Coherent surface and bulk vibrations induced by femtosecond laser excitation of the $\mathrm{Gd}\left(0001\right)$ surface state

Excitation of the $\mathrm{Gd}\left(0001\right)$ surface state by $800\mathrm{nm}$ femtosecond laser pulses initiates transient coherent surface and bulk vibrations. These are investigated by time-resolved second harmonic and linear reflectivity probing simultaneously the motion of the surface layer and its coupling to bulk modes localized near the surface. Initially, the surface vibration frequency of $2.8\mathrm{THz}$ lies $\sim 18\%$ below the frequency detected in linear reflectivity. Within the first $3\mathrm{ps}$ the surface vibration frequency is found to increase while the bulk one decreases. Both types of vibrations persist only during nonequilibrium between electron and lattice temperature and are damped within the electron-phonon relaxation time. We conclude that the observed frequency shifts cannot be accounted for by anharmonic effects but originate from time-dependent changes of the potential energy at and near the surface due to nonequilibrium electron distributions.

Figure 1

Scheme of time-resolved linear reflectivity and second harmonic experiment on epitaxial $\mathrm{Gd}\left(0001\right)$ films grown on $\mathrm{W}\left(110\right)$. Incident beams have a wavelength of $800\mathrm{nm}$. The reflected intensity of the fundamental probe beam and the second harmonic intensity are detected simultaneously.

Figure 2

Pump-induced variations of linear ($엯$, right axis) and second harmonic ($◻$, left axis) reflectivity within the first $3\mathrm{ps}$ after excitation by the pump pulse, measured for a $20\mathrm{nm}$ $\mathrm{Gd}$ film on $\mathrm{W}\left(110\right)$ at $90\mathrm{K}$. Solid lines indicate the incoherent contributions in ${\Delta }^{2\omega }$ and ${\Delta }^{\omega }$. The inset shows the oscillating part in linear reflectivity obtained by subtraction of the incoherent background. Note the difference of three orders of magnitude in scale between ${\Delta }^{\omega }$ and ${\Delta }_{\text{osc}}^{\omega }$.

Figure 3

Experimental data (open circles) of ${\Delta }_{\mathrm{coh}}^{2\omega }$ (a) and ${\Delta }_{\mathrm{coh}}^{\omega }$ (b) after subtraction of incoherent contributions to the transient signals. Solid lines represent fits to a phenomenological function given by Eq. (2). In the inset fits by Eq. (2) with $⟨\partial {\Omega }_S∕\partial t⟩=0$ (dashed line) and finite frequency shift of $0.17\mathrm{THz}∕\mathrm{ps}$ (solid line, see also top panel) are compared. Only the latter reproduces the data up to $3\mathrm{ps}$.

Figure 4

Fourier transforms of the coherent parts ${\Delta }_{\mathrm{coh}}^{2\omega }$ and ${\Delta }_{\mathrm{coh}}^{\omega }$ yielding different frequencies for surface and bulk lattice vibrations, as indicated by arrows. Both peaks show a clear asymmetry, with the bulk mode tending to higher frequencies while the surface mode has a tail in the opposite direction. This corresponds to different frequency shifts for both vibrations (see text).

Figure 5

Surface and bulk phonon frequencies (left axis) as a function of pump-probe delay. Dashed lines represent the linearly chirped frequency determined by fitting the data with Eq. (2). The solid line depicts, for comparison, the incoherent contribution of the $\mathrm{SH}$ intensity (right axis). In the inset the temporal evolution of the amplitudes of surface and bulk vibrations are shown, the solid line represents an exponential decay.