Multicaloric effect refers to a thermal response of materials driven by multiple external fields. In this work, we explore the possibility by adopting multicaloric strategy to improve the transformation reversibility and manipulate the optimal operating temperature window in (Ni43Mn47Sn10)99.5Tb0.5 using a bespoke multicaloric effect characterization system. It is found that the reversibility of stress induced transformation could be significantly improved with the application of an extra magnetic field. More importantly, the operating temperature window of elastocaloric effect is shifted by ∼4 K to the lower temperature by applying a magnetic field of 4 T. Our experimental results reveal that such a dual-field multicaloric strategy is feasible and promising for improving the transformation reversibility and tuning the optimal operating temperature window for alloys with a magnetostructural transformation.

Can solid-state refrigeration replace the vapor-compression refrigerator and enter our daily life? Numerous efforts have been made in developing novel caloric materials and solid-state cooling systems.1–5 Among the various caloric materials, the largest cooling effects are generally originated from the first-order phase transformation.6–8 However, for a certain material, the operating temperature window (OTW) is generally limited in the vicinity of its transformation temperature (Ttr),9,10 which is small for most practical applications. One solution is utilizing the composite materials containing a series of materials with continuous transformation temperatures.11,12 However, such a method broadens the OTW at the cost of reduction in effective isothermal entropy change and adiabatic temperature change.13 Recently, the proposal of multicaloric effect driven by more than one field has provided a new approach to manipulate the OTW.14–19 One multicaloric configuration is a composite structure with a caloric thin film deposited on a substrate. By using the electric field induced stress in the ferroelectric material PMN-PT, the shifts in OTW of magnetoelectric heterostructural LaFeSiH/PMN-PT and NiCoMnIn/PMN-PT laminates have been observed through an indirect method (isothermal entropy change, ΔS).20,21 However, such a multicaloric operation is highly dependent on the thickness and the combination of the two components in the laminate layer, which put a strict requirement on the geometry of the materials. In this context, a multicaloric operation based on a single bulk material with a multiferroic feature is desired, whose configuration and material synthesis process can be much simplified. Furthermore, the experimental verifications of the manipulation of OTW via a direct method (adiabatic temperature change, ΔTad) by a multifield application are desired.2 For example, through the direct measurements of ΔTad, Gràcia-Condal et al. modified the OTW of magnetocaloric effect (MCE) and elastocaloric effect (eCE) by applying an external uniaxial stress and a magnetic field, respectively, in a noble metal based Fe49Rh51 alloy.22 Among the shape memory alloys, Ni–Mn-based Heusler alloys are specific due to the strong magnetoelastic coupling, which makes Ni–Mn-based metamagnetic shape memory alloys promising for multicaloric operation. In addition, the sensitivity of Ttr to both magnetic field and stress makes it possible to manipulate the OTW of the monocaloric effect in these alloys by applying an extra field.23–25 Ni–Mn–Sn Heusler alloys have been demonstrated with an outstanding entropy change associated with the martensitic transformation, and the giant caloric effect can be driven via a small strain.26 Such features make Ni–Mn–Sn Heusler alloys promising candidates for elastocaloric refrigeration. In this work, we directly investigate the ΔTad induced by a uniaxial stress for (Ni43Mn47Sn10)99.5Tb0.5 in cases with and without an external magnetic field. By Tb doping, the mechanical properties of Ni–Mn–Sn can be enhanced, which then fulfill the requirement when subjected to external fields via a common synthesis process.27,28 Our experimental results turn out that, by applying an external magnetic field, an improved transformation reversibility was achieved and (Ni43Mn47Sn10)99.5Tb0.5 can be manipulated to operate in its optimal OTW.

