Thermal field noise from magnetic nanostructures

We show that thermally excited modes in magnetic nanostructures produce GHz-frequency stray field fluctuations, and that these fluctuations are large enough to be detected by diamond NV center magnetometry. In recent work, van der Sar et al. measured fluctuating stray fields 50 nm from a 30 nm-thick Permalloy film using nitrogen vacancy (NV) centers in diamond, demonstrating magnetometry of the thermally excited spin waves.[1] Here, we use micromagnetic modeling to calculate field noise for a series of Permalloy-like disks, 3 nm thick, with diameters ranging from 25 nm to 5000 nm. We calculate the pulsed-field response of the disks and use the fluctuation-dissipation theorem to obtain the stray field noise. Different vector components of the field fluctuations highlight spectral density peaks corresponding to modes with different symmetries. Typical field fluctuation amplitudes are on the order of 1 nT/Hz^1/2 at a spot 100 nm above the disk centers. Field noise at this level is measurable through T₁ relaxometry of NV centers. The NV spin state has a base line T₁ on the order of milliseconds, but field noise accelerates relaxation; at the field noise levels we calculate, T₁ is on the order of 1 μs, well above background.

[1] T. van der Sar, et. al., Nat. Comm, 6, 7886, (2015).