  Two-dimensional (2D) materials enable new types of magnetic and electronic
phases mediated by their reduced dimensionality like magic-angle induced phase
transitions, 2D Ising antiferromagnets and ferromagnetism in 2D atomic layers
and heterostructures. However, only a few methods are available to study these
phase transitions, which for example is particularly challenging for
antiferromagnetic materials. Here, we demonstrate that these phases can be
probed by the mechanical motion: the temperature dependent resonance frequency
and quality factor of multilayer 2D material membranes show clear anomalies
near the phase transition temperature, which are correlated to anomalies in the
specific heat of the materials. The observed coupling of mechanical degrees of
freedom to magnetic and electronic order is attributed to thermodynamic
relations that are not restricted to van der Waals materials. Nanomechanical
resonators, therefore, offer the potential to characterize phase transitions in
a wide variety of materials, including those that are antiferromagnetic,
insulating or so thin that conventional bulk characterization methods become
unsuitable.
