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

Abstract

When the spatial dimensions of metallic heterostructures shrink below the mean free path of its conduction electrons, the transport of electrons and hence the transport of thermal energy by electrons continuously changes from diffusive to ballistic. Electron-phonon coupling sets the mean free path to the nanoscale and the time for equilibration of electron and lattice temperatures to the picosecond range. A particularly intriguing situation occurs in trilayer heterostructures combining metals with very different electronphonon coupling strength: Heat energy deposited in few atomic layers of Pt is transported into a nanometric Ni film, which is heated more than the Cu film through which the heat is released. Femtosecond pump-probe experiments with hard X-ray pulses provide a layer-specific probe of the heat energy. A purely diffusive two-temperature model with increased thermal conductivity of hot electrons excellently reproduces the observed signals from all three layers. At the time when the Ni lattice is maximally heated, no significant heat has entered the Cu lattice. This phenomenon would be enhanced in thinner layers where ballistic transport dominates. In this context it is shown that purely diffusive transport can lead to a linear time-to-length dependence that must not be misinterpreted as ballistic transport.

Generation of spin waves via spin-phonon interaction in a buried dielectric thin film

“…The twotemperature model includes an enhanced electronic heat conductivity κ e = κ 0 × T e /T ph compared with the equilibrium value κ 0 . This enhancement is due to the reduction of the electron-phonon scattering channel if the lattice of Cu is cold compared with its electronic system [32]. The main difference to the previous paper is that the magnetic layer now is the insulating Bi-YIG, which cannot accept the thermal energy in the form of hot electrons.…”

“…Figure 1 shows the UXRD study of the heterostructure, performed with femtosecond x-ray diffraction using a tabletop laser-driven plasma source [47]. In full analogy to the recent publication on a Pt/Cu/Ni heterostructure [32], we were able to model the time-resolved strain in Pt, Cu, and Bi-YIG with a two-temperature model in combination with a one-dimensional masses-and-springs model, using the software package udkm1Dsim-toolbox [48]. The twotemperature model includes an enhanced electronic heat conductivity κ e = κ 0 × T e /T ph compared with the equilibrium value κ 0 .…”

“…2(b)]. The top Pt layer was added due to its high absorption at 800 nm compared with Cu, which also ensured an efficient generation of a hot-electron pulse [24,25,32]. Experimentally, the transmission of the pump light was less than 10 −3 .…”

“…The Cu was chosen for its high hot-electron lifetime [24,25,46]. Thus, the 100nm-thick Cu layer protected the Bi-YIG film from the direct light excitation, while the hot-electron pulses propagated until reaching the back side of the Cu layer [24,25,32].…”

“…Picosecond acoustic pulses can trigger a homogeneous collective spin oscillation (k = 0, i.e., ferromagnetic resonance mode) via inverse magnetostriction in conducting [27][28][29], semiconducting [30], and insulating [31] magnetic materials. Very recently, the geometry for exciting spin dynamics indirectly via pumping a Pt/Cu bilayer that protects a magnetic layer from optical excitation [24,25] was investigated by ultrafast x-ray diffraction (UXRD) [32]. These experiments quantify the arrival of hot electrons, strain waves, and vibrational heat in a magnetic Ni layer.…”