Layer-dependent Debye temperature and thermal expansion of Ru(0001) by means of high-energy resolution core-level photoelectron spectroscopy

The layer-dependent Debye temperature of Ru(0001) is determined by means of high-energy resolution core-level photoelectron spectroscopy measurements. The possibility to disentangle three different components in the Ru 3d5/2 spectrum of Ru(0001), originating from bulk, first-, and second-layer atoms, allowed us to follow the temperature evolution of their photoemission line shapes and binding energies. Temperature effects were detected, namely, a lattice thermal expansion and a layer-dependent phonon broadening, which was interpreted within the framework of the Hedin-Rosengren formalism based on the Debye theory. The resulting Debye temperature of the top-layer atoms is 295 K, lower than that of the bulk T=668 K and second-layer T=445 K atoms. While these results are in agreement with the expected phonon softening at the surface, we show that a purely harmonic description of the motion of the surface atoms is not valid, since anharmonic effects contribute significantly to the position and line shape of the different core-level components.