Full Reconstruction of a Crystal Unit Cell Structure during Coherent Femtosecond Motion

We present a complete characterization of the unit cell dynamics of a laser-excited tellurium crystal using femtosecond x-ray diffraction. The analysis offers a quantitative measure of the unit cell dynamics without making any assumptions on the symmetry of the excited-state motion. The results show a large-amplitude coherently excited $A_1$ mode quantitatively consistent with the predictions of a density functional theory model.

Figure 1

Equilibrium unit cell structure and zero wave vector optical eigenmodes of tellurium. (a) The hexagonal unit cell of tellurium ($a=4.456\AA$, $c=5.921\AA$), showing the three basis atoms arranged along a screw axis parallel to the $c$ axis. With this choice of origin, the basis atoms are located at ($x$, 0, 0) (0, $x$, $\frac{1}{3}$), and ($-x$, $-x$, $-\frac{1}{3}$), where $x=-0.2636$ at room temperature [12]. (b) The eigenmodes of the $\Gamma$-point optical modes in tellurium [13] viewed as a projection onto a plane normal to the $c$ axis of the unit cell.

Figure 2

Summary of femtosecond diffraction data from excited tellurium. All data were taken at a grazing incidence angle of 0.45°. The set of measured diffraction planes have been selected to form a linearly independent set that can be used to solve for the dynamics of the unit cell.

Figure 3

Phonon mode and mean-square displacement dynamics of photoexcited tellurium. An inversion of the diffraction data from Fig. 2 allows a complete solution of the unit cell dynamics, equivalent to tracking the 3D position of each basis atom with 200 fs time resolution. See the EPAPS supplement [23] for animated movies derived from this solution. The solid line superimposed over the $Q_{\mathbf{0}1}$ data shows the results of a fit to a displacive excitation model discussed in the text.