Frustrated magnet for adiabatic demagnetization cooling to milli-Kelvin temperatures

ARTICLE https://doi.org/10.1038/s43246-021-00142-1 OPEN Frustrated magnet for adiabatic demagnetization cooling to milli-Kelvin temperatures 1234567890():,; Yoshifumi Tokiwa Philipp Gegenwart 1,2 ✉, Sebastian Bachus1, Kavita Kavita1, Anton Jesche 1, Alexander A. Tsirlin1 & 1 Generation of very low temperatures has been crucially important for applications and fundamental research, as low-temperature quantum coherence enables operation of quantum computers and formation of exotic quantum states, such as superfluidity and superconductivity. One of the major techniques to reach milli-Kelvin temperatures is adiabatic demagnetization refrigeration. This method uses almost non-interacting magnetic moments of paramagnetic salts where large distances suppress interactions between the moments. The large spatial separations are facilitated by water molecules, with a drawback of reduced stability of the material. Here, we show that the water-free frustrated magnet KBaYb(BO3)2 can be ideal for refrigeration, achieving at least 22 mK. Compared to conventional refrigerants, KBaYb(BO3)2 does not degrade even under high temperatures and ultra-high vacuum. Further, its magnetic frustration and structural randomness enable cooling to temperatures several times lower than the energy scale of magnetic interactions, which is the main limiting factor for the base temperature of conventional refrigerants. 1 Experimental Physics VI, Center for Electronic Correlations and Magnetism, University of Augsburg, Augsburg, Germany. 2 Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, Ibaraki, Japan. ✉email: COMMUNICATIONS MATERIALS | (2021)2:42 | https://doi.org/10.1038/s43246-021-00142-1 | www.nature.com/commsmat 1 ARTICLE COMMUNICATIONS MATERIALS | https://doi.org/10.1038/s43246-021-00142-1 S uppression of thermal fluctuations by lowering temperature gives access to intricate and potentially usable quantum effects. Major discoveries, such as the quantum Hall effect and superfluidity and superconductivity, have been made by explorations of matter close to absolute zero1,2. Recently, the development of quantum computers and sensors for dark matter detection rendered low-temperature refrigeration an important technological challenge3,4. One of the viable methods for reaching the milli-K (mK) temperature range is adiabatic demagnetization refrigeration (ADR) using paramagnetic salts5–7. Its main advantages over the currently dominant technique, 3He–4He dilution refrigeration, are the simple construction of a cooling device and its operation without the usage of expensive 3He. The recent crisis of 3He, which was caused by the increased demand due to the construction of neutron detectors for defense against nuclear terrorism, raised serious concerns about the strong dependence of the current technology on such a scarcely available and ever more expensive gas8–10. This triggered renewed interest in ADR, as well as interesting proposals of completely new types of ADR materials11–19. The only advantage of 3He–4He dilution refrigeration is its capability of continuous cooling while conventional ADR is a single-shot technique. This makes the 3He–4He dilution refrigeration more commonly used than ADR. However, the situation may change thanks to recent developments of continuous ADR cooling20,21 and the availability of commercial continuous refrigerators based on ADR22. Therefore, ADR has the potential of becoming the main cooling technology already in near future, at least in the mK temperature range. ADR uses magnetic moments of almost-ideal paramagnets with very weak magnetic interaction J . Because the interaction is weak, magnetic moments are easily aligned by the external magnetic field, causing a reduction of entropy (Fig. 1a, b). Even at zero external magnetic field H = 0, magnetic moments of such almost-ideal paramagnets experience some small internal magnetic field produced by adjacent magnetic moments through magnetic interactions. This causes a tiny Zeeman splitting and magnetic order at the same energy scale ( Δ0  J ). Therefore, entropy, which is the driving force of ADR, decreases to zero below the temperature of T  J , thus putting a limit on the end temperature T f  J that can be reached via ADR with this material (Fig. 1b). As indicated by a black horizontal arrow in Fig. 1b, the entropy difference between H = 0 and H ≠ 0 is the key for ADR. While a perfect paramagnet with zero magnetic interactions would be an ideal refrigerant, having maximum entropy at zero fields down to zero temperature, there are always weak but finite interactions in real materials. For many decades ever since Debye6 and Giauque7 independently proposed ADR, water-containing paramagnetic salts have been materials of choice for cooling in the mK range5,23,24. In these materials, the interactions are reduced by large distances between the magnetic ions, which are separated by water molecules. However, an abundance of water makes these salts prone to decomposition. They deliquesce in a humid atmosphere and dehydrate in vacuum or upon even mild heating. Therefore, for repeated use without degradation, stable water-free materials with very weak magnetic interactions are desirable. Furthermore, ADR would be certainly beneficial for applications in ultra-highvacuum (UHV) apparatus, especially in scanning tunneling microscopy and angle-resolved photoemission spectroscopy where the necessity of chamber baking at high temperature and high vacuum for reaching UHV makes the use of current ADR materials essentially impossible. It is, therefore, desirable to find suitable ADR materials without water molecules. One promising candidate for H2O-free refrigerant is KBaYb (BO3)2 with magnetic Yb3+ ions. At sufficiently low 2 Fig. 1 Adiabatic demagnetization refrigeration. a Cooling process of a conventional paramagnet (left) and a frustrated magnet with impeded magnetic order (right). Green ovals represent singlet pairings in a shortrange correlated but long-range disordered state, such as a spin liquid caused by magnetic frustration25,33 or a random-singlet state caused by structural disorder34. b Entropy curves at zero and a finite magnetic field as a function of temperature for conventional paramagnets (black) and a system with suppressed magnetic order (red). While the former orders below some temperature Tm around Δ0, or J , the latter remains disordered down to much lower temperatures where Δ0 is an energy level splitting at zero external fields because of the internal field caused by magnetic interaction, J . For simplicity, a Schottky-type increase in entropy is assumed. Note, however, that the entropy increase may be much slower in a spin liquid because of its broad energy spectrum. Arrows with red and black dotted lines represent cooling processes for the conventional paramagnets (black) and frustrated magnets (red). c Crystal structure of KBaYb(BO3)2 with triangular layers of the Yb3+ ions. Black solid (...truncated)