A button-shaped polycrystalline (Ni43Mn47Sn10)99.5Tb0.5 was synthesized by arc melting in Ar atmosphere. A rectangular specimen with a dimension of 3 × 3 × 6 mm3 for compressive test was cut from the middle of the button sample and subsequently annealed at 1073 K for 24 h in a vacuum quartz tube followed by rapid quenching in ice water. A differential scanning calorimeter (DSC 214, NETZSCH) was used to determine the transformation temperatures and latent heat. A superconducting quantum interference device (SQUID) magnetometer (MPMS-3, Quantum Design) was used to measure magnetic properties. The microstructure was observed using a scanning electron microscope (Quanta FEG 250, FEI). The stress–strain curves and ΔTad were directly characterized by using a bespoke multicaloric effect characterization system.17 A low strain rate of 0.001 s−1 was set to ensure a quasi-isothermal condition and minimize the tendency to crack as well, while a high unloading rate of 0.1 s−1 was used to approach a sufficient adiabaticity for an elastocaloric measurement. Before this measurement, cyclic loading and unloading processes, which are known as training processes, were conducted to ensure that the specimen exhibits a stable mechanical performance. The applied strain was set to be 1.4% as a compromise to the reversibility of the transformation within a broad temperature range.

The DSC curves upon heating and cooling for (Ni43Mn47Sn10)99.5Tb0.5 are shown in Fig. 1(a). The starting and finishing temperatures for forward (Ms, Mf) and reverse transformations (As, Af) are determined by the tangent method from the DSC curves, which are evaluated to be 268.5, 242.0, 253.8, and 279.1 K, respectively. The transformation temperature defined as Ttr = (Ms + Mf + As + Af)/4 is 260.8 K, which is slightly below the ambient temperature. The ΔS is calculated by averaging the entropy change upon heating and cooling as ΔS = 2ΔHh/(As + Af) + 2ΔHc/(Ms + Mf), where ΔHh and ΔHc are the transformation enthalpy changes determined from the peak area upon heating and cooling DSC curves, respectively. The entropy change (ΔS) associated with the martensitic transformation is 42.3 J kg−1 K−1. The phase transformation behavior of (Ni43Mn47Sn10)99.5Tb0.5 was also monitored by the change in magnetization during heating and cooling cycles at various magnetic fields from 0.01 to 5 T as shown in Fig. 1(b). Upon cooling, a magnetization drop was observed, indicating that (Ni43Mn47Sn10)99.5Tb0.5 undergoes a martensitic transformation from the ferromagnetic austenite phase to the weak magnetic martensite phase. As the magnetic field increases from 0.01 to 5 T, the magnetostructural transformation shifts to lower temperatures due to the Zeeman energy difference between martensite and austenite.29 Here, Ttr is defined as Ttr = (Ms + Mf + As + Af)/4, where Ms, Mf, As, and Af are determined by the tangent extrapolation approach from the MT curves as indicated in the inset of Fig. 1(b). The dTtr/dH, which refers to the sensitivity of magnetostructural Ttr to an external magnetic field, is found to be −0.90 K T−1 for (Ni43Mn47Sn10)99.5Tb0.5, as plotted in Fig. 1(c). The Ttr shift induced by external magnetic fields can approximately be given by the Clausius–Clapeyron relation,23 
dTtr/dH=ΔM/ΔS,
(1)
where ΔM and ΔS are the magnetization difference under 5 T between austenite and martensite phases and the entropy change associated with the martensitic transformation, respectively. A value of −0.95 K T−1 obtained from Eq. (1) agrees well with the experimental result.
FIG. 1.

(a) DSC curves for (Ni43Mn47Sn10)99.5Tb0.5 upon heating and cooling. (b) Thermomagnetic curves for (Ni43Mn47Sn10)99.5Tb0.5 upon heating and cooling measured in several magnetic fields; the inset illustrates the definition of Ms, Mf, As, and Af. (c) Ttr as a function of magnetic field.

FIG. 1.

(a) DSC curves for (Ni43Mn47Sn10)99.5Tb0.5 upon heating and cooling. (b) Thermomagnetic curves for (Ni43Mn47Sn10)99.5Tb0.5 upon heating and cooling measured in several magnetic fields; the inset illustrates the definition of Ms, Mf, As, and Af. (c) Ttr as a function of magnetic field.

