Quantum-Impurity Relaxometry of Magnetic Berezinskii-Kosterlitz-Thouless Physics

The Berezinskii-Kosterlitz-Thouless (BKT) transition is a hallmark of topology-driven phenomena. Recent advances in exfoliating monolayer van der Waals magnets have opened new avenues for studying magnetic BKT physics and exploring the transport properties of spins and magnetic vortices for spintronic applications. Quantum-impurity relaxometry offers a non-invasive and highly informative probe for magnetic fluctuations on mesoscopic scales, providing high resolution in the desired frequency range. In this work, we theoretically investigate the magnetic fluctuations associated with the magnetic BKT transition and their signatures in relaxometry measurements. This method can effectively extract the phenomenological vortex diffusion constant above the transition temperature, and below the transition temperature, directly reveal the algebraic correlations. We also address finite-size effects, considering potential experiments on flakes of monolayer van der Waals magnet candidates.