Shift-Current Induced Strain Waves in LiNbO3 Mapped by Femtosecond X-Ray Diffraction
[Physical Review B 94 (2016) 104302]
The response of the crystal lattice to an electric shift current induced via the two-photon bulk-photovoltaic effect
in a lithium niobate (LiNbO3) crystal was directly mapped by femtosecond x-ray diffraction in 2016. 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.
This figure shows (A) Ball and stick representation of the crystal structure
of LiNbO3 with highlighted edge-sharing NbO6 octahedra together with the definition of the rotation angle φ, (B) the normalized x-ray reflectivity transients of the (110)
Bragg reflection of LiNbO3 with pump pulses polarized parallel (φ = 0°, red symbols) or
at an angle of φ = 45° (blue symbols) to the polar c-axis and (C) a polar plot representation of the normalized x-ray reflectivity transients
of the (110) Bragg reflection depicting the changes of the normalized x-ray reflectifity when the angel between the crystal’s c-axis, the direction of the current flow, and the polarization of the incident
The experiments are based on a pump-probe scheme where
a subpicosecond 400 nm pulse excites a X-cut LiNbO3 single crystal (crystal structure shown in panel (A) by two-photon absorption. A 100 fs hard x-ray pulse from
a laser-driven Cu Kα (wavelength 0.154 nm) plasma source is
diffracted from the sample in a reflection geometry to map
structural changes upon excitation. The setup was choosen in such a fashion, that the rotation angle could be continously variied without chaning the exitation density.
In panel (B) we present time-resolved transients for two different rotation angles φ. The normalized change of
diffracted intensity (ΔI/I)n is plotted as a function of pump-probe
delay t. Both transients display an increase of diffracted
intensity on a 100 picosecond time scale and reach a maximum
after roughly 300 ps (absolute value ΔI/I ∼ 15%). For
φ = 45°, the signal rise is much faster than for φ = 0°.
The observed changes of diffracted intensity and, in particular,
their rise on a time scale of 100 to 300 ps are a hallmark
of acoustic strain waves propagating through the photoexcited
LiNbO3 crystal. Most interesting and markedly different from
previous experiments on semiconductors and perovskite layers is the variation of rise times with φ, pointing to
a variation in the velocity of sound. Transients calculated according to the dynamic diffration theorie are represented as solid
orange and black lines in panel (B) and match the experimental
results very well, when taking into account a expansive strain front propagation into the crystal. Our data show, that the predominant stress driving anisotropic strain propagation originates from a photovoltaic shift current induced by two-photon excitation, while carrier relaxation and phonon-phonon interactions play a minor role in stress generation.
For a systematic analysis, transients were recorded for the
full range between φ = 0° and 360°. Such data are summarized in the polar plot in panel (C). All transients were normalized to the maximum signal (ΔI/I)n and the radial axis gives the signal relative to its maximum value. The time intervals required to reach a particular signal value is encoded in color according to the legend on the right-hand side. The black contour line corresponds to a delay time of 90 ps. This line has a distinctive non-circular shape, directly reflecting the different rise times of the intensity changes at different φ. The noncircular pattern illustrates the φ -dependency of (ΔI/I)n featuring a 4-fold symmetry, which shows, that the acoustic phonons involved have distinctly different velocities. The φ-anisotropy depicted in panel (C) is interpreted in a way that the propagating strain fronts for φ = (0+m·90)° consist predominantly of medium speed phonons possessing
a mixed character of shear and dilatation strains along the propagating direction,
whereas the propagating strain fronts for φ = (45+m·90)° ∀m ∈ Z consist predominantly of fast longitudinal phonons.
