Non-Equilibrium Heat Transport in Pt and Ru Probed by an Ultrathin Co Thermometer

Abstract

Non-equilibrium of electrons, phonons, and magnons in metals is a fundamental phenomenon in condensed matter physics and serves as an important driver in the field of ultrafast magnetism. In this work, we demonstrate that the magnetization of a sub-nm-thick Co layer with perpendicular magnetic anisotropy can effectively serve as a thermometer to monitor non-equilibrium dynamics in adjacent metals, Pt and Ru, via time-resolved magneto-optic Kerr effect. The temperature evolutions of the Co thermometer embedded in Pt layers of different thicknesses, 6-46 nm, are adequately described by a phenomenological three temperature model with a consistent set of materials parameters. We do not observe any systematic deviations between the model and the data that can be caused by a non-thermal distribution of electronic excitations. We attribute the consistently good agreement between the model and the data to strong electron-electron interaction in Pt. By using Pt/Co/Pt and Pt/Co/Pt/Ru structures, we determine the electron-phonon coupling parameters of Pt and Ru, g_ep(Pt)=(6+/-1)x10^17 W m-3 K-1 and g_ep(Ru)=(9+/-2)x10^17 W m-3 K-1. We also find that the length scales of non-equilibrium between electrons and phonons are l_ep=({\Lambda}_e/g_ep)^1/2 =9 nm for Pt and 7 nm for Ru, shorter than their optical absorption depths, 11 and 13 nm, respectively. Therefore, the optically thick Pt and Ru layers show two steps of temperature rise: The initial jump of electron temperature that occurs within 1 ps is caused by direct optical excitation and electronic heat transport within a distance l_ep for the Co layer. The second temperature rise is caused by heat transport by electrons and phonons that are near thermal equilibrium. We contrast two-temperature modeling of heat transport in Pt an Ru films to calculations for Cu, which has a much longer non-equilibrium length scale, l_ep=63 nm.