Experimental Determination of a Single Atom Ground State Orbital through Hyperfine Anisotropy

Historically, electron spin resonance (ESR) has provided excellent insight into the electronic, magnetic, and chemical structure of samples hosting spin centers. In particular, the hyperfine interaction between the electron and the nuclear spins yields valuable structural information of these centers. In recent years, the combination of ESR and scanning tunneling microscopy (ESR-STM) has allowed to acquire such information on individual spin centers of magnetic atoms bound atop a surface, while additionally providing spatial information about the binding site. Here, we conduct a full angle-dependent investigation of the hyperfine splitting for individual titanium atoms on MgO/Ag(001) by measurements in a vector magnetic field. We observe strong anisotropy in both the g-factor and the hyperfine tensor. Combining the results of the hyperfine splitting with the symmetry properties of the binding site obtained from STM images and a basic point charge model allows us to predict the shape of the electronic ground state configuration of the titanium atom. Relying on experimental values only, this method paves the way for a new protocol for electronic structure analysis for spin centers on surfaces.