a A cross-section of AMR setup2,24. The AMR constitutes a superconducting magnet, magnetocaloric materials, refrigerant space, and heat baths (low- and high-temperature sides). The magnetocaloric materials have different phase transition temperatures to obtain a large magnetocaloric effect at each position. b Possible setup of the proposed magnetic refrigeration (MR) system using a small change in magnetic field. The system constitutes pairs of permanent magnets, magnetocaloric material (holmium), refrigerant space, and heat baths. The set of permanent magnets generate a magnetic field gradient from 0.2 to 1.2 T as a bias magnetic field μ0H0 to change the magnetic phase transition temperature of the magnetocaloric material Ho. The magnetic field change Δμ0H is realized by mechanically moving the magnetocaloric material in the horizontal direction in this figure. c The MR cycle of the proposed AMR system. The gray color in the magnetic field and temperature graphs denotes the bias field μ0H0 and the original temperature T0, respectively. The colored areas in the graphs are the changes in the magnetic field Δμ0H and temperature ΔT.