Frustrated magnet for adiabatic demagnetization cooling to milli-Kelvintemperatures
Y. Tokiwa1,2), S. Bachus2), K. Kavita2), A. Jesche2) A. A. Tsirlin2) and P. Gegenwart2)
1): Materials Physics for Heavy Element Systems Gr., JAEA 2): Univ. Augsburg

Generation of very low temperatures has been crucially
important for applications and fundamental research, as lowtemperature quantum coherence enables operation of quantum
computers and formation of exotic quantum states, such as
superfluidity and superconductivity. Recently, the developmentof quantum computers and sensors for dark matter detection
rendered low-temperature refrigeration an important
technological challenge [1,2]. One of the viable methods forreaching milli-K (mK) temperature range is adiabatic
demagnetization refrigeration (ADR) using paramagnetic salts.
Its main advantages over the currently dominant technique, 3He4He dilution refrigeration, are the simple construction of acooling device and its operation without the usage of expensive
3He. The recent crisis of 3He, which was caused by the increased
demand due to construction of neutron detectors for defense
against nuclear terrorism, raised serious concerns about thestrong dependence of the current technology on such a scarcely
available and ever more expensive gas [3]. This triggered
renewed interest in ADR.
The only advantage of 3He-4He dilution refrigeration is its
capability of continuous cooling, while conventional ADR is asingle-shot technique, which heats up once after reaching its
lowest temperature. This makes the 3He-4He dilution
refrigeration more commonly used than ADR. However, thesituation may change thanks to recent developments ofcontinuous ADR cooling [4,5] and availability of commercial
continuous refrigerators based on ADR. Therefore, ADR has thepotential of becoming the main cooling technology already innear future, at least in the mK temperature range.
In ADR, fluctuations of magnetic moments absorb heat fromsurroundings. Usually a magnet orders magnetically below
some temperature, which is about equal to strength ofinteraction between magnetic moments. Below such ordering
temperatures magnets cannot cool by ADR process anymore
because magnetic moments stop fluctuating. This sets a limit for
the final temperature which refrigerant materials can achieve.
A key to overcome this limitation is quantum fluctuations. Inclassical thermodynamics, magnetic moments or particles likeatoms are completely stationary at absolute zero temperature.
However, according to quantum mechanics, magnetic momentsor particles fluctuate even at absolute zero. This is called
quantum fluctuations. For example, Helium does not solidify
and remains to be fluid even at absolute zero temperature
because of quantum fluctuations, although most of materials
solidify at low temperatures because of reduction of thermalfluctuations. For magnets, geometrical frustration of magnetic
interaction suppresses ordering of magnetic moments and maylead magnets to fluctuating states even at zero temperature(Fig.1). Therefore, such “frustrated magnets” may be able toreach very low temperature even below the limitation.
We demonstrate the effective refrigeration with an frustrated
magnet KBaYb(BO3)2 that shows excellent ADR performanceon par with conventional paramagnetic salts, and achieve an end
temperature Tf of 22 mK, starting from a temperature of 2 K ata magnetic field of 5 T (Fig.2) [6]. In this compound, magnetic
Yb3+ ions, forming frustrated triangular lattice, are responsible
for magnetic properties. From Curie-Weiss behavior ofmagnetic susceptibility, the strength of magnetic interaction of
Yb3+ moments is estimated to be 40 mK, below which magnetic
ordering is usually expected. From our measurements, however,magnetic ordering is absent down to 22 mK, well below thestrength (Fig.2). This is due to suppression of magnetic ordering
because of geometrical frustration. We believe that this study
will pave a road for usage of frustrated magnets for ADR,
cooling even below the conventional limit for magneticrefrigeration.

Fig. 1 (a) Antiferromagnetic ordering on square lattice. (b) Frustrated
antiferromagnetic interaction on triangular lattice.

Fig. 2 Refrigeration test under nearly adiabatic conditions. The blackand red lines are temperature (left axis) and external magnetic
field (right axis), respectively. The final temperature is 22mK [6].

References[1] X. Zhu, et. al., Nature 478, 221-224 (2011).
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[3] A. Cho, Science 326, 778-779 (2009).
[4] P. Shirron, et. al, Cryogenics 44, 581-88 (2004).
[5] J. Bartlett, et. al., Cryogenics 50, 582-590 (2010).
[6] Y. Tokiwa, et. al, Commun. Mater. 2 42 (2021).