Adiabatic demagnetization is currently gaining strong interest in searching for alternatives to 3He-based refrigeration techniques for achieving temperatures below 2 K. The main reasons for that are the recent shortage and high price of the rare helium isotope 3He. Here we report the discovery of a large magnetocaloric effect in the intermetallic compound YbPt2Sn, which allows adiabatic demagnetization cooling from 2 K down to 0.2 K. We demonstrate this with a home-made refrigerator. Other materials, for example, paramagnetic salts, are commonly used for the same purpose but none of them is metallic, a severe limitation for low-temperature applications. YbPt2Sn is a good metal with an extremely rare weak magnetic coupling between the Yb atoms, which prevents them from ordering above 0.25 K, leaving enough entropy free for use in adiabatic demagnetization cooling. The large volumetric entropy capacity of YbPt2Sn guarantees also a good cooling power.
Usage of 3He is found in a variety of fields encompassing medical applications, military purpose and scientific research1,2,3. In science and engineering, 3He is one of the essential ingredients to achieve very low temperatures4 or to detect radioactivity1. We experience today a period of supply cutbacks for miscellaneous demands and very high costs for pure 3He: For example, low-temperature physicists have required only 1.3% of the available 3He between 2004 and 2010, and the price rose by a factor of 15 (refs 2, 3). Before this cutback, they were the major consumers of 3He, since temperatures down to 0.3 K and below were mostly reached by 3He systems and 3He/4He dilution refrigerators4. Given that 3He has been solely obtained as a byproduct from decay of tritium in nuclear weapons stockpiles or nuclear reactors, global agreement to reduce those facilities still holds, it seems unlikely to generate a smooth supply of 3He in the future. Consequently, we are now obliged to search alternatives to circumvent this 3He crisis.
Fortunately, low-temperature physicists already developed a 3He-free system, the adiabatic demagnetization refrigerator (ADR). This device makes use of magnetocaloric materials (MCMs) which are essentially paramagnetic compounds5. The term magnetocaloric was reported for the first time by Weiss and Piccard6, and the magnetocaloric effect (MCE) has been defined as reversible adiabatic variation in temperature of a material by an applied magnetic field. Compared with cumbersome gas-handling for 3He containing fridges, ADRs provide much easier operation: simple ramping-up and -down a magnet while operating (opening) a heat-switch cools down the system (see later). But further development of ADRs was delayed due to widespread adoption of the dilution refrigerator since the 1970s, because of its specific continuous cooling capacity. Although continuous cooling is also available in ADR since the initiation of space projects requiring zero-gravity cryostats7,8, most popular MCMs at low temperatures are still the paramagnetic salts which were independently proposed by Debye and Giauque9,10,11 80 years ago. Until recently, the MCE was best known for the working principle of ADR but it has also yielded invaluable information about magnetic phase transitions12, quantum criticality13,14,15 and alternative refrigeration techniques16,17 in modern science.
An ideal MCM for low-temperature applications should be made of magnetic atoms, which are in a degenerate paramagnetic state down to the lowest possible temperature in zero magnetic field. Then, it should have a large volumetric entropy capacity for a good cooling power. In addition, it is preferred to be metallic and non-superconducting for better conduction of heat and easy machining. And finally, it should not degrade over time. So far, most of the materials used for temperatures below 2 K have only fulfilled the first two requirements7, but sophisticated treatments are mandatory to meet the standard of operation: To protect the MCMs and for a sufficient thermal contact, those non-metallic MCMs must be prepared inside a canister with special metallic structures18,19.
In this article, we demonstrate that the metallic compound YbPt2Sn, which satisfies all aforementioned prerequisites for a MCM at low temperatures. We have measured the specific heat capacity C(T,B) of polycrystalline YbPt2Sn20 down to a temperature T=0.05 K and magnetic field B up to 7 T by using a compensated heat-pulse method21. The entropy S(T,B) converted from C(T,B) is used to estimate the MCE and the minimum temperature accessible by adiabatic demagnetization, which results to be <0.2 K. Finally, we show a direct measurement of the MCE performed in a home-made ADR with an YbPt2Sn ingot and demonstrate how an ADR made with YbPt2Sn is a feasible and durable alternative to 3He-cryostats.
