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The Ca$^+$, Sr$^+$, Ba$^+$, and Yb$^+$ ions immersed in an ultracold gas ofthe Cr atoms are proposed as experimentally feasible heteronuclear systems inwhich ion-atom interactions at ultralow temperatures can be controlled withmagnetically tunable Feshbach resonances without charge transfer and radiativelosses. \textit{Ab initio} techniques are applied to investigateelectronic-ground-state properties of the (CaCr)$^+$, (SrCr)$^+$, (BaCr)$^+$,and (YbCr)$^+$ molecular ions. The potential energy curves, permanent electricdipole moments, and static electric dipole polarizabilities are computed. Thespin restricted open-shell coupled cluster method restricted to single, double,and noniterative triple excitations, RCCSD(T), and the multireferenceconfiguration interaction method restricted to single and double excitations,MRCISD, are employed. The scalar relativistic effects are included within thesmall-core energy-consistent pseudopotentials. The leading long-range inductionand dispersion interaction coefficients are also reported. Finally, magneticFeshbach resonances between the Ca$^+$, Sr$^+$, Ba$^+$, and Yb$^+$ ionsinteracting with the Cr atoms are analyzed. The present proposal opens the waytowards robust quantum simulations and computations with ultracold ion-atomsystems free of radiative charge transfer losses.

Ultracold magnetically tunable interactions without radiative charge transfer losses between Ca$^+$, Sr$^+$, Ba$^+$, and Yb$^+$ ions and Cr atoms