Measurement of the Electronic Grüneisen Constant Using Femtosecond Electron Diffraction

We report the first accurate measurement of the electronic Grüneisen constant ${\gamma }_e$ using a novel method employing the new technique of femtosecond electron diffraction. The contributions of the conduction electrons and the lattice to thermal expansion are differentiated in the time domain through transiently heating the electronic temperature well above that of the lattice with femtosecond optical pulses. By directly probing the associated thermal expansion dynamics in real time using femtosecond electron diffraction, we are able to separate the contributions of hot electrons from that of lattice heating, and make an accurate measurement of ${\gamma }_e$ of aluminum at room temperature. This new approach opens the possibility of distinguishing electronic from magnetic contributions to thermal expansion in magnetic materials at low temperature.

Figure 1

Left: Diffraction pattern of polycrystalline freestanding thin-film aluminum of 20 nm thickness. It is recorded with $\sim 2\times {10}^7$ electrons of 60 keV beam energy ($\lambda =0.0487\AA$) at approximately $1.3\mathrm{mJ}/{\mathrm{cm}}^2$ laser excitation fluence. Right: The corresponding radial averaged intensity curve. Inset: A typical fit of (311) Bragg peak to a Gaussian profile. The peak center position is determined to be $0.81780\pm 0.00003({\AA }^{-1})$ ($474.99\pm 0.02\mathrm{\text{pixel}}$).

Figure 2

Temporal evolution of Bragg peak positions. The averaged data are obtained by arithmetic averaging of all the Bragg peak vibration data and shifted for viewing clarity. Positive time delays correspond to probe electron pulses arriving after the excitation laser pulses. The error bars represent one standard deviation in the Gaussian peak profile fitting for determining the peak centers. The solid curve is a fit to the experimental data using Eqs. (2, 3).

Figure 3

Temporal evolution of lattice temperature as a function of delay time. The solid line is a fit to the data using an exponential function with a time constant $t_{e\mathrm{\text{−}}\mathrm{ph}}=550\pm 80\mathrm{fs}$.