Ultrafast soft-mode driven charge relocation
in an ionic crystal [Proceedings
of the National Academy of Sciences of the United States of America
109 (2012) 5207-5212]
Ionic crystals display an interplay of
lattice motions and relocations of electronic charge which is important
for their macroscopic electric propoerties and for transitions between
different structural phases. The dynamics of such phenomena occurs
ion ultrafast time scales and is addressed here by applying femtosecond
x-ray diffraction as a structural probe. From an extended set of
time-resolved diffraction data generated by x-ray powder diffraction,
we derived transient electron density maps of the prototype material
potassium dihydrogen phosphate [KH2PO4 KDP]
the crystal structure of which is shown in panel (A)
This figure shows A) the unit cell
of the KDP crystal [yellow spheres: phosporous atoms (P), pink:
potassium (K), red: oxygen (O), white: hydrogen (H)]. (B) Electron
density map ρ0(r) before laser excitation in the
plane defined by the rectangle in (A). The black lines indicate
boxes enclosing the different atoms which are used to measure the
charge and center of gravity of atoms. (C) and (D) Transient change
of the electron density distribution in the plane defined in (A):
red means increase and blue decrease. (E) Positions of atoms in
the plane together with a schematic view of the main features emerging
from the measurements: charge transfer from phosphorous atom to
the oxygen atoms and the prolate-oblate deformation of the charge
around the potassium atom
In panel (A) the unit ell of KDP is depicted. Its
space group at room temperature is I¯42d (No. 122). The unit
cell dimensions are a=b=0.74529 nm, c=0.69751 nm with four formula
units. The crystal consists of K+ ions and covalently
tetrahedral PO4 groups which are linked by O-H-O hydrogen
bonds. Ionic bonds exist between the K+ cations and H2PO4-
In an optical pump/x-ray probe scheme, the KDP powder sample was
excited by a 50 fs pulse at 266 nm, the third harmonic of amplified
pulses from a Ti:sapphire laser system, and the resulting structure
changes were mapped by diffracting a 100 fs hard x-ray pulse from
a laser-driven Cu Kα (wavelength 0.154 nm) plasma source from
the excited sample. In the optical excitation process, the two-photon
interband absorption of KDP was exploited. The diffracted x-rays
were re-corded with a large-area CCD detector.
In panel (B), an electron density map as calculated from steady-state
literature data is shown. The position and orientation of this plane
is sketched in (A): it goes through the top and bottom K atoms,
the central P atom and two of the surrounding O atoms. To extract
transient charge density maps from the time-resolved diffraction
data, we developed a novel method and applied it to this non-centrosymmetric
material. In Figs. 5(g,h), the corresponding changes of the electron
density on the plane for a delay t=-0.1 and +0.5 ps are shown.
The ultrafast charge relocations were analyzed in detail by (i)
integrating ηΔρ(x,y,z,t) over the volume VA
of a particular atom A [the borders between different VA
are shown as solid lines in Figs. 5(g,h,i)] giving the total charge
change ηΔqA(t), and (ii) by determining its
transient broadening along the c-axis ηΔz2(t)
and a/b-axes ηΔx2(t) within this volume.
Upon photoexcitation, we observe both an oscillatory charge transfer
between the P- to the O-atoms and a concomitant quadrupolar distortion
of the K+ charge distribution. The oscillation frequencies
are the low-frequency TO soft mode of the paraelectric crystal,
its LO counterpart, and various combination tones. Interestingly,
the modulation of the electronic charge distribution occurs on the
length scale of interatomic distances, much larger than the vibrational
amplitude. The coherent LO and TO phonon motions which dephase on
a time scale of several picoseconds, drive the charge relocation,
similar to a soft (TO) mode driven phase transition between the
ferro- and paraelectric phase of KDP.
Femtosecond X-ray diffraction using the
rotating crystal method: In 2011 we presented the first
implementation of the rotating crystal method in femtosecond x-ray
Freyer et al.; Opt. Express 19 (2011) 15506-15515].
scheme maps structural dynamics of a photoexcited bismuth crystal
via changes of the diffracted intensity of many Bragg reflections.
A drawback of the powder method is that it cannot
resolve reflections which have accidentally or systematically the
same diffraction angle. In contrast, the rotation method with single
crystals gives diffraction spots instead of rings, and, thus, allows
for resolving reflections with equal diffraction angle.
