Introduction

On account of environmental concerns and the limited thermodynamic efficiency of the traditional refrigeration technology based on vapor compression, magnetic refrigeration technology based upon the magnetocaloric effect (MCE) has generated a worldwide interest during the past decades [1, 2]. Magnetic refrigeration technology would thoroughly avoid the utilization of ozone-depleting volatile refrigerants usually used in the traditional refrigerators [3]. Furthermore, the efficiency of magnetic refrigeration technology is expected to exceed the efficiency of vapor compression technology, resulting in much reduction in energy consumption compared with traditional technologies [4]. The search for optimal magnetocaloric materials is a crucial parameter in the development of magnetic refrigeration technology. Up to now, several alloy systems showing magnetostructural transformation and giant MCE have been discovered, like Gd–Si–Ge [5], La–Fe–Si [6], Fe–Rh [7], Mn–Fe–P–As [8], Mn–Co–Ge [9], and Ni–Mn–X-based (X = Sn, In, Sb, Ga) magnetic shape memory alloys [10,11,12,13]. Among them, Ni–Mn–X-based (X = Sn, In, Sb, Ga) magnetic shape memory alloys are considered to be promising candidates for magnetic refrigeration applications thanks to their fascinating MCE, relatively low cost of raw elements, and non-toxicity. In addition to fascinating MCE, these Heusler alloys also show other interesting multifunctional properties, like magnetic shape memory effect [14], magnetoresistance [15], and elastocaloric effect [16]. The multifunctional properties make these magnetic shape memory alloys have the great potential to be used in a wide range of applications from actuators and sensors to solid-state refrigeration. Recently, many efforts have been spent on developing high-performance magnetocaloric materials in Ni–Mn–X-based (X = In, Sn, Sb, Ga) magnetic shape memory alloys [17,18,19,20]. However, there are still several standing problems that need to be resolved urgently. For these alloys, the large ΔS is usually obtained in a limited operating temperature window. Moreover, reproducible MCE cannot be achieved during the magnetic field cycling.

For a given material, the magnitude of MCE is directly linked to the fraction of material which undergoes the martensitic transformation or reverse transformation when the applied magnetic field is applied or removed [21]. The minimum applied field Δ(μ 0 H)com required to induce the complete (denoted as “com”) magnetostructural transformation can be expressed as Δ(μ 0 H)com = ΔT int/(ΔT/μ 0ΔH), where ΔT int is the phase transformation interval and ΔT/μ 0ΔH is the sensitivity of phase transformation temperatures to applied magnetic field [19]. However, irreversibility of the magnetostructural transformation is commonly encountered due to the thermal and magnetic hysteresis, which will reduce the effective value of MCE during the second and subsequent field cycles [11]. The irreversibility of MCE in these alloys strictly limits their utilization in magnetic refrigeration applications. Actually, the minimum applied field Δ(μ 0 H)com-rev needed to induce the complete and reversible (denoted as “com-rev”) magnetostructural transformation can be expressed as Δ(μ 0 H)com-rev = (ΔT hys + ΔT int)/(ΔT/μ 0ΔH), where ΔT hys is the thermal hysteresis [19]. Additionally, it was well demonstrated in literature that the ΔT int, ΔT hys, and ΔT/μ 0ΔH increase simultaneously with the decrease of phase transformation temperature caused either by magnetic field or by composition variation [22]. On the other hand, ΔT/μ 0ΔH equals to ΔM/ΔS tr according to the Clausius–Clapeyron relation, where ΔM is the magnetization difference between austenite and martensite across transformation and ΔS tr is the transformation entropy change, and ΔS tr corresponds to the maximum obtainable magnetic entropy change, an important parameter characterizing the MCE. If ΔS tr is large, the ΔT/μ 0ΔH is reduced and a high magnetic field is required to obtain a reasonably large MCE. If ΔS tr is small, the ΔT/μ 0ΔH is enhanced and the required field is lowered, but the attainable MCE is reduced. Thus, it is an arduous task to optimize magnetocaloric properties of a given material. The challenge for optimizing the magnetocaloric properties of Ni–Mn-based magnetic shape memory alloys is the best balanced tuning of ΔT hys, ΔT int, and ΔT/μ 0ΔH.

