Dynamics of the Self-Energy of the Gd(0001) Surface State Probed by Femtosecond Photoemission Spectroscopy

Transient changes of the complex self-energy of the $5d_{z^2}$ surface state on Gd(0001) after intense optical excitation are investigated by femtosecond time-resolved photoemission. We observe an ultrafast ($<100\mathrm{fs}$) broadening of the linewidth due to $e\mathrm{\text{−}}e$ scattering followed by a decrease of the binding energy due to thermal expansion of the lattice. In addition, we resolve a periodic breathing of the band structure which originates from a coherent phonon. An amplitude of 1 pm is derived from the binding energy shift upon lattice displacement calculated by density functional theory.

Figure 1

False color representation of the TRPE intensity in normal emission as a function of binding energy $E_B$ and pump-probe delay $\Delta t$ for an absorbed IR fluence of $F=1.0\pm 0.1\mathrm{mJ}/{\mathrm{cm}}^2$. The dashed horizontal line denotes $E_B=0.18\mathrm{eV}$, which is the equilibrium value; the vertical one denotes $\Delta t=0$. The inset depicts TRPE schematically.

Figure 2

(a) TRPE spectra at indicated time delays with fits (solid lines). (b) The time evolution of the linewidth $\Gamma$ of the occupied SS component (○). The accuracy of the fitting analysis is about $\pm 5\mathrm{meV}$. The solid line represents a model description based on the TTM with two contributions: (i) $e\mathrm{\text{−}}e$ scattering (dotted curve) and (ii) $e$-magnon and $e$-phonon scattering (dashed curve). The equilibrium temperature is 30 K.

Figure 3

(a) Time evolution of $E_B$ with a coherent part on an incoherent thermal background (solid line). Inset: $E_B$ increase upon contraction of $d_{12}$ as calculated by DFT. Note that $E_B$ increases from top to bottom. (b) The oscillatory component. The solid line is a fit by an exponentially damped cosine; the dashed line shows its extrapolation to time zero.

Figure 4

Processes leading to transient changes in photoemission. Left: QP scattering due to relaxation of the excited state. Right: Periodic change of $E_B$ due to the coherent phonon along $d_{12}$.