosecond x-ray diffraction

Marcel Holtz, Christoph Hauf, Antonio-Andres Hernández Salvador, Rene Costard, Michael Woerner, and Thomas Elsaesser

Phys. Rev. B 94, 104302 – Published 19 September 2016

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Physical Review B

covering condensed matter and materials physics

Shift-current-induced strain waves in LiNbO3 mapped by femtosecond x-ray diffraction

Marcel Holtz, Christoph Hauf, Antonio-Andres Hernández Salvador, Rene Costard, Michael Woerner, and Thomas Elsaesser

Phys. Rev. B 94, 104302 – Published 19 September 2016

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Shift-current-induced strain waves in ${LiNbO}_{3}$ mapped by femtosecond x-ray diffraction