Magnetic noise due to interactions between bulk impurities and electrons in nitrogen vacancy center diamonds

Nitrogen Vacancy (NV) Centers diamond present great interest as robust atomic-scale magnetic field sensors. One of the serious problems of NV center diamond devices is electric and magnetic field noise. The noise causes ODMR line-broadening, which reduce sensitivity of the devices. In this work we theoretically study the magnetic field noise caused by the magnetic dipole-dipole interactions between the impurities of carbon-13 and nitrogen-14 and the electron in the NV center. We use the cluster correlation expansion method to calculate the magnetic field fluctuations, and then, obtain the noise spectrum. The noise is greater at lower frequencies but rapidly decrease at higher frequencies.