Spin-Qubit Noise Spectroscopy of Magnetic Berezinskii-Kosterlitz-Thouless Physics.

We propose using spin-qubit noise magnetometry to probe dynamical signatures of magnetic Berezinskii-Kosterlitz-Thouless (BKT) physics. For a nitrogen-vacancy (NV) center coupled to two-dimensional XY magnets, we predict distinctive features in the magnetic noise spectral density in the sub-MHz to GHz frequency range. In the quasi-long-range ordered phase, the spectrum exhibits a temperature-dependent power law characteristic of algebraic spin correlations. Above the transition, the noise reflects the proliferation of free vortices and enables quantitative extraction of the vortex conductivity, a key parameter of vortex transport. These results highlight NV as a powerful spectroscopic method to resolve magnetic dynamics in the mesoscopic and low-frequency regimes and to probe exotic magnetic phase transitions.