# A multicaloric cooling cycle that exploits thermal hysteresis

## Abstract

The giant magnetocaloric effect, in which large thermal changes are induced in a material on the application of a magnetic field, can be used for refrigeration applications, such as the cooling of systems from a small to a relatively large scale. However, commercial uptake is limited. We propose an approach to magnetic cooling that rejects the conventional idea that the hysteresis inherent in magnetostructural phase-change materials must be minimized to maximize the reversible magnetocaloric effect. Instead, we introduce a second stimulus, uniaxial stress, so that we can exploit the hysteresis. This allows us to lock-in the ferromagnetic phase as the magnetizing field is removed, which drastically removes the volume of the magnetic field source and so reduces the amount of expensive Nd–Fe–B permanent magnets needed for a magnetic refrigerator. In addition, the mass ratio between the magnetocaloric material and the permanent magnet can be increased, which allows scaling of the cooling power of a device simply by increasing the refrigerant body. The technical feasibility of this hysteresis-positive approach is demonstrated using Ni–Mn–In Heusler alloys. Our study could lead to an enhanced usage of the giant magnetocaloric effect in commercial applications.

## Main

Although there have been improvements in efficiency, the working principle for conventional cooling—vapour compression—has remained largely unchanged for more than 100 years1. However, with the world’s increasingly affluent population demanding more comfortable living and working conditions, it is vital that we address the development of much more efficient cooling technologies as an urgent priority2,3. Most research is focused on solid-state refrigeration and one of the caloric effects—electrocaloric4,5, magnetocaloric6,7, barocaloric8,9 or elastocaloric10,11—in which the material’s entropy is forced to change under the application of an electrical, magnetic or mechanical field. The magnetocaloric effect (MCE), the most studied of the three, manifests itself as a change in the material’s temperature as it is exposed to a magnetic field. This remarkable effect makes it possible to set up a magnetic cooling cycle12.

Even though dozens of MCE demonstrators have been constructed13, no commercially competitive magnetic refrigerator has been produced14. The problem is that in a field produced by permanent magnets (in the range of 1 T), the MCE of the existing materials is too small, which leads to small operating ranges. It is possible to increase the temperature range of a MCE device by employing what is called an active magnetic regeneration (AMR) cycle15, but then only a small percentage of the MCE material contributes to the cooling16. The design of such an AMR machine is sketched in Fig. 1a—the magnetic field is varied by rotating either the MCE material or the magnet. Conventionally, the rare earth element (REE) gadolinium17 is used as the MCE material, but there are also demonstrators that operate with La–Fe–Si or Fe2P-type compounds18. As the MCE in these materials is completely, or at least mostly, reversible, the magnetic field needs to be maintained during the whole heat-exchange process. Consequently, the quantity of REE-based Nd–Fe–B permanent magnets needed is at least four times the amount of MCE material and even larger when Halbach arrangements are used, which makes the system expensive and overly dependent on critical raw materials19,20.

## An alternative to conventional solid-state refrigeration

We present an alternative solid-state cooling cycle that exploits the thermal hysteresis inherent in MCE materials that undergo a first-order transition. After the phase transformation is driven by the magnetic field, removing the field leaves the material ‘locked’ in the phase with high magnetization because of the hysteresis, and so the magnetic field is only required for a very short time to tap the cold of the material. This concept drastically reduces the costs of the magnetic field source because, in this case, the volume over which the magnetic field needs to be generated and maintained is very small21. At the same time, focusing the magnetic field means we can double the magnetic field strength up to 2 T. As the MCE scales with the change in magnetic field, this can expand the temperature range of the refrigeration cycle. However, it requires an additional external stimulus, that is, a mechanical stress, to ‘unlock’ the MCE material and return it to its original state22. Consequently, a material with susceptibility to multiple external stimuli is a prerequisite to exploit the thermal hysteresis.

