Gallium Transformation under femtosecond laser excitation: Phase coexistence and incomplete melting

The reversible phase transition induced by femtosecond laser excitation of Gallium has been studied by measuring the dielectric function at $775\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ with $\ensuremath{\sim}200\phantom{\rule{0.3em}{0ex}}\mathrm{fs}$ temporal resolution. The real and imaginary parts of the transient dielectric function were calculated using the Fresnel formulae from the absolute reflectivity of a Gallium layer measured at two different angles of incidence. The time-dependent effective electron-phonon collision frequency; the heat conduction coefficient; and the volume fraction of the new phase were recovered directly from the experimental data. The time and space dependent electron and lattice temperatures in the layer undergoing the phase transition were reconstructed without ad hoc assumptions. We converted the temporal dependence of the electron-phonon collision rate into its temperature dependence, and demonstrated that the electron-phonon collision rate has a nonlinear character. This temperature dependence converges to the known equilibrium function during the cooling stage. The maximum fraction of the new phase in the laser-excited Gallium layer reached only 60% even when the deposited energy was twice the equilibrium enthalpy of melting. We demonstrate that the rate at which the phase transition proceeds and a fraction of the material transformed into the new phase depends strongly on the temperature of the laser-excited Gallium layer, and is restricted by the thickness of this layer which is only several tens of nanometers for the whole range of the pump laser fluences. The kinetics of the phase transformation after the laser excitation can be understood on the basis of the classical theory of the first-order phase transition.