Specific heat of YbPt2Sn
The relevant actors in our study are the Yb3+ ions, which are in the magnetic 3+ valence state with total angular momentum J=7/2. They are exposed to a crystalline electric field (CEF) with hexagonal symmetry, which lifts the degenerate 4f-shell energy levels into four doublets leaving a Kramers doublet as ground state with effective spin 1/2 and maximum entropy Rln2=5.76 J K−1 mol−1 (with R the gas constant)20. This is best shown in Fig. 1a, where the specific heat capacity C(T,B) of YbPt2Sn is plotted over a broad range of temperatures 0.06T200 K and at selected magnetic fields 0B7 T. We start to look at C/T in zero field (black symbols). At high temperatures, C/T displays two broad maxima, at about 50 and 6 K, which are due to phonons and a Schottky peak caused by thermal occupation of the first excited CEF level, respectively. Below 3 K, C/T increases steeply with a 1/T2 dependence which is attributed to the emergence of short-range (intersite) magnetic correlations, which are not sufficient to induce long-range magnetic ordering20. Eventually, at Tm=0.25 K short-range magnetic ordering sets in and is manifested as a kink in C(T)/T, similar to the parent compound YbPd2Sn22. Such a low Tm is very uncommon in Yb-based intermetallic systems with no sizeable Kondo interaction (like YbPt2Sn), which usually have transition temperatures of a few Kelvin. The nature of the magnetic ordering and the reason for the very weak magnetic exchange (≈0.8 K (ref. 20)) are still unknown, but this unique behaviour allows us to use the full unquenched entropy between Tm and 4 K for AD cooling in the same T-range of 3He systems.
At T<Tm, C/T increases again as 1/T3 because of the nuclear contribution Cn to the specific heat from the nuclear moment of Yb, see Supplementary Fig. 1 and Supplementary Note 1. This is emphasized by the measurements at different fields where the 1/T3 increase does not change much with B but becomes more visible. In fact, increasing B rapidly suppresses the phase transition at Tm. The kink at Tm transforms into a Schottky peak, which shifts to higher T, uncovering the large increase of Cn/T below 1 K. This Schottky peak is the result of the Zeeman splitting of the ground state doublet and is the fundamental effect needed for the MCE.
To demonstrate this we have subtracted from all C(T)/T curves the small conduction-electron contribution Ce/T(T→0)=γ and the nuclear contribution Cn/T=αn/T3 to obtain the pure 4f-electron specific heat C4f (see Supplementary Fig. 1 and Supplementary Note 1). In this temperature range, the phonon contribution is negligible. For B=0 the results are shown in Fig. 1b with γ=0.03 J K−2 mol−1 and αn=5.8 mJ K mol−1 (yellow symbols). Now, evaluating the 4f-electron entropy S4f from the integral of C4f/T between 0.06 and 4 K (cf. yellow area in Fig. 1b), we obtain exactly Rln2, the maximum entropy for a doublet ground state. Increasing the field results in a shift of this entropy to higher T, as shown in Fig. 1c (coloured areas), inducing the MCE we are after.
Entropy and MCE
By integrating C4f/T for all fields we can extract the full 4f-electron entropy S4f(T,B). To investigate useful adiabatic paths, we have generated a surface plot interpolating the S4f(T,B) curves, which is shown in Fig. 2a. As a result, the coloured surface clearly exhibits a notable MCE: The isothermal suppression of entropy (black arrow) followed by the isentropic trace (red arrow) allows to decrease the temperature. Ti and Tf designate the initial and the final temperature. The same is illustrated in Fig. 2b, that is, the projection of the data into the S–T plane. In Fig. 2c, we have plotted the expected Tf of YbPt2Sn as a function of Ti marked in Fig. 2a. The lower Ti the lower Tf. Tf is further decreased as we suppress the entropy with stronger field. It is clear that this material can always be cooled down below 0.2 K, in a reasonable range of T and B for a standard 4He-cryostat and a superconducting magnet. This is because the transition at Tm does not quench much of the entropy and the MCE allows to cool down the system below Tm. However, while theory suggests that it should be possible to cool down well-below 0.2 K, in real experiments (see below and Supplementary Fig. 3), only temperatures slightly below 0.2 K were achieved.