The working principle of such a cycle as well as a scheme for the corresponding design of the machine is illustrated in Fig. 1b,c. In general, any first-order magnetocaloric material with a tunable thermal hysteresis could be utilized in this cycle, even though inverse magnetocaloric materials, such as Heusler alloys, are more favourable because they cool when the magnetic field is applied, and thereby simplify the heat exchange. In contrast, conventional compounds, such as the La–Fe–Si type, heat up when being magnetized and cool when applying the mechanical load23. The necessity for a direct contact between the loading unit and the cold heat exchanger makes the implementation of an efficient design more complicated.

## Experimental proof of concept

In this study we focus on Ni–Mn–In Heusler alloys with a metamagnetic martensitic transition that shows an inverse MCE, which means a decrease in temperature when they are adiabatically magnetized (step 1 in Fig. 1c), and a tunable thermal hysteresis24. Besides other extrinsic and intrinsic effects, the hysteresis width is dominantly determined by the lattice mismatch between the cubic austenite and the tetragonally distorted martensite phase, which can be adjusted by varying the chemical composition25,26. The high elastic energy barriers that separate the parent and martensitic phases ensure, to a very good approximation, the athermal character of the transition. Consequently, the transformed fraction does not change while the temperature, stress and magnetic field are kept constant27. In our hysteresis-positive approach, the magnetic field needs to be sufficiently high to transform the material completely. Then, due to the appropriately tuned thermal hysteresis, the reverse transition does not take place during demagnetization, as sketched in step 2 (Fig. 1c). This is the fundamental difference compared to the conventional AMR cooling cycle. In this way, we turn the thermal hysteresis from being a problem for magnetocalorics into an advantage for multistimuli caloric materials. The irreversibility of the magnetostructural transition allows us to reduce the magnetized volume to a minimum, which means that we can abandon the large, expensive REE magnets that are required to produce a magnetic field over a large volume.

After locking the material in the ferromagnetic phase in step 3 in Fig. 1c, the heat can be extracted from the cooling compartment in the absence of a magnetic field. To return the material to its original state, a loading unit is required, as illustrated by the wheel system in Fig. 1b. In the case of Ni–Mn–In, the application of a mechanical load shifts the hysteresis curve to higher temperatures and consequently the material transforms back into the low-temperature phase. This process is accompanied by a large heating effect because the reverse transformation is induced (steps 4 and 5 in Fig. 1c). The excess heat can then be expelled to the surroundings in step 6, the final step (Fig. 1c). Note that part of the excess heat from the multicaloric material could also flow into the loading unit due to the direct contact. Therefore, the wheel system should either be thermally insulated or kept at the temperature of the hot reservoir. As for the magnetization step, the high stress field is only required over a very small volume. Further details of the six-step hysteresis-positive cycle is given in Supplementary Information, in particular Supplementary Fig. 1.

Figure 2 shows a demonstration of the cycle on a laboratory scale. In this experiment, the Heusler material was loaded by a uniaxial stress of 75 MPa to turn it into the low-temperature martensite phase, which resulted in significant heating. The mechanical load was created by a piston connected to a screw system. For technical reasons, the application of the mechanical stress must be performed with care to prevent overshooting, whereas unloading the sample can happen instantaneously. After a certain waiting time, a short magnetic field pulse of 1.8 T with a duration of approximately 2 s was applied by an electromagnet and the Heusler sample cooled down. The key point is that the MCE was not reversed when removing the magnetic field because of the thermal hysteresis. As the sample is in thermal contact with the surroundings, its temperature relaxed back with time. This simulates the extraction of heat from the cooling compartment. Afterwards, the cycle can start over again.

