Nonequilibrium 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 electronelectron 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)×10 17 W m -3 K -1 and gep(Ru)=(9±2)×10 17 W m -3 K -1 . We also find that the length scales of non-equilibrium between electrons and phonons are lep=(Λe/gep) 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

Ultrafast lattice dynamics and electron–phonon coupling in platinum extracted with a global fitting approach for time-resolved polycrystalline diffraction data

“…This value is in agreement with experimental results for the heat capacity of platinum at room temperature, as discussed in Ref. 17 . Here, we do not assume a linear relationship for c e and directly use the results provided by Lin et al For the lattice heat capacity, we use the high-temperature limit derived from equipartition, 24.943 (corresponding to ).…”

“… 18 An alternative way to access is by using a ferromagnetic detection layer in combination with time-resolved MOKE measurements. 17 However, this approach relies on modeling the nonequilibrium responses of both platinum as well as of the detection layer, which limits the precision of the method. In contrast, time-resolved photoemission spectroscopy provides direct access to transient electron temperatures.…”

Parametric dependence of hot electron relaxation timescales on electron-electron and electron-phonon interaction strengths

“…Our model predictions for τ E % 0:15 ps in Al and τ E % 0:16 ps in Pt are shorter than experimental values extracted from measurements of nonequilibrium heat transfer in metals. Tas and Maris report τ E % 0:23 ps in Al 5 , while Jang et al report τ E % 0:2 ps for Pt 55 . To illustrate the universal dependence of τ E and τ H on the ratio of interaction strengths γ ep /β ee , we report τ E and τ H normalized by the time-scales γ À1…”

“…The values of γ ep in Table 1 for all metals were determined in a crude manner based on Debye temperatures and an analysis of experimental electrical resistivity data 56 . Such an approach is likely to have significant error for a metal like Pt, where the electronic density of states is a strong function of energy near the Fermi-level 55 .…”

Heat Transport without Heating?—An Ultrafast X‐Ray Perspective into a Metal Heterostructure

“…Despite the purely diffusive character of our model, the analysis considering the rise time to a relative threshold f (orange lines in Figure 5b) also yields a linear dependence z ∝ t which is therefore obviously not a sufficient observation to conclude ballistic electron transport. [46] For comparison, the black dashed line in Figure 5b depicts the arrival time of ballistic electrons with Fermi velocity v F = 1.57 × 10 6 m s −1 [28] at the backside of a Cu layer of thickness d. For very thin Cu films and small relative temperature thresholds the diffusion appears to be faster than the ballistic motion. This is partially caused by the slight direct optical excitation of the Cu layer (see experimental section and arrows in Figure 5b).…”