When covered by gadolinium (Gd) atoms, silicene, a freestanding monolayer of Si atoms in a honeycomb network, remains stable above the room temperature and becomes a two-dimensional (2D) ferromagnetic semiconductor, despite the antiferromagnetic ground state of three-dimensional bulk GdSi2 crystal. In thin GdSi2 multilayers, even if magnetic moments are ordered parallel in the same Gd atomic planes, they are antiparallel between nearest Gd planes; hence they exhibit a ferrimagnetic behavior. In contrast, a freestanding Gd2Si2 monolayer constructed by covering silicene from both sides by Gd atoms is a stable antiferromagnetic metal due to the mirror symmetry. While multilayers covered by Gd from both sides having an odd number of Gd planes have a ferrimagneticlike ground state, even-numbered ones have antiferromagnetic ground state, but none of them is ferromagnetic. Silicon atoms intervening between Gd planes are responsible for these intriguing magnetic orders conforming with the recent experiments performed on Si(111) surface. Additionally, the magnetic states of these 2D gadolinium disilicide monolayers can be monitored by applied tensile strain and by the coverage/decoration of Gd. These predictions obtained by using first-principles, spin-polarized, density functional theory calculations combined with Monte Carlo simulations herald that C, B, Si, Ge, Sn, and their compounds functionalized by rare-earth atoms can lead to novel nanostructures in 2D spintronics.