Ultrafast negative thermal expansion driven by spin disorder

We measure the transient strain profile in a nanoscale multilayer system composed of yttrium, holmium, and niobium after laser excitation using ultrafast x-ray diffraction. The strain propagation through each layer is determined by transient changes in the material-specific Bragg angles. We experimentally derive the exponentially decreasing stress profile driving the strain wave and show that it closely matches the optical penetration depth. Below the Néel temperature of Ho, the optical excitation triggers negative thermal expansion, which is induced by a quasi-instantaneous contractive stress and a second contractive stress contribution increasing on a 12-ps timescale. These two timescales were recently measured for the spin disordering in Ho [Rettig et al., Phys. Rev. Lett. 116, 257202 (2016)]. As a consequence, we observe an unconventional bipolar strain pulse with an inverted sign traveling through the heterostructure.

Figure 1

(a) Specific heat of Ho [38, 39] separated into the three contributions $C_{\text{e,ph,sp}}\left(T\right)$, where the electron contribution $C_{\text{e}}\left(T\right)$ is hardly visible and the spin contribution $C_{\text{sp}}$ even exceeds the phonon contribution $C_{\text{ph}}$ at some temperatures. (b) $c$ axis of the Ho thin film as a function of temperature, showing large NTE below $T_{\text{N}}=132\mathrm{K}$. (c)–(e) Schematics of the hexagonal lattice illustrating the $c$-axis lattice change and the helical spin order below $T_{\text{N}}$. (f) Schematic of the layer stacking and the pump-probe geometry. (g) The RSM including separated Bragg peaks of Y, Ho, sapphire, and Nb. The slices of the RSM used for (h) and the time-resolved measurements are shown in red (Nb) and blue (Ho+Y). (h) The projection of the full RSM (gray) and measurements along the slices with a fixed angle $\omega$ (red and blue).

Figure 2

Transient lattice strain $\varepsilon$ for (a) Ho, (b) Y, and (c) Nb after laser excitation in the PM (red) and AFM (blue) phases as determined from UXRD. The thin solid line at 17 ps indicates the time it takes the maximum expansion starting at the surface to propagate to the Ho/Y interface. At this time Ho is maximally expanded, and Y is fully compressed since the expansive part of the bipolar strain is fully in the Ho layer, whereas the leading compressive part is only in the Y layer. The thin line at 26 ps indicates the same fully compressed situation for the Nb layer. In the AFM phase Ho [in (a)] has a 6-ps delay of the maximal contraction compared to the maximal PM expansion.

Figure 3

(a) Zoom of the first 45 ps of the Nb data from Fig. 2. The black line shows an exponential fit to the strain in the PM phase, which is used to extract the driving stress via Hooke's law. (b)–(f) Stress (dashed) and strain profiles for selected delays in the heterostructure from a simulation. To avoid unimportant rapid oscillations in this graph, the temporal stress profile was smoothed by a 0.5-ps Gaussian function. The NTE stress in Ho rises with $\tau =12\mathrm{ps}$. The inverted strain profile is most prominently seen in (c) and (d) in the Y and Nb layers, respectively. As an illustration, a video sequence of this temporal evolution of the stress profile and the strain wave is given in the Supplemental Material [41].

Figure 4

The simulated spatiotemporal strain profiles show the traveling sound waves in the heterostructure in the (a) PM and (b) AFM phases. (c)–(e) Simulated strain for the PM phase in the three layers (red) is compared to the data. (f)–(h) Simulations for the AFM phase with varying time constant $\tau =0$, 6, 12, and 18 ps. The best match to the data is obtained for $\tau =12\mathrm{ps}$.