Dynamical magnetotropic susceptibility as a new probe of Kitaev materials and beyond
The magnetotropic susceptibility $k(\omega)$ probes ultra-low-frequency uniform fluctuations. For a crystal mounted on an oscillating cantilever in a magnetic field, it is defined as the ratio of torque to angular-displacement amplitude. Its real and imaginary parts determine the oscillation-frequency shift and crystal-induced damping. It is a low-energy probe of uniform $q=0$ spin and charge degrees of freedom. We demonstrate this by deriving $k(\omega)$ within linear response theory for a generic correlated-electron Hamiltonian with charge and spin degrees of freedom. Although it covers metallic and insulating magnets, correlated paramagnets, and exotic quantum critical points, we focus on limiting cases. For insulating spin systems $k(0)$ is sensitive to magnetic anisotropy whereas its finite-frequency imaginary part probes uniform dynamical spin susceptibility even in spin-symmetric models. For metallic systems we identify when eddy currents cause low-frequency damping. Our numerical results focus on Kitaev-material magnetotropic response. Using auxiliary-field quantum Monte Carlo with machine-learning-based sign-problem optimization we compute $k(\omega)$ for several models proposed for $\alpha$-RuCl$_3$. The observed low-temperature scaling of $k(0)/T$ with $B/T$ results from dominant Kitaev couplings: parameter sets without dominant Kitaev coupling do not exhibit this scaling. It remains robust upon inclusion of optical phonons. Beyond the static response, $k''(\omega)$ for the $\alpha$-RuCl$_3$ parameter set reproducing the experimental $k(0)$ data shows local-moment features at high and low $T$, with a single peak at the Larmor frequency. Beyond Kitaev systems we highlight broader applications. Probing ultra-low-energy uniform charge fluctuations is pertinent to Kondo destruction quantum criticality, of broad interest in strange metallicity and unconventional superconductivity.