To demonstrate the performance of our method, we
realized a rotating crystal experiment on bismuth which is presented
in the following. X-ray probe pulses are generated by a 1 kHz laser
driven plasma source and focused onto the sample. The spot diameter
on the sample is 200 μm and the flux of x-ray photons is about
106 s-1. We used a single crystal of bismuth
with a cylindrical shape. The sample has a diameter of 8 mm, a thickness
of 2 mm, and a surface roughness of 30 nm. The sample is excited
by an 800 nm pump pulse and probed by a hard x-ray (λ = 0.154
nm) pulse under respective angles of grazing incidence of 7°
and 1.5°. We chose the grazing incidence scheme to adapt the
penetration depth of the probe to the penetration depth of the pump.
The latter is not affected by the incidence angle. The pump pulse
is p-polarized and the area density of absorbed energy has a value
of 1 mJ / cm2. To ensure that the angle of incidence
remains constant while rotating the sample we aligned the rotation
axis to be exactly perpendicular to the sample surface. As a reference
for the fluctuations of the x-ray source we used the (111) reflection
of a 60 mm thick diamond crystal in the incident x-ray beam. This
x-ray beamsplitter reflects approximately 5% of the incoming x-ray
To enhance the signal-to-noise ratio we oscillated
the sample within a 15° range and slowed down the angular velocity
at positions where reflections occur. All reflections, including
the reflection from the diamond crystal are measured simultaneously
and integrated on a deep depletion CCD. Aver-aging over a large
number of individual pump-probe scans gives the transients shown
in Fig. 4. The diffracted x-ray intensity is plotted as a function
of pump-probe delay for the (222), (111), (322) and (323) diffraction
peaks. Note, that the oscillatory behavior of the (111) reflection
is clearly visible even though the effect size is only ~5%. This
proofs the high time resolution and the high sensitivity of our
method. In the third and fourth panel of Fig. 4 we show the first
measurement of the (322) and (323) transient reflection, the (322)
reflection shows an oscillation with identical frequency and phase
as those of the (111) transient.
We wish to emphasize that in the rotation method, as well as in
the powder method, all reflection are measured simultaneously. This
fact makes sure that all reflections are measured under the same
conditions, e.g., pump intensity, spatial overlap and temporal overlap.
In contrast to powder-diffraction, the rotation method allows for
a separation of different reflections which have the same diffraction
The longer the better: Optical long-wavelength pulses generate brilliant ultrashort hard x-ray flashes
10th November 2014
Researchers from the Max-Born-Institut and the Technical University of Vienna present a novel table-top source of ultrashort hard x-ray pulses with an unprecedented photon flux.
X-rays are a key tool for imaging materials and analyzing their composition - at the doctor, in the chemistry lab and in materials research. Shining so-called hard x-rays of a wavelength comparable to the distance between atoms on the material, one can determine the atomic arrangement in space by analyzing the pattern of scattered x-rays. This method has unraveled equilibrium time-averaged structures of increasing complexity, from simple inorganic crystals to highly complex biomolecules such as DNA or proteins.
Today, there is a strong quest for mapping atoms ‘on the fly’, that is, for following atomic motions in space, during a vibration, a chemical reaction, or a change of the material’s structure. Atomic motions typically occur in the time range of femtoseconds (1 femtosecond = 10-15s), requiring an exposure by extremely short x-ray flashes to take snapshots. There are essentially two complementary approaches to generate ultrashort hard x-ray pulses, large scale facilities based on electron accelerators such as the free electron lasers in Stanford (LCLS at SLAC) or at SACLA in Japan, or highly compact table-top sources driven by intense ultrashort optical pulses. While the overall x-ray flux from accelerator sources is much higher than from table-top sources, the latter are versatile tools for making femtosecond x-ray ‘movies’ with a quality that is eventually set by the number of x-ray photons scattered from the sample. A joint research team from the Max-Born-Institut (MBI) in Berlin and the Technical University in Vienna has now accomplished a breakthrough in table-top x-ray generation, allowing for an enhancement of the generated hard x-ray flux by a factor of 25. As they report in the current issue of Nature Photonics. the combination of a novel optical driver providing femtosecond mid-infrared pulses around a 4000 nm (4µm) wavelength with a metallic tape target allows for generating hard x-ray pulses at a wavelength of 0.154 nm with unprecedented efficiency.
