ABSTRACT Background: Magnetic dipole (M1) excitation is the leading mode of nuclear excitation by the magnetic field, which couples unnatural-parity states. Since the M1 excitation occurs mainly in open-shell nuclei, the nuclear pairing effect is expected to play a role. Considering the M1 operator form, it can provide the information on the spin-related properties, including the spin component of dinucleon correlations. Purpose: We investigate the M1 excitation of the systems with two valence nucleons above the closed-shell core. The corresponding version of the M1 sum rule, which can be used to validate theoretical and experimental approaches, is also discussed. Methods: Three-body model, which consists of a rigid spherical core and two valence nucleons, is employed. Interactions for its two-body subsystems are phenomenologically determined so as to reproduce the two-body and three-body energies. The M1 operator up to the one-body-operator level is utilized to compute the M1 transitions between the 0+ ground state and 1+ excited states. Results:Thethree-body-modelcalculationsfor 18O, 18Ne,and 42Ca nucleidemonstrateasignificanteffectofthe pairing correlation on the low-lying M1 transitions. The introduced M1 sum rule can be utilized as a benchmark for model calculations of these systems. The total sum of the M1 transition strength is shown to be relative with the coupled spin of valence nucleons in the open shell. Conclusions: The M1 excitation can be a suitable tool to investigate the pairing correlation in medium. Further studies of M1 transitions are on demand to validate and optimize the pairing models.