Nonequilibrium heat transport in Pt and Ru probed by an ultrathin Co thermometer

Nonequilibrium 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 subnanometer-thick Co layer with perpendicular magnetic anisotropy can effectively serve as a thermometer to monitor nonequilibrium 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 nonthermal 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, gep(Pt)=(6±1)×1017Wm-3K-1 and gep(Ru)=(9±2)×1017Wm-3K-1. We also find that the length scales of nonequilibrium between electrons and phonons are lep=(Λe/gep)1/2≈9nm for Pt and ≈7nm 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 lep 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 nonequilibrium length scale, lep≈63nm.