Ultrafast x-ray diffraction thermometry measures the influence of spin excitations on the heat transport through nanolayers

We investigate the heat transport through a rare earth multilayer system composed of yttrium (Y), dysprosium (Dy), and niobium (Nb) by ultrafast x-ray diffraction. This is an example of a complex heat flow problem on the nanoscale, where several different quasiparticles carry the heat and conserve a nonequilibrium for more than 10 ns. The Bragg peak positions of each layer represent layer-specific thermometers that measure the energy flow through the sample after excitation of the Y top layer with fs-laser pulses. In an experiment-based analytic solution to the nonequilibrium heat transport problem, we derive the individual contributions of the spins and the coupled electron-lattice system to the heat conduction. The full characterization of the spatiotemporal energy flow at different starting temperatures reveals that the spin excitations of antiferromagnetic Dy speed up the heat transport into the Dy layer at low temperatures, whereas the heat transport through this layer and further into the Y and Nb layers underneath is slowed down. The experimental findings are compared to the solution of the heat equation using macroscopic temperature-dependent material parameters without separation of spin and phonon contributions to the heat. We explain why the simulated energy density matches our experiment-based derivation of the heat transport, although the simulated thermoelastic strain in this simulation is not even in qualitative agreement.

Figure 1

(a) Schematic of the sample. (b) Reciprocal space map at $T_i=165$ K of the sample with (0002) reflections of two Y and Dy layers, the (220) reflection of Nb layer, and the ($22\overline{4}0$) substrate (${\text{Al}}_2{\text{O}}_3$) reflection, respectively. (c) Bragg reflections along $Q_z$ obtained by integration of the RSM.

Figure 2

Transient strain $\varepsilon \left(t\right)$ for different initial temperatures $T_i$ after ultrafast laser heating at 3 mJ/${\text{cm}}^2$ fluence: solid lines depict the measured transient strain of (a) the two Y layers, (b) the Dy layer ${\varepsilon }_{Dy}$, and (c) the Nb layer. The dashed lines in panel (b) represent the unsuccessful attempt to simulate the strain ${\varepsilon }_{Dy}^{av}\left(t\right)$ by the heat equation, i.e., without taking into account the fact that magnetic excitations and phonons contribute to the heat propagation and the strain.

Figure 3

(a) Transient increase of the energy density in the Dy layer ${\rho }_{Dy}^Q$ after optical excitation derived from the measurement according to Eq. (4). (b) Simulation of the energy density transported into the substrate according to the heat equation. (c) Symbols show the experimentally determined transient energy densities ${\rho }_{Y,Dy,Nb}^Q$ in each material. Solid lines represent simulations according to heat equation. Dotted lines show the experimentally derived energy densities in the spin and phonon system of Dy ${\rho }_{S,P}^Q$.

Figure 4

Temperature change in each layer after excitation at (a) 276 K and (b) 136 K. The temperature in the spin system is only well defined at $T<T_N$. Solid lines represent running averages as a guide to the eye.