There are several materials, like paramagnetic salts or magnetic garnets (see Table 1), which are used for AD cooling in the same temperature range, but the advantage of YbPt2Sn is that it is a good metal and it can easily be cast into rods, making preparation of cooling pills quite simple, in contrast to salts or garnets. To test our material, we built a simple home-made ADR with a 10 g ingot pillar of YbPt2Sn (shown in Fig. 3c). More details will be found in Methods: ADR set-ups. Direct measurements of the MCE with the YbPt2Sn ingot are shown in Fig. 3a. Along the path from 6 T (red line), starting at 1.45 K, with a sweep rate of 0.1 T min−1, the temperature of the pillar, Tpillar, had reached 0.19 K, which is about 0.1 K higher than the Tf estimated from Fig. 2. After that, the pillar began to warm up due to inevitable heat loads from the electrical wiring and supporting structures (cf. Fig. 3b). The magnet power supply was the source of oscillations and occasional spikes in Tpillar(B). Another adiabatic path from 4 T, starting from 1.75 K with higher sweep rate of 0.13 T min−1 ended at 0.22 K, which is also 0.1 K higher than the estimated Tf. The uppermost cycle shows a ramping-up from 0 T and 0.26 K to 2 T and 1.3 K, and a successive ramping-down to 0 T and 0.27 K after 1 h of intermission. Also here, the 0.27 K achieved by MCE from 2 T and 1.3 K is about 0.1 K higher than the estimation. The discrepancy between Tpillar(0) and Tf is reasonable given that thermal and mechanical insulations were not as good as in a commercial standard ADR. In fact, the Kapton tubes guarantee good thermal insulation only below 1 K. We have also tested YbPt2Sn in a commercial physical properties measurement system (PPMS) (Quantum Design) by using an even simpler design without a heat-switch (see Supplementary Figs 2 and 3) and reached about 0.16 K. However, our experimental set-up provided a good enough thermal insulation at the lowest temperatures, which is reflected in a warming-up rate of 0.01 K h−1 at about 0.2 K, as shown in Fig. 3b. The reversibility and linearity of Tpillar(B), regardless of the sweep rate, indicates negligible eddy-current heating (see green curves in Fig. 3a). Consequently, the MCE observed in YbPt2Sn is reminiscent of that of an ideal paramagnet. An ideal paramagnet is universally described by (T/B)S=(T/B) and Tf=Ti(Bf/Bi) regardless of material parameters, where Bi and Bf are the initial and final magnetic fields along an adiabatic path, respectively. This means that at Bf=0, Tf=0. This is not the case for YbPt2Sn where we observe a finite Tf=Tpillar(0)≈0.2 K at Bf=0 (see black straight lines in Fig. 3a). This is certainly due to the magnetic weak exchange interaction, which is of the same order of magnitute of Tpillar(0) and Tm (ref. 20).
How good is YbPt2Sn compared with standard MCM materials for the same T-range? In a MCM, a weak magnetic interaction is beneficial to achieve a low base temperature. Moreover, the spin JGS of the ground state determines the saturation entropy Rln(2JGS+1) and, therefore, a large JGS is advantageous for a stronger cooling power. It is worth mentioning that for practical purposes it is not the molar entropy but it is the entropy density of the material which is the relevant quantity. Finally, a large g-factor is desirable because the suppression of entropy by a magnetic field becomes more susceptible. Hence, for a MCM large JGS, g, density d and a weak magnetic interaction are desirable, but large values of the first three parameters promote a strong magnetic interaction. Thus creating a low-temperature magnet with a weak interaction usually is in conflict with having a large cooling capacity and vice versa. Table 1 shows relevant parameters for paramagnetic salts and garnets, which are popular MCMs for ADR <1 K. In chromium potassium alum and ferric ammonium alum, first order magnetic phase transitions appear near Tm≈10 mK (ref. 23) and Tm≈30 mK (ref. 24), respectively. Normally, the ordering temperature Tm is indicative of the lowest possible temperature as entropy is quenched with a phase transition. As mentioned above, the intuitive approach to keep large distance between magnetic ions to obtain low Tm (typical of these materials) is accompanied by the downside of having low volumetric entropy capacity, Sv. For gadolinium gallium garnet25 and dysprosium gallium garnet26, one can have much higher Sv than salts at the expense of Tm. Moreover, it is common to have higher Tm as JGS is increased27. In comparison to salts, YbPt2Sn has more than eight times larger d, and roughly three times larger Sv while it orders at 0.25 K. At first glance, the tendency to relinquish a low Tm over Sv seems to be obeyed. However, in contrast to rare-earth garnets and other rare-earth MCMs28, the magnetic ordering around 0.2 K cannot be accounted for by neither JGS nor d dependence. Most of all, the weak and continuous magnetic ordering makes YbPt2Sn unique because it can be practically cooled below Tm. It is also worth noting that similar compounds like YbPd2Sn (with Tm=0.23 K (refs 22, 29)) and YbPt2In (with Tm=0.18 K (ref. 20)) all show doublet ground states and weak ordering, but YbPd2Sn becomes superconducting at 2.3 K (that is, a bad thermal conductor) and YbPt2In has not yet been tested. It is worth mentioning that there are materials which show maximal MCE at the verge of metamagnetic transitions30. However, those materials require a demagnetization towards a nonzero field and the small entropy change would provide a weaker cooling effect when compared with that of YbPt2Sn.