Close modal

The dTtr/dH with a negative value indicates that the external magnetic field stabilizes the ferromagnetic austenite phase and the application of a bias magnetic field may promote reverse transformation and improve reversibility. Motivated by this, we recorded the stress–strain curves and the corresponding ΔTad at selected temperatures and magnetic fields to uncover the effect of an external magnetic field on the stress induced martensitic transformation and caloric effect. As shown in Fig. 2(a), (Ni43Mn47Sn10)99.5Tb0.5 exhibits a quasi-linear tendency and no transformation plateau was observed, which is different from that of the non-doped Ni–Mn–Sn alloys with a single phase.26 Such a phenomenon may be ascribed to the Tb doping and the formation of a Tb-rich secondary phase, as shown in the inset of Fig. 2(a). At the interfaces between the matrix and the secondary phase, there exists a large amount of lattice defects and distortions. These interfacial defects can serve as the preexisting nucleation sites, weakening the energy barrier for the martensite upon forward transformation or for the austenite upon reverse transformation.30 Upon loading, the martensite gradually and continuously nucleates and grows from the interface into the matrix,31–33 differing from a stress induced martensitic transformation with a transformation plateau in the stress–strain curves. The orientation is another factor affecting the stress–strain behavior.34–36 For a non-textured polycrystalline specimen, the grains could have various critical stresses along the compressive direction. This could also result in a continuous transformation. Both factors consequently lead to the exhibition of a quasi-linear stress–strain behavior. However, an apparent deviation from linearity upon loading [Fig. 2(a)] and the hysteresis loop after isothermal unloading suggest the occurrence of the stress-induced transformation. For the stress–strain curve recorded at 295 K without an external magnetic field, an apparent residual strain of 0.4% was observed after unloading. It is worth pointing out that this unrecovered strain is not a consequence of permanent plastic deformation but the so-called temporary residual strain arising from the non-completed reverse transformation at such testing temperature.37 The temporary residual strain indicates the existence of remanent martensite and leads to a reduction of reverse transformation volume fraction, as shown in the top of Fig. 2(c), and, consequently, a degradation in |ΔTad|.38 In contrast, a complete superelastic loop can be obtained as an external magnetic field of 4 T was applied. Accordingly, as plotted in Fig. 2(b), at 295 K, |ΔTad| = 4.0 K was achieved under 4 T, which is larger than that without a bias magnetic field (|ΔTad| = 3.5 K). Because the magnetic field stabilizes the ferromagnetic austenite, the application of a bias magnetic field promotes the reverse transformation, and hence, a larger reverse transformation volume fraction can be obtained, consequently leading to a smaller residual strain and a larger cooling effect. For (Ni43Mn47Sn10)99.5Tb0.5, dTtr/dH with a value of 0.9 K T−1 suggests that a magnetic field of 4 T can bring the Ttr ∼ 4 K (3.6 K) further away from the testing temperature, which is equivalent to elevating the ambient temperature by ∼4 K. To verify this, the stress–strain curve and ΔTad were also recorded at 299 K without an external magnetic field. As predicted, the stress–strain curves corresponding to dual fields at 295 K are almost coincident with those at 299 K with no bias magnetic field. The corresponding |ΔTad| are 4.0 and 3.9 K, respectively, which are close as well. As illustrated in the bottom of Fig. 2(c), a higher temperature is beneficial to improve the reversibility of phase transformation and reduce the proportion of residual martensite. However, in practical applications, it is not possible to change the ambient temperature to satisfy the materials’ properties. Here, it was found that the application of an external magnetic field can also promote the reverse martensitic transformation, and consequently, the reverse transformation volume fraction and cooling effect can be enhanced, which is schematically illustrated in the center of Fig. 2(c).39 

FIG. 2.

(a) Stress–strain curves recorded upon isothermal loading and unloading at selected temperatures and magnetic fields; the inset illustrates the scanning electron microscopy (SEM) image of (Ni43Mn47Sn10)99.5Tb0.5. (b) |ΔTad| corresponding to (a). (c) Schematic illustrating the improvement in reversibility via applying an external magnetic field or increasing the ambient temperature. RT refers to the room temperature. σ is the stress inducing the martensitic transformation, and the size of the arrows refers to the magnitude of σ. H is the magnetic field applied on the specimen. A and M refer to austenite and martensite, respectively.

