Background: Ground-state spins and magnetic moments are sensitive to the nuclear wave function, thus they are powerful probes to study the nuclear structure of isotopes far from stability.Purpose: Extend our knowledge about the evolution of the 1/2+ and 3/2+ states for K isotopes beyond the N=28 shell gap.Method: High-resolution collinear laser spectroscopy on bunched atomic beams.Results: From measured hyperfine structure spectra of K isotopes, nuclear spins, and magnetic moments of the ground states were obtained for isotopes from N=19 up to N=32. In order to draw conclusions about the composition of the wave functions and the occupation of the levels, the experimental data were compared to shell-model calculations using SDPF-NR and SDPF-U effective interactions. In addition, a detailed discussion about the evolution of the gap between proton 1d3/2 and 2s1/2 in the shell model and ab initio framework is also presented.Conclusions: The dominant component of the wave function for the odd-A isotopes up to K45 is a π1d−13/2 hole. For K47,49, the main component originates from a π2s−11/2 hole configuration and it inverts back to the π1d−13/2 in K51. For all even-A isotopes, the dominant configuration arises from a π1d−13/2 hole coupled to a neutron in the ν1f7/2 or ν2p3/2 orbitals. Only for K48, a significant amount of mixing with π2s−11/2⊗ν(pf) is observed leading to a Iπ=1− ground state. For K50, the ground-state spin-parity is 0− with leading configuration π1d−13/2⊗ν2p−13/2.< Réduire