Intrinsic spin noise in MgO magnetic tunnel junctions

We consider two intrinsic sources of noise in ultra-sensitive magnetic field sensors based on MgO magnetic tunnel junctions, coming both from $^{25}$Mg nuclear spins ($I=5/2$, 10% natural abundance), and S=1 Mg-vacancies. While nuclear spins induce noise peaked in the MHz frequency range, the vacancies noise peaks in the GHz range. We find that the nuclear noise in submicron devices has a similar magnitude than the $1/f$ noise, while the vacancy-induced noise dominates in the GHz range. Interestingly, the noise spectrum under a finite magnetic field gradient may provide spatial information about the spins in the MgO layer.