In this paper, we present a brief review of our recent progress in exploring Ni–Mn-based magnetic shape memory alloys with a variety of novel magnetocaloric properties for different application potentials by the balanced tuning of all the magnetostructural transformation parameters (phase transformation temperature, ΔT hys, ΔT int, ΔM, ΔS tr, etc.). This paper is organized as follows: In Sect. 2, we briefly introduce the methods for estimation of magnetic entropy change ΔS m, refrigeration capacity RC, and the effective refrigeration capacity RCeff. In Sect. 3, we review a variety of Ni–Mn-based magnetic shape memory alloys with different features for different application potentials: (1) large magnetic entropy change of 31.9 J kg−1 K−1 under a magnetic field of 5 T [23]; (2) giant effective magnetic refrigeration capacity (251 J kg−1) with a broad operating temperature window (33 K) under a magnetic field of 5 T [24]; (3) large reversible magnetic entropy change (ΔS m) of 14.6 J kg−1 K−1 and large reversible effective refrigeration capacity (76.6 J kg−1) under 5 T [25]. In Sect. 4, we give some conclusions and extension remarks.

Methods for Estimation of ΔS m, RC, and RCeff

The MCE is mainly characterized by the adiabatic temperature change ΔT ad and isothermal entropy change ΔS m. ΔT ad can be determined by calorimetric measurements under magnetic fields [7] or direct adiabatic temperature measurement. However, these measurements are very complex, so the MCE is usually reported in terms of ΔS m that can be calculated based on isothermal magnetization measurements with the aid of the Maxwell relation [8, 17]. In order to estimate the ΔS m, the M(H) curves at different temperatures approaching the austenitic transformation temperature should be measured. Before each M(H) measurement, the sample must be first cooled to a certain temperature (<M f) to ensure the same initial state of a fully transformed martensite and then heated to the target temperature. Based on the M(H) data, ΔS m can be estimated using the Maxwell relation [8, 17]:

$$\Delta S_{m} = S_{m} (T,H) - S_{m} (T,0) = \int_{0}^{{\mu_{0} H}} {\frac{\partial M}{\partial T}} d(\mu_{0} H).$$
(1)

It should be noted that currently it is questionable whether the calculation using the Maxwell relation could yield reliable ΔS m values for first-order magnetostructural transformation due to the coexistence of martensite and austenite [26]. In order to check the validity of the calculated results, the ΔS m values should also be estimated with the Clausius–Clapeyron relation which can be used to correctly determine the magnetic field-induced entropy change associated with the metamagnetic transition [27]:

$$\Delta S_{\text{m}} = - \Delta M' \cdot \frac{{{\text{d}}H_{\text{cr}} }}{{{\text{d}}T}},$$
(2)

where H cr is the critical field value of the inflection point within the metamagnetic transition region and ΔM′ corresponds to the magnetization difference between the high and low field phases, which can be evaluated from the isothermal M(H) curves. If the results obtained from the Clausius–Clapeyron relation and the Maxwell relation are consistent, it can be confirmed that the ΔS m values are reliable.

For practical applications, the magnetic cooling efficiency considering not only the magnitude of the MCE but also the operating temperature range is another figure of merit for judging the potential of the magnetic refrigerants [28]. The refrigeration capacity (RC) which stands for the amount of thermal energy that can be transferred between the cold and hot sinks in one thermodynamic cycle, is defined as

$$RC = \int_{{T_{cold} }}^{{T_{hot} }} {\Delta S_{m} } dT,$$
(3)

where T cold and T hot are the corresponding temperatures at half maximum of the ΔS m versus temperature (T) curve. It can be estimated by numerically integrating the area under the ΔS m ~ T curve between T cold and T hot.

