Vector magnetometry based on S=3/2 electronic spins

Electronic spin systems with S > 1/2 provide an efficient method for dc vector magnetometry, since the conventional electron spin resonance spectra at a given magnetic field reflect not only the field strength but also orientation in the presence of strong spin-spin interactions. S = 1 spins, e.g., the nitrogen-vacancy centers in diamond, have been intensively investigated for such a purpose. In this report, we compare S = 1 and 3/2 spins, and discuss how one can apply general principles for the use of high-spin systems as a vector magnetometer to the S = 3/2 spin systems. We find analytical solutions which allow a reconstruction of the magnetic field strength and polar angle using the observed resonance transitions if a uniaxial symmetry exists for the spin-spin interaction as in S = 1 systems. We also find that an ambiguity of determining the field parameters may arise due to the unique properties of S = 3/2 systems, and present solutions for it utilizing additional transitions in the low-field region. The electronic spins of the silicon vacancy in silicon carbide will be introduced as a model for the S = 3/2 dc vector magnetometer and the practical usage of it, including the magic-angle spinning type method, will be presented too.