Accurate Prediction of the Magnetic Ordering Temperature of Ultralow-Temperature Magnetic Refrigerants

Adiabatic demagnetization refrigeration is known to be the only cryogenic refrigeration technology that can achieve ultralow temperatures (≪1 K) at gravity-free conditions. The key indexes to evaluate the performance of magnetic refrigerants are their magnetic entropy changes (-ΔS_m) and magnetic ordering temperature (T₀). Although, based on the factors affecting the -ΔS_m of magnetic refrigerants, one has been able to judge if a magnetic refrigerant has a large -ΔS_m, how to accurately predict their T₀ remains a huge challenge due to the fact that the T₀ of magnetic refrigerants is related to not only magnetic exchange but also single-ion anisotropy and magnetic dipole interaction. Here, we, taking GdCO₃F (1), Gd(HCOO)F₂, Gd₂(SO₄)₃·8H₂O, GdF₃, Gd(HCOO)₃ and Gd(OH)₃ as examples, demonstrate that the T₀ of magnetic refrigerants with very weak magnetic interactions and small anisotropy can be accurately predicted by integrating mean-field approximation with quantum Monte Carlo simulations, providing an effective method for predicting the T₀ of ultralow-temperature magnetic refrigerants. Thus, the present work lays a solid foundation for the rational design and preparation of ultralow-temperature magnetic refrigerants in the future.