For justifying the usefulness of a magnetic refrigerant during a thermodynamic cycle, the magnetic hysteresis loss (estimated from the area between the M(H) curves measured during increasing and decreasing fields) must be taken into account. Accordingly, a more reasonable criterion for assessing the cooling efficiency is the effective refrigeration capacity RCeff which can be obtained by subtracting the average hysteresis loss (\(\overline{HL}\)) from the RC value [28]

$$RC_{eff} = RC - \overline{HL} .$$
(4)

Optimization of Magnetocaloric Performance

Large Magnetic Entropy Change in a Ni41Co9Mn40Sn10 Magnetic Shape Memory Alloy

For practical applications, magnetocaloric materials should have large ΔS m. Although large ΔS m has been reported in many Ni–Mn-based alloys [29,30,31,32,33], the values of ΔS m were just computed from the Maxwell relation and they were not compared with the results estimated from DSC measurements or from the Clausius–Clapeyron relation or from the temperature dependence of specific heat capacity at different magnetic fields. Those results might be unreliable. Thus, it is necessary to discover Ni–Mn–X-based (X = In, Sn, Sb, Ga) magnetocaloric materials with a large and reliable ΔS m. It is known that, for magnetocaloric materials with a first-order phase transformation, the maximum ΔS m that can be obtained is almost equivalent to the transformation entropy change ΔS tr and the structural contribution to ΔS tr is proportional to the unit cell volume change ΔV/V (ΔV is the volume difference between high-temperature and low-temperature phases, V is the unit cell volume of the high-temperature phase) across the phase transformation. Therefore, in order to obtain large ΔS m, it is important develop new Ni–Mn–X-based (X = In, Sn, Sb, Ga) magnetocaloric materials with large ΔV/V and optimize the existing Ni–Mn–X-based (X = In, Sn, Sb, Ga) magnetocaloric materials with large ΔV/V.

The Ni45Co5Mn40Sn10 alloy was reported to exhibit large ΔM and large ΔS tr [34]. However, this alloy has a major drawback for MCE applications; that is, the Δ(μ 0 H)com is relatively large (larger than 7 T) due to the small ΔT/μ 0ΔH. In Ni–Mn-based alloys, the Co substitution for Ni was proved to be an effective way to enhance ΔT/μ 0ΔH [35]. In order to enhance the ΔT/μ 0ΔH of this particular alloy, we continue to increase the Co content in the Ni45Co5Mn40Sn10 alloy. The DSC curves of the Ni50−x Co x Mn40Sn10 (x = 6, 7, 8, and 9) alloys are shown in Fig. 1. We found that when the Co content reaches 9 at.% the martensitic transformation temperature is lower than the Curie temperature of austenite (about 433 K, determined from the DSC curve in Fig. 1) and the difference between them is moderate, indicating ΔT/μ 0ΔH is significantly enhanced [35], but its ΔS tr is still large (≈32.1 J kg−1 K−1).

Fig. 1
figure 1

DSC curves of the Ni50−x Co x Mn40Sn10 (x = 6, 7, 8, and 9) alloys

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In order to determine ΔT/μ 0ΔH and Δ(μ 0 H)com in the Ni41Co9Mn40Sn10 alloy, we carried out isofield magnetization measurements. Figure 2 shows the temperature dependence of magnetization [M(T) curve] measured under 0.01 T and 4 T, respectively. According to the M(T) curve under 0.01 T, M s, M f, A s, and A f , are 351, 339, 357, and 368 K, respectively. Compared with A s under 0.01 T, the A s is decreased by 11 K under 4 T, with a rate of ΔA s/μ 0ΔH = 2.75 K/T. As can be seen from Fig. 2, the high-temperature austenite shows ferromagnetic feature while the low-temperature martensite exhibits weak magnetic state. A large magnetization difference (ΔM ≈ 90 emu/g as determined from the M(T) curve under 4 T) between the two phases across magnetostructural transformation can be observed. The Δ(μ 0 H)com is determined to be about 4 T according to Δ(μ 0 H)com = (A f − A s)/(ΔT/μ 0ΔH). Based on the Clausius–Clapeyron relation ΔT/μ 0ΔH = ΔM/ΔS tr [14], ΔS tr under 4 T can be determined to be 32.7 J kg−1 K−1, which agrees well with the result determined from DSC measurements (≈ 32.1 J kg−1 K−1).