The x-ray generation process consists of 3 steps (Fig. 1), (i) electron extraction from the metal target induced by the electric field of the driving pulse, (ii) electron acceleration in vacuum by the strong optical field and return into the target with an increased kinetic energy, and (iii) generation of x-rays in the target by inelastic collisions of electrons with atoms. Longer optical wavelengths are equivalent to a longer oscillation period of the optical field and, thus, to a longer period of electron acceleration in vacuum. As a result, the accelerated electrons acquire a higher kinetic energy before they re-enter the target and generate x-rays with a higher efficiency. A simple analogy of the acceleration process is the mechanical acceleration when jumping from platforms at different height into water (Fig. 2). Here, the time interval Δt between leaving the platform and reaching the water surface increases with height and the kinetic energy at the water surface is proportional to Δt2. The electron pathways in vacuum were analyzed in detail by theoretical calculations and are shown in the movie attached (Fig. 3).
The experiments were performed at the TU Vienna combining a novel driver system based on Optical Parametric Chirped Pulse Amplification (OPCPA) with an x-ray target chamber from MBI. Pulses of 80 fs duration and up to 18 mJ energy at a center wavelength of 3900 nm (3.9 µm) were focused down onto a 20 µm thick copper tape. This scheme allows for generating an unprecedented number of 109 hard x-ray photons at a 0.154 nm wavelength per driving pulse. A comparison with previous experiments performed with 800 nm driver pulses shows that the enhancement of the x-ray flux in the new scheme scales with the square of the wavelength ratio, i.e., (3900 nm/800 nm)2 ≈ 25. This behavior is in quantitative agreement with a theoretical analysis of the 3-step generation scheme of Fig. 1. The results pave the way for a new generation of table-top hard x-ray sources, providing up to 1010 x-ray photons per pulse at elevated, e.g., kilohertz repetition rates.
Jannick Weisshaupt, Vincent Juvé, Marcel Holtz, ShinAn Ku, Michael Woerner, Thomas Elsaesser, Skirmantas Ališauskas, Audrius Pugzlys and Andrius Baltuška
High-brightness table-top hard X-ray source driven by sub-100 femtosecond mid-infrared pulses
Nature Photonics doi:10.1038/nphoton.2014.256.
Fig. 1: Left: x-ray generation in a conventional x-ray tube. Electrons which were emitted from the heated cathode (-) are accelerated by a constant electric field towards the anode (+). Within the metal target (e.g. copper) inelastic collisions of the accelerated electrons with atoms lead to the generation of both characteristic line emission of x-rays (sharp lines in the spectrum at the bottom) and Bremsstrahlung. Right: Femtosecond mid-infrared pulses (λ = 3900 nm) from a OPCPA system are focused onto a copper band target. Electrons are extracted from the surface, accelerated into the vacuum and smashed back into the target by the strong electric field of the light. During deceleration in the metal target the energetic electrons produce characteristic line emission and Bremsstrahlung which can be measured by an x-ray detector.
|Fig. 1 (click to enlarge)
Fig. 2: Analogy of electron acceleration in the vacuum to the acceleration by gravity when jumping from platforms at different height into water. Longer optical wavelengths are equivalent to a longer oscillation period of the optical field and, thus, to a longer period of electron acceleration in vacuum. The time interval Δt between leaving the platform and reaching the water surface increases with height and the kinetic energy at the water surface is proportional to Δt2. As a result, electrons accelerated in longer time interval Δt acquire a higher kinetic energy before they re-enter the target and generate x-rays with a higher efficiency.
|Fig. 2 (click to enlarge)
|| Movie of the acceleration of electrons (blue balls) in the vacuum above a metal surface when applying the strong oscillating electric field of the laser pulse (black line).
Jannick Weisshaupt Tel: 030 6392 1471
Vincent Juvé Tel: 030 6392 1472
Michael Wörner Tel: 030 6392 1470
Thomas Elsaesser Tel: 030 6392 1400
Andrius Baltuška Tel: +43 1 58801 38749