Room temperature relaxometry of single nitrogen-vacancy centers in proximity to $\alpha$-RuCl$_3$ nanoflakes

Investigating spin and charge noise in strongly correlated electron systems is a valuable way to analyze their physical properties and unlock new phases of matter. In this context, nitrogen-vacancy (NV) center-based magnetometry has been proven to be a versatile sensor for various classes of magnetic materials in broad temperature and frequency ranges. Here, we use longitudinal relaxation time $T_1$ of single NV centers to investigate the spin dynamics of nanometers-thin flakes of $\alpha$-RuCl$_3$ at room temperature. We observe a significant reduction in the $T_1$ in the presence of $\alpha$-RuCl$_3$ in proximity to our NVs, which we attribute to paramagnetic spin noise confined in the 2D hexagonal plane. Furthermore, the $T_1$ time exhibits an almost linear increase with an applied external magnetic field. We associate this trend with the alteration of spin and charge noise in $\alpha$-RuCl$_3$ under an external magnetic field. These findings suggest that the influence of the room-temperature spin dynamics of $\alpha$-RuCl$_3$ on the longitudinal relaxation time of the NV center can be used to gain information on the material itself and the technique to be used on other 2D materials.