The aforementioned exceptional properties of YbPt2Sn allowed us to build an ADR with a metallic MCM operable below the base temperature of a 3He-cryostat. This material can be easily cast into various shapes and directly attached to the cooling target without any complications. It is a good metal and no additional metallic structures are needed for the thermal conduction unlike in paramagnetic salts or garnets, which are very poor thermal conductors <1 K. In this sense, while the physical origin of the weak interaction still needs to be clarified, it is an important feature that makes YbPt2Sn a viable new metallic refrigerant material for ADR. YbPt2Sn makes ADR more accessible by resolving complications of preparing non-metallic materials, which have been used since the 1930s. At the same time, it provides low enough base temperatures so that it can be chosen as an alternative to 3He-cryostats. We hope that our discovery will accelerate low-temperature physicists to escape from the ongoing 3He crisis.
Despite the high vapour pressure of divalent Yb metal, YbPt2Sn can easily be prepared in a standard arc-melting furnace by first reacting Yb with the low melting Sn and then adding Pt. Details are given in ref. 20. The pillar used for the PPMS set-up (see Supplementary Fig. 2) and the rod for the home-made ADR were obtained by casting pre-reacted YbPt2Sn in an appropriate mould in an arc-melting furnace and in a commercial high-frequency casting system (see Supplementary Movie 1), respectively.
Measurements of heat capacity have been carried out in a dilution refrigerator (Oxford Instruments) for temperatures 0.05T4 K and magnetic field B up to 7 T by using a compensated heat-pulse method described in ref. 21. For T>2 K, the measurements were performed in a 7 T PPMS.
To test the cooling capability and MCE of YbPt2Sn, we have built two different refrigeration systems. One follows the standard structure of commercial ADR, which is equipped with a mechanical heat-switch, and the other is a simple miniaturized version without heat-switch that can be used in a commercial PPMS, as shown in Supplementary Fig. 2. In the former set-up, we have modified a top-loading 1 K pot cryostat. The sample stage (thin brass disc) is fixed below the 1 K pot by using a pair of Kapton straws and is located at the stray-field compensation zone of the superconducting magnet. Beneath this stage, two thin brass rods are stretched to the magnet centre from opposite edges of the sample stage, and the end of each rod is joined perpendicular to each arms of ‘Φ’-shaped brass part. The mass of the whole brass structure is about 30 g. The YbPt2Sn ingot pillar shown in Fig. 3c is clamped at the centre of this thin metal piece. A push-pull manual actuator is used to activate the mechanical heat-switch. Further details and specifications of this set-up will be reported elsewhere.
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We are indebted to D. Aoki, F. M. Grosche, A. Mackenzie, W. Schnelle and K. Winzer for useful discussions. This work is supported by the Max Planck-POSTECH Center for Complex Phase Materials KR2011-0031558 and by the DFG Research Unit 960 Quantum Phase Transitions.
The authors declare no competing financial interests.
Supplementary Figures 1-3, Supplementary Notes 1-3 and Supplementary References (PDF 583 kb)
Preparation of the metallic magnetocaloric material YbPt2Sn. The new magnetocaloric material YbPt2Sn is cast into a rod in a cold crucible system. A strong radio frequency (RF) magnetic field induces large electrical currents in pre-reacted YbPt2Sn pieces which heat them up and let them melt, while the water-cooled copper crucible stays cold. Turning of the RF generator lets the melt drop into a cylindrical mold underneath the crucible. (MOV 7448 kb)
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Jang, D., Gruner, T., Steppke, A. et al. Large magnetocaloric effect and adiabatic demagnetization refrigeration with YbPt2Sn. Nat Commun 6, 8680 (2015). https://doi.org/10.1038/ncomms9680
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