Quantum spin liquid candidate as superior refrigerant in cascade demagnetization cooling

The quest for efficient low-temperature refrigeration is crucial for various applications, including space exploration and quantum computing. Adiabatic demagnetization refrigeration (ADR), utilizing the magnetocaloric effect (MCE), has been a cornerstone technology for achieving sub-Kelvin temperatures for nearly a century. However, conventional ADR systems employing paramagnetic salts face limitations in cooling power and thermal conductivity at low temperatures, particularly when operating between higher base temperatures (a few Kelvin) and ultra-low target temperatures (below 100 mK). The development of superior magnetocaloric materials with enhanced MCE properties is thus highly desirable to address these challenges and enable more efficient and powerful cooling systems. This research explores the potential of quantum spin liquid (QSL) candidates as novel refrigerants. QSLs are a class of highly frustrated quantum magnets that exhibit no long-range magnetic order down to zero temperature due to strong quantum fluctuations. Their unique properties, especially near quantum critical points (QCPs), suggest they could significantly enhance the performance of magnetic cooling systems. This study investigates the magnetocaloric properties of QSLs through theoretical simulations and experimental analysis of realistic materials, aiming to demonstrate their potential for a new paradigm of quantum critical refrigeration (QCR) that can be combined with conventional ADR to achieve substantially improved cooling performance.

The magnetocaloric effect (MCE), the change in temperature of a material upon exposure to a magnetic field, has been known for over a century and has formed the basis of adiabatic demagnetization refrigeration (ADR) since its inception in the 1930s. Early ADR systems relied primarily on paramagnetic salts, but these materials have limitations in terms of cooling power and operating temperature range. Recent advances in materials science and a deeper understanding of quantum magnetism have opened up new possibilities for improving ADR. The study of quantum criticality, where a quantum phase transition occurs at absolute zero temperature, has revealed that materials near their QCPs can exhibit enhanced MCE properties. This has spurred research into utilizing quantum critical systems for magnetic cooling, leading to the concept of 'quantum critical refrigeration' (QCR). Several studies have shown promising results using various quantum magnets, demonstrating the potential of this approach. However, the exploration of QSLs as QCR refrigerants remains a relatively unexplored area, despite the rapidly increasing interest in QSLs and their unique magnetic properties. This research builds upon this growing body of work by specifically investigating the suitability of QSLs as high-performance refrigerants.

This study employed a multi-pronged approach combining theoretical simulations with experimental analysis. First, the authors performed simulations of Heisenberg spin models on kagome and triangular lattices—models known to exhibit QSL behavior. The Hamiltonian for these models was defined as H = J Σ⟨ij⟩ Si • Sj + J' Σ⟨⟨ij⟩⟩ Si • Sj - B Σi Siz, where J and J' are antiferromagnetic spin couplings between nearest and next-nearest neighbors, respectively, and B is the external magnetic field. The simulations focused on the highly frustrated regime, where J'/J is small, known to be conducive to QSL ground states. To accurately compute the thermodynamic properties, particularly at low temperatures, the researchers utilized state-of-the-art thermal tensor network methods: linearized tensor renormalization group (LTRG) for 1D systems and exponential tensor renormalization group (XTRG) for 2D systems. These methods allow for accurate calculation of entropy, magnetization, and other relevant thermodynamic quantities. The polarization field Bc (where spins become fully polarized) was determined using semi-classical analysis and DMRG calculations. The MCE was characterized by examining entropy changes as a function of temperature and magnetic field. To evaluate the potential of QSLs in a practical setting, a cascade refrigeration design was proposed, combining QCR (using QSLs) and ADR (using paramagnetic salts) stages. This design leverages the complementary MCE characteristics of the two types of coolants to enhance the overall cooling capacity via magnetothermal pumping. The simulated QSL models were compared with an unfrustrated square lattice model to highlight the effects of frustration. Furthermore, the study incorporated experimental thermal data from two realistic materials—the 1D Tomonaga-Luttinger liquid (TLL) material YbAIO3 (YAO) and the triangular-lattice QSL candidate Na2BaCo(PO4)2 (NBCP)—to validate the theoretical findings. The experimental data were used to assess the cooling performance of these realistic QSL candidates in the proposed cascade refrigeration scheme.

The simulations revealed a strong MCE in the frustrated QSL models near their QCPs. The entropy curves showed that the QSL materials exhibited significantly larger entropies near the QCP than an unfrustrated square lattice model, implying a greater potential for cooling. The QSLs demonstrated a much larger temperature drop (ΔTM) during adiabatic demagnetization compared to paramagnetic salts. A key finding was the significant magnetothermal pumping effect observed when combining QSLs and paramagnetic salts in the cascade refrigeration design. This pumping effect results in a substantial increase in the overall cooling capacity. The simulations showed a marked enhancement in the isothermal entropy change at very low temperatures (e.g., 100 mK) for the QSL models, unlike paramagnetic salts that exhibit negligible change. The analysis of the magnetic Grüneisen parameter (Γs) further highlighted the distinct MCE properties of QSLs, showing a divergence near the QCP, in contrast to the peak near zero field for paramagnetic salts. Analysis of two realistic QSL candidate materials, YbAIO3 and Na2BaCo(PO4)2, demonstrated a giant enhancement in cooling capacity. Specifically, when combined with CrK(SO4)2·12H2O (CPA) in a cascade refrigerator operating between a 3 K heat sink and a 30 mK load, the enhancement exceeded 200%. This enhancement in cooling capacity translates to a significant increase in the hold time (duration of the cooling process), indicating a significant improvement in the practical performance of the refrigerator. The study also showed that the QSL materials in the upper stage of the cascade system act as effective thermal guards, preventing parasitic heat from the heat sink from negatively affecting the lower stage.

The findings of this study provide strong evidence that QSL materials are promising candidates for superior refrigerants, surpassing the performance of conventional paramagnetic salts used in ADR systems. The enhanced MCE near the QCPs of QSLs, coupled with the magnetothermal pumping effect in the cascade design, leads to a significant boost in cooling capacity and hold time. The validation of these findings using experimental data from two realistic QSL candidates further reinforces the potential for practical applications. This work demonstrates the feasibility of quantum critical refrigeration (QCR) as a viable alternative to, or enhancement of, conventional ADR. The significantly improved cooling capacity and hold time offer compelling advantages for various applications requiring ultra-low temperatures, particularly in space-based experiments and emerging quantum technologies. The results highlight the importance of spin frustration and low dimensionality as key factors in searching for superior magnetocaloric materials.

This research establishes the significant potential of quantum spin liquids (QSLs) as superior refrigerants for sub-Kelvin cooling. Through simulations and experimental analysis, the study demonstrates a giant enhancement in cooling capacity achieved through a cascade refrigeration design combining QSLs and paramagnetic salts. The results highlight the importance of spin frustration and low dimensionality in designing high-performance magnetocaloric materials. Future research could focus on exploring a broader range of QSL candidates, optimizing the cascade refrigeration design, and investigating the long-term stability and scalability of this technology for practical applications.

The study primarily relies on theoretical simulations and analysis of two specific QSL candidates. While the results are validated by experimental data from these materials, further experimental validation with a wider range of QSL materials is needed to confirm the generality of the findings. The proposed cascade refrigeration design is a theoretical model. Further engineering and experimental work are required to build a functional device and assess its overall efficiency and practicality. The simulations focused on specific spin models, and the influence of additional factors, such as lattice contributions and impurities, could warrant further investigation.