In this paper, we discuss the theoretical framework and the experimental measurements of the magnetic moment of the charm baryons. The $Lambda_c^+$ magnetic moment is particularly interesting since it is equal to the magnetic moment of the charm quark. The measurements of the magnetic moments of other charm baryons, such as $Xi_c$, allow to perform detailed spectroscopy studies. The magnetic moment of the $Lambda_c$ can be determined using radiative charmonium decay and the present results show a tension with majority of theoretical predictions. As recently pointed out, the magnetic moment of the charm baryons can be directly measured using bent-crystal experiments at LHC. The possibility of precisely measure the magnetic moments of charm baryons needs precise measurement of their polarisation and weak decay parameters. In this paper, we revisit the formalism of the angular analysis needed for these measurements and make a detailed evaluation of initial polarisation of deflected $Lambda_c$ baryons as a function of crystal orientation. We found a special orientation of the crystal that gives the opportunity to measure the $Lambda_c$ dimensionless electric dipole moment almost with the same precision as its $g$-factor, which is more than an order of magnitude more efficient than suggested before. In conclusion, we stress the importance to perform precise measurements of initial polarisation and weak decay parameters of $Lambda_c$ baryon to effectively compare the direct and from decay measurements of magnetic moments.
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