Nanomechanical probing and strain tuning of the Curie temperature in suspended Cr${}_2$Ge${}_2$Te${}_6$ heterostructures

Two-dimensional (2D) magnetic materials with strong magnetostriction are interesting systems for strain-tuning the magnetization, enabling potential for realizing spintronic and nanomagnetic devices. Realizing this potential requires understanding of the magneto-mechanical coupling in the 2D limit. In this work, we suspend thin Cr${}_2$Ge${}_2$Te${}_6$ layers, creating nanomechanical membrane resonators. We probe its mechanical and magnetic properties as a function of temperature and strain. Pronounced signatures of magneto-elastic coupling are observed in the temperature-dependent resonance frequency of these membranes near $T_{\mathrm{C}}$. We further utilize Cr${}_2$Ge${}_2$Te${}_6$ in heterostructures with thin layers of WSe${}_2$ and FePS${}_3$, which have positive thermal expansion coefficients, to compensate the negative thermal expansion coefficient of Cr${}_2$Ge${}_2$Te${}_6$ and quantitatively probe the corresponding $T_{\mathrm{C}}$. Finally, we induce a strain of $0.016\mathrm{\%}$ in a suspended heterostructure via electrostatic force and demonstrate a resulting enhancement of $T_{\mathrm{C}}$ by $2.5\pm 0.6$ K in the absence of an external magnetic field.