Precision spectroscopy of the $3s-3p$ fine-structure doublet in $Mg^+$

We apply a recently demonstrated method for precision spectroscopy on strong transitions in trapped ions to measure both fine-structure components of the 3s−3p transition in 24Mg+ and 26Mg+. We deduce absolute frequency reference data for transition frequencies, isotope shifts, and fine-structure splittings that in particular are useful for comparison with quasar absorption spectra, which test possible space-time variations of the fine-structure constant. The measurement accuracy improves previous literature values, when existing, by more than two orders of magnitude.