For the cyclic tests, a Heusler alloy in bulk form with the composition Ni49.6Mn35.6In14.8 was selected. Its martensitic transition with a thermal hysteresis of about 10 K occurs slightly below room temperature, as can be seen from Fig. 3a; the magnetization measurements in 0.2, 1 and 2 T are shown in the upper panel. The magnetic field shifts the hysteresis curve towards lower temperatures as the austenitic high-magnetization state is stabilized. In contrast, the application of uniaxial stress favours the low-temperature martensite phase and therefore the transition temperature is increased. In the lower panel of Fig. 3a, the compressive strain of the sample is plotted as a function of temperature under a constant uniaxial load up to 60 MPa. For these measurements, a mechanical testing machine was equipped with a heating and cooling chamber that allowed us to sweep the sample temperature. We observed that the magnetic field shifts the transition by approximately −3.7 K T−1, whereas uniaxial stress increases the transformation temperature by about +0.23 K MPa−1. These values are in agreement with data in the literature for similar samples28. In other words, a uniaxial load of 16 MPa is comparable to a magnetic field of 1 T, although the transition is shifted in the opposite direction.

The results of the cycling experiments under multiple stimuli are illustrated in Fig. 3b. The magnetic field and the uniaxial stress were applied alternately at minute intervals. The whole measurement set-up was heated in the background with a sweeping rate of 0.1 K min−1 to test the properties of the materials at different temperatures. Despite the simplicity of the set-up and its poor thermal insulation, the feasibility of the hysteresis-exploiting concept is demonstrated in a sequence of cycles. The basic idea to obtain an irreversible MCE in a cyclic manner is demonstrated, even though it accounts for little more than 1 K. In this example the sample was loaded with about 75 MPa. However, the application of such a large uniaxial stress is a harsh process that can lead to fatigue and even to the magnetocaloric material being destroyed. In tests on similar arc-melted Heusler alloys, several samples failed. One reason for this is that the grain sizes in those compounds are in the range of millimetres29. Therefore, cracks can propagate easily. One possibility to enhance the mechanical stability of the material is to refine the microstructure by suction casting the materials.

Figure 4 summarizes the results for the suction-cast material with a similar chemical composition to the bulk material. In Fig. 4a both the magnetization (top) and the compressive strain (bottom) of the sample are plotted. When a magnetic field is applied, the transition shifts by about −1 K T−1, whereas uniaxial stress increases the transition temperature Tt by approximately 0.1 K MPa−1. Compared to the bulk sample in Fig. 3, the $${\textstyle{{{\rm{d}}T_{\rm{t}}} \over {{\rm{d}}H}}}$$ and $${\textstyle{{{\rm{d}}T_{\rm{t}}} \over {{\rm{d}}\sigma }}}$$ values are significantly smaller because the transition of the suction-cast sample is close to the Curie temperature of the austenite phase. In comparative measurements of the adiabatic temperature change, ΔTad (Supplementary Information) in cyclic magnetic fields of 1.9 T, we were able to demonstrate that the suction-cast material provides only a vanishingly small reversible MCE related to the first-order transition. As shown in Supplementary Fig. 2, the irreversible ΔTad in this field change accounts for −1.28 K in the first field application of a ‘fresh’ material. By applying the multistimuli hysteresis cycle, it is possible to exploit almost the entire potential ΔTad. For the cyclic tests in Fig. 4c, it is apparent that an irreversible temperature change of −1.2 K can be achieved. Furthermore, the mechanical integrity of the specimen is much improved due to the fine microstructure. Figure 4b shows a light-microscopy image of a sample in the martensite state with fine needle-like structures. However, the grain boundaries of the parent austenite phase that separate the different martensitic regions are still visible. During the suction casting of the melt, the grains grow in a radial direction towards the centre of the rod and have a typical width between 100 and 250 μm. This special microstructure can withstand much larger uniaxial stresses than the conventionally arc-melted counterparts, even beyond 100 MPa.

Figure 4c shows the thermal response of the suction-cast material when a magnetic field pulse of about 1.8 T (even minutes) and mechanical load of 80 MPa (odd minutes) are alternately applied. The temperature of the holder was increased from 290 to 298 K at 0.25 K min−1 to study the response in different temperature regions of the martensitic transition. The diagonal curve in Fig. 4c represents the absolute temperature profile of the sample (right-hand axis). To illustrate the temperature profile of the material in a clearer form, the baseline heating curve was subtracted, as shown on the left-hand axis of Fig. 4c. It is possible to distinguish three different regions. Below approximately 292 K (minutes 0–7, blue shading), the magnetocaloric cooling effect is predominantly reversible and the sample temperature reverts instantly after the field pulse. At this low temperature, the material is mainly in the martensite state.