FIG. 2.

(a) Stress–strain curves recorded upon isothermal loading and unloading at selected temperatures and magnetic fields; the inset illustrates the scanning electron microscopy (SEM) image of (Ni43Mn47Sn10)99.5Tb0.5. (b) |ΔTad| corresponding to (a). (c) Schematic illustrating the improvement in reversibility via applying an external magnetic field or increasing the ambient temperature. RT refers to the room temperature. σ is the stress inducing the martensitic transformation, and the size of the arrows refers to the magnitude of σ. H is the magnetic field applied on the specimen. A and M refer to austenite and martensite, respectively.

Close modal
Although our specimen exhibits a quasi-linear stress–strain behavior, the strain (Δε) associated with the transformation can still be roughly estimated. In addition, thus, we can verify that whether these data obey the Clausius–Clapeyron equation,
Δε×dσcr=ρΔS×dT.
(2)
From Fig. 2(a), the dσcr/dT is estimated to be 4.7 MPa K−1, and the Δε at 295 K under 4 T is found to be ∼1.12%. Then, the entropy change during this cycle can be calculated as −6.1 J kg−1 K−1, where the density for Ni–Mn–Sn–Tb is ∼8700 kg m−3.40 Based on ΔTad, the entropy change can also be estimated from
ΔS=ΔTadT×Cp,
(3)
where the ΔTad recorded at 295 K under 4 T is −4.0 K and the specific heat Cp for Ni–Mn–Sn–Tb is ∼400 J kg−1 K−1.41 Thus, the ΔS can be calculated as −5.2 J kg−1 K−1. Both values basically agree with each other, indicating that these data obey the Clausius–Clapeyron equation. The difference between two values could be ascribed to two factors: (1) the deviation from an ideal adiabatic condition; and (2) the measuring error of the strain associated with the transformation. It is worth noting that the calculated ΔS is much lower than that obtained via DSC measurements. This could be ascribed to the limitation on εappl, which is set to be 1.4% as a compromise to the reversibility of the transformation within a broad temperature range. Such a εappl is insufficient to drive the transformation completely, consequently leading to the lower ΔS than the fully transformed ΔS from DSC measurements.

The improvement in reversibility originating from the application of an external magnetic field makes it possible to tune the optimal OTW toward a lower temperature region. To experimentally reveal the effect of an external magnetic field on the OTW, the cooling effect for (Ni43Mn47Sn10)99.5Tb0.5 under 0 and 4T was recorded within a broad temperature range from 285 to 320 K. The stress–strain curves upon isothermal loading and adiabatic unloading recorded at various temperatures under 0 and 4 T are shown in Figs. 3(a) and 3(b), respectively. The cooling effects corresponding to Figs. 3(a) and 3(b) are shown in Fig. 3(c). In the absence of a magnetic field, the temperature dependence of |ΔTad| exhibits a “trapezium-like” tendency: as the testing temperature decreases, the |ΔTad| first gradually increases and reaches a peak value of 4.3 K at 300 K and then decreases rapidly to |ΔTad| = 1 K at 285 K.42,43 The degradation in |ΔTad| at a low temperature region could be attributed to the forementioned non-complete transformation [Fig. 2(a)]. When an external magnetic field of 4 T is applied, |ΔTad| vs T curve exhibits a similar tendency to that in the absence of a magnetic field. More importantly, by applying a 4 T magnetic field, the whole |ΔTad| vs T curve is shifted to a lower temperature. In addition, the introduction of an external magnetic field does not modify the overall magnitude of the curves and |ΔTad| with the peak value of 4.0 K was achieved at 295 K under dual fields. It can be seen that the introduction of an external magnetic field brings in a shift of the OTW toward a lower temperature in our Ni–Mn–Sn–Tb alloys, and by modulating the external magnetic field continuously, the optimal OTW could be tuned accordingly.

FIG. 3.

