The characterization of thermal and elastic properties at the nanometer length scale is fundamental for the implementation of materials in nanotechnology. Here, we show how four-wave mixing of extreme ultraviolet ultrashort pulses allows for high-precision measurements of nanoscale elasticity in thin suspended silicon nitride membranes through the generation and detection of Lamb waves at 10's of nm wavelengths. Our approach is contact-free and nondestructive, and it provides an estimate of both shear and longitudinal elastic moduli, without the need of nanopatterning. The data provide important information on nanoscale thermal transport and reveal a heat carrier behavior compatible with the diffusive regime. By controlling the fluence of the free-electron laser excitation pulses, we study the dependence of elastic moduli and the thermal relaxation rate on the sample temperature, which increases by hundreds of kelvins due to radiation absorption. At the same time, the experimental data allow us to estimate the characteristic time of phonon attenuation. The capability of determining this parameter, as well as the elastic moduli, at nanoscale wavelengths is a key aspect for the fundamental understanding of solids without translational invariance.

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