High-efficiency magnetic refrigeration using holmium

Abstract

Magnetic refrigeration (MR) is a method of cooling matter using a magnetic field. Traditionally, it has been studied for use in refrigeration near room temperature; however, recently MR research has also focused on a target temperature as low as 20 K for hydrogen liquefaction. Most research to date has employed high magnetic fields (at least 5 T) to obtain a large entropy change, which requires a superconducting magnet and, therefore, incurs a large energy cost. Here we propose an alternative highly efficient cooling technique in which small magnetic field changes, Δμ₀H ≤ 0.4 T, can obtain a cooling efficiency of -ΔS_M/Δμ₀H = 32 J kg^-1K^-1T^-1, which is one order of magnitude higher than what has been achieved using typical magnetocaloric materials. Our method uses holmium, which exhibits a steep magnetization change with varying temperature and magnetic field. The proposed technique can be implemented using permanent magnets, making it a suitable alternative to conventional gas compression-based cooling for hydrogen liquefaction.

Fig. 1. Comparison between conventional ferromagnet and antiferromagnet with a metamagnetic phase transition in entropy−temperature diagram.

a Thermal variation of magnetic entropy change in typical magnetic fields (H) from H/J = 0 to H/J = 5.0 (where J is the ferromagnetic exchange constant) for ferromagnetic cases simulated in a previous theoretical study in ref. . The temperature is normalized to the Curie temperature T_C. b Schematic illustration of magnetic refrigeration (MR) cycle for the case of antiferromagnetic (AFM) material that shows a metamagnetic phase transition. Magnetic fields are represented by zero field μ₀H = 0 and finite fields H₁ < H₂ < H₃ < H₄ < H₅. For the AFM case in b, the metamagnetic phase transition occurs over a small magnetic field change, ΔH = ∣H₂ − H₃∣, during the MR cycle A′ → B′ → C′ → A′.

Fig. 2. Magnetization curves in holmium single crystal.

The magnetic field was applied along the hexagonal $\left[10\overline{1}0\right]$ direction at temperature from 2 to 200 K.

Fig. 3. Magnetic entropy change ΔS_M as a function of temperature and magnetic field along the hexagonal [101¯0] direction in holmium single crystal.

The ΔS_M data are estimated by Eq. (1) with an integral range from μ₀H₁ = 0 T to μ₀H₂ = μ₀H from the observed magnetization data.

Fig. 4. Magnetic field dependence of magnetic caloric efficiency, −ΔS_M/Δμ₀H (J kg⁻¹ K⁻¹), for the temperature range from 20 to 45 K in Ho.

The magnetic field was applied along the hexagonal $\left[10\overline{1}0\right]$ direction. The −ΔS_M/Δμ₀H data are calculated by −ΔS_M divided by Δμ₀H = 0.1 T. The −ΔS_M is estimated by using Eq. (1) with the integration range from μ₀H₁ = μ₀H to μ₀H₂ = μ₀H + Δμ₀H. For comparison between the present results and those for a typical magnetocaloric material, the efficiency for ferromagnetic HoAl₂ is also shown in the inset. The data for HoAl₂ were taken from a previous paper.

Fig. 5. Results of the direct measurement of temperature change in holmium.

a Mapping of temperature change ΔT as a function of the bias magnetic field μ₀H₀ and temperature. b Typical heat cycles when the magnetic field rises from each μ₀H₀ by Δμ₀H = 0.4 T. The inset shows a magnification of the most efficient cycle for μ₀H₀ = 0.5 T and T = 28.2 K.

Fig. 6. Schematic illustration of active magnetic regenerator (AMR) using permanent magnets and holmium.

a A cross-section of AMR setup^,. 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.