Stress–strain curves upon isothermal loading and quasi-adiabatic unloading measured under 0 T (a) and 4 T (b). (c) Temperature dependence of |ΔTad| under 0 and 4 T.

FIG. 3.

Stress–strain curves upon isothermal loading and quasi-adiabatic unloading measured under 0 T (a) and 4 T (b). (c) Temperature dependence of |ΔTad| under 0 and 4 T.

Close modal

It is seen that, by applying an external magnetic field, the shift of |ΔTad| vs T curves basically follows the shift of Ttr induced by a magnetic field. So, |dTtr/dH|, the sensitivity of Ttr to magnetic field, is an important parameter to assess the response of the OTW to the magnetic field. In our case, the |dTtr/dH| for (Ni43Mn47Sn10)99.5Tb0.5 with a value of 0.9 K T−1 is relatively low, which is not outstanding among metamagnetic shape memory alloys as shown in Fig. 4.22,23,41,44–51 Based on Eq. (1), the |dTtr/dH| can be estimated by using ΔM and ΔS. To get significant |dTtr/dH|, a larger ΔM and a smaller ΔS are tended to be required. Meanwhile, a large ΔS is the prerequisite for a giant caloric effect. For Ni–Mn-based alloys with a metamagnetic transformation from weak magnetic martensite to ferromagnetic austenite, the ΔS and ΔM are closely related. Since the contrary contribution between magnetic entropy and lattice entropy changes in such materials, the large ΔM between martensite and austenite corresponds to the weakened total entropy change. Thus, the ΔS is basically inversely proportional to the ΔM,52 and with the increase in |dTtr/dH| (ΔMS), the ΔS changes in an inverted parabolic form as illustrated in Fig. 4. For practical applications, a large |dTtr/dH| is preferred, and thus, the OTW can be manipulated in a larger temperature range by a relatively small magnetic field supplied by permanent magnets. Meanwhile, the ΔS is also essential to be taken into consideration. Thus, from the perspective of materials, we need to achieve a balance between multicaloric effect and thermal performance.

FIG. 4.

Comparison between the sensitivity of transformation temperature to an external magnetic field (dTtr/dH) and the transformation entropy change (ΔS).22,23,41,44–51

FIG. 4.

Comparison between the sensitivity of transformation temperature to an external magnetic field (dTtr/dH) and the transformation entropy change (ΔS).22,23,41,44–51

Close modal

In summary, the multicaloric effect of polycrystalline metamagnetic shape memory alloy (Ni43Mn47Sn10)99.5Tb0.5 was investigated using a bespoke multicaloric characterization system. By applying an external magnetic field of 4 T, the whole OTW of elastocaloric effect is shifted toward the lower temperature by ∼4 K. The reversibility of transformation is improved as well with the application of magnetic field. Our work experimentally revealed that the multicaloric effect based on magnetoelastic coupling is a feasible strategy to manipulate the optimal OTW of the metamagnetic shape memory alloys.

This research, leading to these results, received funding from the National Key Research and Development Program of China (Grant No. 2021YFB3501203), the National Natural Science Foundation of China (Grant No. 52371192), the Zhejiang Provincial Natural Science Foundation of China (Grant No. LD21E010001), the Ningbo Natural Science Foundation (Grant No. 2022J292), the Ningbo Yongjiang Talent Introduction Program (Grant No. 2022A-090-G), the Hundred Talents Programs in the Chinese Academy of Science, and the Foundation of the director of Ningbo Institute of Materials Technology and Engineering of CAS.

The authors have no conflicts to disclose.

Hanyang Qian: Conceptualization (equal); Data curation (equal); Investigation (equal); Methodology (equal); Writing – original draft (equal). Zhiyang Wei: Conceptualization (equal); Investigation (equal); Methodology (equal); Writing – review & editing (equal). Guowei Li: Formal analysis (equal); Validation (equal); Writing – review & editing (equal). Jian Liu: Conceptualization (equal); Investigation (equal); Project administration (equal); Supervision (equal); Writing – review & editing (equal).

The data that support the findings of this study are available within the article.

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