Magnetic ordered structure dependence of magnetic refrigeration efficiency

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. {\bf 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.