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Magnetometers based on ensembles of nitrogen-vacancy centres are a promisingplatform for continuously sensing static and low-frequency magnetic fields.Their combination with phase-sensitive (lock-in) detection creates a highlyversatile sensor with a sensitivity that is proportional to the derivative ofthe optical magnetic resonance lock-in spectrum, which is in turn dependant onthe lock-in modulation parameters. Here we study the dependence of the lock-inspectral slope on the modulation of the spin-driving microwave field. Given thepresence of the intrinsic nitrogen hyperfine spin transitions, weexperimentally show that when the ratio between the hyperfine linewidth andtheir separation is $\gtrsim 1/4$, square-wave based frequency modulationgenerates the steepest slope at modulation depths exceeding the separation ofthe hyperfine lines, compared to sine-wave based modulation. We formulate amodel for calculating lock-in spectra which shows excellent agreement with ourexperiments, and which shows that an optimum slope is achieved when thelinewidth/separation ratio is $\lesssim 1/4$ and the modulation depth is lessthen the resonance linewidth, irrespective of the modulation function used.

Optimised frequency modulation for continuous-wave optical magnetic resonance sensing using nitrogen-vacancy ensembles