Recently, a joint research team led by Professor Gang Su from Kavli Institute for Theoretical Physics (Kavli ITS) at University of Chinese Academy of Sciences (UCAS) and Professor Wei Li from Institute of Theoretical Physics (ITP), Chinese Academy of Sciences, through large-scale calculations by utilizing state-of-the-art finite-temperature tensor network states method, has comprehensively mapped out the temperature-magnetic field phase diagram of the Kitaev honeycomb lattice model in both ferromagnetic and antiferromagnetic cases. They discovered a giant magnetocaloric effect driven by topological excitations and proposed a new mechanism for ultra-low temperature cooling without the use of liquid helium, pointing to a new direction for the potential applications of Kitaev magnets. This work was recently published in Nature Communications 15, 7011 (2024).

In certain paramagnetic salts, it has been observed that free magnetic ions can induce a significant magnetocaloric effect. By using paramagnetic salt hydrates, sub-Kelvin cooling can be achieved through adiabatic demagnetization, a technique widely adopted in traditional adiabatic demagnetization refrigeration. However, while paramagnetic salts are relatively efficient for cooling, they have inherent limitations such as low magnetic ion density, poor chemical stability due to their hydrated structures, low thermal conductivity, and possible corrosiveness, etc., which might significantly restrict their practical applications as refrigerants.

Frustrated quantum magnets, on the other hand, may exhibit a high density of magnetic ions, strong spin fluctuations, and enhanced thermal conductivity due to magnetic excitations. Their stable material structures make them promising candidates for a new type of magnetic refrigerants, potentially enabling solid-state cooling at ultra-low temperatures. The Kitaev quantum spin liquid, due to the interplay of frustration and quantum fluctuations, does not form magnetic long-range order even at temperatures far below the interaction energy scale or at zero temperature. Its low-energy topological excitations carry a large low-temperature entropy, which can be effectively controlled by external fields to realize a significant magnetocaloric effect and, consequently, achieve ultra-low temperature cooling via topological excitations. This paves the way for exploring new mechanisms of solid-state refrigeration.

The research team utilized a state-of-the-art finite-temperature tensor network states method to systematically compute the temperature-magnetic field phase diagram of ferromagnetic and antiferromagnetic Kitaev honeycomb lattice models. They discovered that the fractional liquid phase in the intermediate temperature range of the ferromagnetic system exhibits a significant magnetocaloric effect. This effect is attributed to the nearly free Z₂ gauge flux generated by spin fractionalization, which can be described by a paramagnetic equation of state. Furthermore, thermodynamic calculations showed that, in the antiferromagnetic case, the intermediate magnetic field phase is a gapless U(1) quantum spin liquid phase with a spinon Fermi surface. This phase exhibits a large low-temperature entropy and an even more pronounced magnetocaloric effect, enabling ultra-low temperature solid-state cooling via adiabatic demagnetization. The results indicate that the cooling mechanism in this system differs from the traditional magnetothermal effect, where the magnetic entropy change is driven by the alignment of individual magnetic moments with the external field. Instead, this is a new type of magnetocaloric effect induced by collective excitations, such as topological excitations and emergent gauge fields, which the researchers have named the magnetocaloric effect of topological excitations.

The research team also investigated how to realize the topological excitation magnetocaloric effect in candidate Kitaev magnet materials, such as the Co-based honeycomb lattice magnet Na₂Co₂TeO₆. By exploring the effects of non-Kitaev interactions, such as Heisenberg interactions, on the magnetocaloric effect in these materials, they found that spin fractionalization and topological excitations stably exist within a certain energy/temperature range. The magnetocaloric effect induced by topological excitations is robust. This research demonstrates that Kitaev quantum magnets not only is essential for realizing topological quantum computing but also have broad potential applications in ultra-low temperature solid-state cooling without the need for liquid helium.

Figure 1: Schematic of the cooling mechanism by topological excitations in Kitaev honeycomb lattice magnets. In the traditional high-temperature paramagnetic phase, the magnetic moment M = CB/T, where C is the Curie constant, B is the magnetic field, and T is the temperature. In the fractional liquid phase at intermediate temperatures, the research team found that the magnetic moment also exhibits M = C_KB/T behavior, where C_K is the modified Curie constant. They discovered that the magnetic entropy carried by topological excitations accounts for half of the system's total entropy, leading to a significant magnetocaloric effect.

This work is the result of close collaboration between Professor Gang Su’s team at the UCAS and Professor Wei Li’s team at the ITP, CAS. The project was completed with contributions from Dr. Han Li (first author, postdoc at the Kavli ITS), Enze Lü (PhD student at the ITP), Ning Xi (postdoc at the ITP), Yuan Gao (PhD student at Beihang University), and Professor Yang Qi (Fudan University). The corresponding authors are Wei Li (ITP) and Gang Su (UCAS). The work was supported by the Chinese Academy of Sciences, the Ministry of Science and Technology, the National Natural Science Foundation of China, and the Fundamental Research Funds for the Central Universities.

Article link: https://www.nature.com/articles/s41467-024-51146-7