Above approximately 292 K (minutes 7–23, red shading in Fig. 4c), increasing amounts of austenite are locked by the thermal hysteresis, which prevents it from transforming back into martensite. For this reason, the cooling effect becomes irreversible during the magnetic field pulse with a maximum value of −1.2 K obtained at 295.5 K (minute 22). Here the temperature change of the material is maintained long after the magnetic field pulse and it takes about 1 min to relax back to the background temperature. Furthermore, the heating of the sample is intensified during the stress application, which indicates that a larger amount of austenite is switched back into martensite. In contrast, above 296 K (minutes 24–29, pink shading in Fig. 4c), the transition turns into a conventional MCE, which is reversible. At these high temperatures, the austenite phase is dominant and, because its Curie temperature, being approximately 305 K, is rather close, a temperature increase of 1.3 K is observed. However, the temperature change is immediately reversed when the magnetic field decreases. A small irreversible part is also present at these temperatures, as a small amount of martensite could be formed by the applied stress application, but this is not significant.

## On the potential of exploiting the hysteresis cycle

In conclusion, our experiments demonstrate that the hysteresis-exploiting cycle works on a laboratory scale. In particular, the suction-cast Ni–Mn–In Heusler alloy is a very promising innovation, due to its enhanced mechanical strength and reasonably large thermal hysteresis. These inverse magnetocaloric materials have the advantage that they cool during the field-application step, in which no mechanical contact is required, which simplifies the heat transfer. However, most first-order MCE alloys could be used for such a cycle. The only requirements are a tuned thermal hysteresis, a sufficient magnetic field dependence of the transition temperature and an external stimulus that can transform the material back to its original state. This cycle represents a multicaloric approach to magnetic refrigeration that exploits the thermal hysteresis of a MCE material instead of attempting to avoid it. The advantage is that the full potential of the Heusler compound can now be utilized in a cyclic process, even if it shows no reversible ΔTad in conventional magnetic field cycling. In the Supplementary Information, an approximation of the energy balance derived from experimental data is given (Supplementary Figs. 3–5). In an exemplary six-step cooling cycle, the extra work associated with the deformation, Wela (per unit mass) due to the application of a uniaxial stress can be approximated at the material level from Fig. 4a to Wela ≈ 17.6 J kg−1 (mass density ρ = 7.0 g cm−3), which is about 60% larger than the magnetization work Wmag ≈ 10.6 J kg−1. Instead, a conventional four-step magnetocaloric cooling cycle requires a magnetic field change of about 4 T to obtain a similar ΔTad. The corresponding magnetic work then amounts to about 22.2 J kg−1, which is less than the sum of Wela and Wmag in the exploiting hysteresis cycle. However, it is important to remember that the magnetic field strength cannot be increased much beyond 2 T when using permanent magnets as the field source for the refrigerator. Fortunately, this impasse might be overcome by combining the magneto- and elastocaloric effects as described here.

In the proof of concept, we obtained a temperature change of −1.2 K. The largest irreversible temperature changes reported in a field of approximately 2 T amount to −8 K in Ni–Mn–In–Co (ref. 30) and as much as −9.2 K for the compound Fe–Rh (ref. 31). The next step is to match these large temperature changes to the hysteresis-exploiting cycle with designed-for-purpose materials. A simple refrigerator would only require two stages with tailored transition temperatures switched in series to build up a sufficiently large temperature span in which 50% of the magnetocaloric material is active in cooling compared to the few percent that is active in a conventional AMR cycle (further information on the heat flow management, on segmentation issues and on cascade devices with two and more stages is given in Supplementary Figs. 6 and 7).

