  Unusual behavior of quantum materials commonly arises from their effective
low-dimensional physics, which reflects the underlying anisotropy in the spin
and charge degrees of freedom. Torque magnetometry is a highly sensitive
technique to directly quantify the anisotropy in quantum materials, such as the
layered high-T$_c$ superconductors, anisotropic quantum spin-liquids, and the
surface states of topological insulators. Here we introduce the magnetotropic
coefficient $k=\partial^2 F/\partial \theta^2$, the second derivative of the
free energy F with respect to the angle $\theta$ between the sample and the
applied magnetic field, and report a simple and effective method to
experimentally detect it. A sub-$\mu$g crystallite is placed at the tip of a
commercially available atomic force microscopy cantilever, and we show that $k$
can be quantitatively inferred from a shift in the resonant frequency under
magnetic field. While related to the magnetic torque $\tau=\partial F/\partial
\theta$, $k$ takes the role of torque susceptibility, and thus provides
distinct insights into anisotropic materials akin to the difference between
magnetization and magnetic susceptibility. The thermodynamic coefficient $k$ is
discontinuous at second-order phase transitions and subject to Ehrenfest
relations with the specific heat and magnetic susceptibility. We apply this
simple yet quantitative method on the exemplary cases of the Weyl-semimetal NbP
and the spin-liquid candidate RuCl$_3$, yet it is broadly applicable in quantum
materials research.
