We have investigated the relation between magnetic ordered structure and magnetic refrigeration efficiency in the Ising model on a simple cubic lattice using Monte Carlo simulations. The magnetic entropy behaviors indicate that the protocol, which was first proposed in [Appl. Phys. Lett. 104, 052415 (2014).], can produce the maximum isothermal magnetic entropy change and the maximum adiabatic temperature change in antiferromagnets. Furthermore, the total amount of heat transfer under the proposed protocol reaches a maximum. The relation between measurable physical quantities and magnetic refrigeration efficiency is also discussed. FIG. 2. (Color online) Schematics of ordered magnetic structures in the Ising models on a simple cubic lattice. The signs of the magnetic interactions J ab and Jc and the wave vector k, when the lattice constant is set to unity, are shown for each magnetic structure. These figures were drawn by VESTA 84 .