Electron thermalization and relaxation in laser-heated nickel by few-femtosecond core-level transient absorption spectroscopy

Direct measurements of photoexcited carrier dynamics in nickel are made using few-femtosecond extreme ultraviolet (XUV) transient absorption spectroscopy at the nickel $M_{2,3}$ edge. It is observed that the core-level absorption line shape of photoexcited nickel can be described by a Gaussian broadening ($\sigma$) and a red shift (${\omega }_s$) of the ground-state absorption spectrum. Theory predicts and the experimental results verify that after initial rapid carrier thermalization, the electron temperature increase ($\mathrm{\Delta }T$) is linearly proportional to the Gaussian broadening factor $\sigma$, providing quantitative real-time tracking of the relaxation of the electron temperature. Measurements reveal an electron cooling time for 50 nm thick polycrystalline nickel films of $640\pm 80$ fs. With hot thermalized carriers, the spectral red shift exhibits a power-law relationship with the change in electron temperature of ${\omega }_s\propto \mathrm{\Delta }{T}^{1.5}$. Rapid electron thermalization via carrier-carrier scattering accompanies and follows the nominal 4-fs photoexcitation pulse until the carriers reach a quasithermal equilibrium. Entwined with a <6 fs instrument response function, carrier thermalization times ranging from 34 fs to 13 fs are estimated from experimental data acquired at different pump fluences and it is observed that the electron thermalization time decreases with increasing pump fluence. The study provides an initial example of measuring electron temperature and thermalization in metals in real time with XUV light, and it lays a foundation for further investigation of photoinduced phase transitions and carrier transport in metals with core-level absorption spectroscopy.

Figure 1

(a) Experimental setup of the XUV TA experiment. (b) shows the spectra of incident and transmitted XUV pulses through the 50 nm thick Ni sample.

Figure 2

(a) Static absorption spectrum of nickel $M_{2,3}$ edge and (b), the measured XUV TA spectra of nickel between $-50$ fs and 1.9 ps time delay. (c) displays the experimental XUV TA spectra between $-20$ fs and 35 fs time delay. The experimental pump fluence of the results in (b) and (c) are 41 and 33 mJ/${\mathrm{cm}}^2$, respectively.

Figure 3

(a) A typical XUV TA spectrum of nickel at 40 fs time delay (blue line). $\mathrm{\Delta }A$ denotes the change of XUV absorbance and the blue shade in (a) shows the uncertainty of the TA spectrum. The red line is the fitting result of Eq. (1) on the experimental data. The Gaussian broadening and shift obtained from the fitting are $0.25\pm 0.02$ eV and $-0.16\pm 0.01$ eV, respectively. (b) Absorbance change $\mathrm{\Delta }A$ (circles) after optical excitation at 40 fs time delay with five different laser fluences. The static absorption spectrum of nickel $M_{2,3}$ edge is displayed in gray as a reference. Results of the fitting of measured data with Eq. (1) are shown in black lines and the obtained $\sigma$ and ${\omega }_s$ as a function of the simulated electron temperature rise $\mathrm{\Delta }{T}_{\mathrm{est}}$ are shown in (c) and (d), respectively. The results of linear fitting of $\sigma$ vs $\mathrm{\Delta }{T}_{\mathrm{est}}$ is displayed as a black line in (c) and the inset in (d) exhibits the fitting of $|{\omega }_s|$ vs $\mathrm{\Delta }{T}_{\mathrm{est}}$ with a power function (black line) in a log-log plot. The uncertainties in the fitting are shown as gray areas in (c) and (d), respectively.

Figure 4

(a) Results of fitting the TA spectra in Fig. 2 with Eq. (1) and the fitting parameters ${\omega }_s$ and $\mathrm{\Delta }T$ at different time delays are shown as dots in (b). The fitting of the changes of ${\omega }_s$ and $\mathrm{\Delta }T$ as a function of time delay with single exponential decay convoluted with a Gaussian instrument response function are shown as the blue and red line, respectively.

Figure 5

(a) Fitting results of Fig. 2 with Eq. (1). The fitted edge shift (${\omega }_s$) and broadening ($\sigma$) as a function of time delay are plotted in (b) as dots and the fitting of ${\omega }_s\left(t\right)$ and $\sigma \left(t\right)$ with Eq. (E1) are depicted as blue and red lines, respectively. (c) shows the lineouts of $\mathrm{\Delta }A$, shown in circled dots, at 65.75 eV and 67.4 eV [Fig. 2, white dashed lines] and their fitting results (dashed black lines) with Eq. (E1).

Figure 6

Simulated electronic occupation as a function of energy during photoexcitation. The results of fitting each time slice to a Fermi-Dirac function are shown in black dashed lines.

Figure 7

(a) The typical spectrum and (b) temporal profile of the pump pulses measured by dispersion scan [91]. (c) displays the typical transient absorption spectra of helium 2snp autoionization states taken subsequently after each scan through all time delay points on the nickel sample for time delay calibration.

Figure 8

A sample time zero drift trace taken in an XUV TA experiment on nickel. The time zero is extracted from XUV TA measurements on He autoionization lines. The red arrows indicate the scans to be discarded from data analysis due to >3 fs drifts over a single scan.