To make use of the fact that the multicaloric material retains its temperature drop after the magnetization and demagnetization step, there is no necessity for a fast flow of the exchange fluid (Supplementary Information gives further details) as required in the classical AMR12. This claim originates from the restriction that the amount of the magnetocaloric material is more or less fixed for a given magnet arrangement. Therefore, an enhancement of the cooling power is obtainable solely by increasing the operating frequency of the AMR device. However, many technical problems, such as the pressure drop of the fluid through the regenerator or the slowness of the valve system, limit the frequency to typically 1 Hz (ref. 13). In great contrast, in the hysteresis-positive approach, the ratio between the magnetocaloric and magnet material, and therefore the cooling power, is scalable by enlarging the heat-exchanger body with the magnetic system, loading unit and operating frequency kept the same (Supplementary Fig. 8), which is an essential advantage of the multistimuli approach. This concept will allow a drastic reduction in the amount of expensive and raw-material-critical Nd–Fe–B permanent magnets needed for a cooling machine and, at the same time, in terms of efficiency outperform magnetic refrigerators that use the AMR principle.

## Methods

Samples with the nominal composition Ni50.0Mn35.5In14.5 were prepared by arc melting. The ingots were turned upside down and remelted several times to ensure chemical homogeneity. One batch was further treated using the suction-casting option of the arc melter to prepare rods with a diameter of 3 mm. Both specimens were subsequently annealed at 900 °C for 24 h, followed by water quenching. The bulk sample was cut and polished into a block with dimensions of 2 × 2 × 5.5 mm3. The suction-cast material was prepared with a length of 4.9 mm. The magnetic measurements were made on a commercial vibrating sample magnetometer using small fragments. Temperature-dependent dilatometry measurements involved a mechanical-testing machine that operated in the constant-load mode. The set-up included a variable-temperature chamber to cool and heat the piston unit at a rate of 1 K min−1. The sample temperature and height were directly measured with a type-T thermocouple and a strain-gauge sensor, respectively, attached to both pistons. For the experimental demonstration of the cooling cycle, an in-house-constructed set-up was used in which uniaxial stress was applied mechanically by a screw. The load was determined via a force sensor installed in the piston axis. The temperature of the sample, measured directly by a type-T thermocouple, could be varied by a thermal bath connected to the base plate of the piston unit. For the application of the magnetic field pulse, a commercial electromagnet was used. A Hall probe situated near the sample detected the magnetic field strength. Comparative measurements of the adiabatic temperature change (in the absence of a mechanical load) of the suction-cast material in a magnetic-field change of 1.9 T in the continuous and discontinuous protocol were performed in a purpose-built device using standard type-T thermocouples24.

## Data availability

The data that support the findings of this study are available from the corresponding authors upon reasonable request.

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## Acknowledgements

The work was supported by funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant no. 743116—project Cool Innov), the DFG (grant no. SPP 1599), the CICyT (Spain) project MAT2016-75823-R and the HLD at HZDR, a member of the European Magnetic Field Laboratory.

## Author information

Authors

### Contributions

T.G., M.F., A.T., L.P. and K.P.S. were responsible for the sample preparation. T.G., A.G.-C., A.P. and L.M. designed and performed the tensile test and cycling experiments. A.T., M.F. and K.P.S. took care of the adiabatic temperature-change measurements and microscopy. All the authors discussed the results and developed the explanation of the experiments. T.G. wrote the manuscript supported by all the co-authors. O.G. led the project.

### Corresponding authors

Correspondence to Tino Gottschall or Oliver Gutfleisch.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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## Supplementary information

### Supplementary Information

Supplementary Figures 1–8, Supplementary References 1–2

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Gottschall, T., Gràcia-Condal, A., Fries, M. et al. A multicaloric cooling cycle that exploits thermal hysteresis. Nature Mater 17, 929–934 (2018). https://doi.org/10.1038/s41563-018-0166-6

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