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\item[Background] Ground-state spins and magnetic moments are sensitive tothe nuclear wave function, thus they are powerful probes to study the nuclearstructure of isotopes far from stability. \item[Purpose] Extend our knowledgeabout the evolution of the $1/2^+$ and $3/2^+$ states for K isotopes beyond the$N = 28$ shell gap. \item[Method] High-resolution collinear laser spectroscopyon bunched atomic beams. \item[Results] From measured hyperfine structurespectra of K isotopes, nuclear spins and magnetic moments of the ground stateswere obtained for isotopes from $N = 19$ up to $N = 32$. In order to drawconclusions about the composition of the wave functions and the occupation ofthe levels, the experimental data were compared to shell-model calculationsusing SDPF-NR and SDPF-U effective interactions. In addition, a detaileddiscussion about the evolution of the gap between proton $1d_{3/2}$ and$2s_{1/2}$ in the shell model and {\it{ab initio}} framework is also presented.\item[Conclusions] The dominant component of the wave function for the odd-$A$isotopes up to $^{45}$K is a $\pi 1d_{3/2}^{-1}$ hole. For $^{47,49}$K, themain component originates from a $\pi 2s_{1/2}^{-1}$ hole configuration and itinverts back to the $\pi 1d_{3/2}^{-1}$ in $^{51}$K. For all even-$A$ isotopes,the dominant configuration arises from a $\pi 1d_{3/2}^{-1}$ hole coupled to aneutron in the $\nu 1f_{7/2}$ or $\nu 2p_{3/2}$ orbitals. Only for $^{48}$K, asignificant amount of mixing with $\pi 2s_{1/2}^{-1} \otimes \nu (pf)$ isobserved leading to a $I^{\pi}=1^{-}$ ground state. For $^{50}$K, theground-state spin-parity is $0^-$ with leading configuration $\pi 1d_{3/2}^{-1}\otimes \nu 2p_{3/2}^{-1}$.

Shell structure of potassium isotopes deduced from their magnetic moments