Ultrafast Structural Dynamics along the $\ensuremath{\beta}\ensuremath{-}\ensuremath{\gamma}$ Phase Transition Path in MnAs

Ultrafast Structural Dynamics along the $β - γ$ Phase Transition Path in MnAs

Franck Vidal, Yunlin Zheng, Lounès Lounis, Leticia Coelho, Claire Laulhé, Carlo Spezzani, Alessandra Ciavardini, Horia Popescu, Eugenio Ferrari, Enrico Allaria, Jialin Ma, Hailong Wang, Jianhua Zhao, Matthieu Chollet, Matthew Seaberg, Roberto Alonso-Mori, James M. Glownia, Mahmoud Eddrief, and Maurizio Sacchi

Phys. Rev. Lett. 122, 145702 – Published 9 April 2019

Abstract

We investigate the orthorhombic distortion and the structural dynamics of epitaxial MnAs layers on GaAs(001) using static and time-resolved x-ray diffraction. Laser-induced intensity oscillations of Bragg reflections allow us to identify the optical phonon associated with orthorhombic distortion and to follow its softening along the path towards an undistorted phase of hexagonal symmetry. The frequency of this mode falls in the THz range, in agreement with recent calculations. Incomplete softening suggests that the $β - γ$ transformation deviates from a purely second-order displacive transition.

Received 21 December 2018

DOI:https://doi.org/10.1103/PhysRevLett.122.145702

Physics Subject Headings (PhySH)

Phase transitions

Thin films

X-ray diffraction

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Franck Vidal^1,*, Yunlin Zheng¹, Lounès Lounis^1,2, Leticia Coelho^1,3, Claire Laulhé^4,5, Carlo Spezzani^6,7, Alessandra Ciavardini⁴, Horia Popescu⁴, Eugenio Ferrari^7,8,†, Enrico Allaria⁷, Jialin Ma⁹, Hailong Wang⁹, Jianhua Zhao⁹, Matthieu Chollet¹⁰, Matthew Seaberg¹⁰, Roberto Alonso-Mori¹⁰, James M. Glownia¹⁰, Mahmoud Eddrief¹, and Maurizio Sacchi^1,4

¹Sorbonne Université, CNRS, Institut des NanoSciences de Paris, INSP, F-75005 Paris, France
²PSL Research University, 75231 Paris, France
³Instituto de Física, Universidade de Brasília UnB, Brasília—DF, CEP 70910-900, Brazil
⁴Synchrotron SOLEIL, L’Orme des Merisiers, Saint-Aubin BP 48, 91192 Gif-sur-Yvette Cedex, France
⁵Université Paris-Saclay (Université Paris-Sud), F-91405 Orsay Cedex, France
⁶Laboratoire de Physique des Solides, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay Cedex, France
⁷ELETTRA – Sincrotrone Trieste, in Area Science Park, S.S.14, Km 163.5, I-34149 Trieste, Italy
⁸Particle Accelerator Physics Laboratory, Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
⁹State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, P.O. Box 912, Beijing 100083, People’s Republic of China
¹⁰Linac Coherent Light Source (LCLS), SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA

^*Corresponding author. franck.vidal@insp.jussieu.fr
^†Present address: Paul Scherrer Institut, Forschungsstrasse 111, 5232 Villigen PSI, Switzerland.

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Vol. 122, Iss. 14 — 12 April 2019

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Figure 1
(a) $α / γ$ -MnAs hexagonal crystal structure. The orthorhombic system is used in order to describe each phase of MnAs with a common Bravais lattice. The shaded area indicates the hexagonal cell. (b) $β$ -MnAs orthorhombic crystal structure. Arrows indicate the displacement along the $A_{g}$ mode coordinates, corresponding to a reduction of the orthorhombic distortion $η$ . Dashed lines are a guide to the eye, highlighting the distortion. (c) Intensity of the $α$ (triangles) and $β$ (disks) 006 Bragg reflections as a function of the temperature. (d) Left panel: ratio of the 307 and 006 Bragg reflection intensities for the $β$ phase in $MnAs / GaAs (001)$ as a function of the temperature. Right panel: calculated ratio of the squared modulus of structure factors of the 307 and 006 Bragg reflections as a function of the orthorhombic distortion $η$ . The shaded area indicates the $η$ range probed in our experiment. All Bragg reflections are indexed within the orthorhombic axes.
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Figure 2
(a) Experimental setup used for time-resolved x-ray diffraction measurements. Scans were performed in the vertical bisecting mode, with $ω$ the incidence angle of x rays with respect to the sample surface, and $2 θ$ the detection angle. $Δ t$ is the time delay between the x-ray probe and optical pump. (b) Delay-angle map for the 006 reflection at $T = 320 K$ , $Φ = 8 mJ / {cm}^{2}$ . (c) Time dependence of the normalized intensity of the 307 Bragg reflection at $T = 293 K$ for several pump fluences.
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Figure 3
(a) Variation of $| F_{206}^{β} |^{2}$ , $| F_{307} |^{2}$ , and $| F_{406}^{β} |^{2}$ with the orthorhombic distortion $η$ . The shaded areas represent qualitatively the $η$ intervals that are spanned after the laser pulse arrival at delay 0, with $U$ -turn arrows symbolizing the coherent oscillations of $η$ . (b) Simulated time dependence of $I_{206}^{β}$ , $I_{307}$ , and $I_{406}^{β}$ starting from $η_{0} = 0.15$ and $η_{0} = 0.40$ at negative delay. (c) Time dependence of the normalized diffracted intensity for the 206, 307, and 406 Bragg reflections measured at $T = 293$ ( $Φ = 0.7$ ) and $T = 303 K$ ( $Φ = 1.5 mJ / {cm}^{2}$ ).
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Figure 4
(a) Normalized $I_{307}$ vs delay ( $Φ = 0.7 mJ / {cm}^{2}$ ) at three different temperatures (symbols) and corresponding fits (lines) obtained using Eq. (3). Data are shifted vertically for clarity. (b) Fitted parameters associated with data in (a). (c) Frequency $ν$ of $β$ -MnAs zone-center optical phonon as a function of the temperature, obtained by fitting the time-dependent intensities of 107, 206, 307, and 406 reflections ( $Φ = 0.7 mJ / {cm}^{2}$ ). (d) Same values as in (c) plotted against $η_{0}$ . The straight line fits $ν (η_{0})$ values for $η_{0} < 0.2$ , pointing at $ν (0) = 0.53 THz$ .
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Physical Review Letters

Ultrafast Structural Dynamics along the β−γ Phase Transition Path in MnAs

Phys. Rev. Lett. 122, 145702 – Published 9 April 2019

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Ultrafast Structural Dynamics along the $β - γ$ Phase Transition Path in MnAs