Fig. 2
figure 2

M(T) curves measured under magnetic fields of 0.01 and 4 T, respectively, for the Ni41Co9Mn40Sn10 alloy. Adapted from [23]

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In order to determine the ΔS m, we measured the M(H) curves at different temperatures close to the austenitic transformation temperature, as shown in Fig. 3. As can be seen from this figure, the slope of M(H) curves changes abruptly at a critical magnetic field in the temperature range from 344 K to 364 K, indicating the occurrence of magnetic field-induced transformation from martensite to austenite. We estimated the ΔS m using the Maxwell relation [Eq. (1)] from the M(H) curves. The temperature dependence of the estimated ΔS m at different magnetic fields is illustrated in Fig. 4. It can be found that the maximum value of ΔS m under 5 T is about 31.9 J kg−1 K−1 at 358 K. As indicated from Fig. 3, the magnetic field-induced transformation is complete around 358 K; so in this case, the ΔS m should be comparable to the ΔS tr determined from DSC. As a matter of fact, the ΔS m (31.9 J kg−1 K−1) is indeed close to ΔS tr (≈ 32.1 J kg−1 K−1), confirming that the maximum ΔS m we achieved is reliable. This ΔS m (31.9 J kg−1 K−1 under 5 T) is among the highest values reported so far in Ni–Mn–Sn-based alloys [23].

Fig. 3
figure 3

M(H) curves measured at different temperatures close to the austenitic transformation temperature, for the Ni41Co9Mn40Sn10 alloy. Adapted from [23]

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Fig. 4
figure 4

The magnetic entropy change (ΔS m) as a function of temperature at different magnetic fields, for the Ni41Co9Mn40Sn10 alloy. Adapted from [23]

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To shed light on the origin of the large ΔS m (which is related to the large ΔS tr) obtained in our Ni41Co9Mn40Sn10 alloy, we performed in situ synchrotron high-energy X-ray diffraction (HEXRD) experiments. The HEXRD results are shown in Fig. 5. All the diffraction peaks of the austenite can be well indexed according to the L21-type cubic Heusler structure (Fig. 5a); the diffraction pattern of martensite can be well indexed according to the six-layered modulated (6 M) monoclinic structure [36] (Fig. 5b). Based on the lattice parameter changes determined from the HEXRD results during the heating process, a significant unit cell volume contraction of 1.31% was found.

Fig. 5
figure 5

a, b High-energy X-ray diffraction patterns experimentally collected at 400 K (a) and 100 K (b) corresponding to austenite and martensite phases, respectively, for the Ni41Co9Mn40Sn10 alloy. Adapted from [23]

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As mentioned above, for first-order magnetostructural transformation, the structural part of the transformation entropy change is proportional to the unit cell volume change across phase transformation. Therefore, the significant unit cell volume change (≈1.31%) lies at the origin of the large structural entropy change and, consequently, large magnetic entropy change was observed in the presently studied alloy. As a matter of fact, in the Fe–Rh [37], Gd–Si–Ge [38], and La–Fe–Si [39] materials with large unit cell volume change (0.9%, 0.4%, 1.3%, respectively) during phase transformation, large magnetic entropy change was also observed. Most remarkably, in the B-doped Mn–Co–Ge alloy with the large unit cell volume change of 4.0% [40], giant magnetic entropy change of about 47.3 J kg−1 K−1 (under 5 T) was recently reported by Trung et al. [40]. The correlation between the unit cell volume change and magnetic entropy change is helpful for predicting high-performance magnetocaloric materials from the crystallographic data.

Giant Magnetic Refrigeration Capacity Near Room Temperature in Ni40Co10Mn40Sn10 Magnetic Shape Memory Alloy

Although the magnitude of ΔS m under 5 T is very large for the Ni41Co9Mn40Sn10 alloy, its operating temperature window with large ΔS m is very narrow. For practical applications of the Ni–Mn–X-based (X = In, Sn, Sb, Ga) magnetocaloric materials, it is urgent to surmount the obstacle of limited operating temperature window. On the other hand, it is of great significance to enhance the refrigeration capacity of these materials to facilitate their more efficient use for magnetic refrigeration. Furthermore, the magnetocaloric effect should occur near room temperature. Thus, in order to meet the above-mentioned requirements, the ΔT/μ 0ΔH should be further enhanced. Therefore, we further tuned the magnetostructural transformation parameters via Co addition. We found that the Curie temperature of austenite (about 446 K, determined from the DSC curve in Fig. 1) of the Ni40Co10Mn40Sn10 alloy is increased to a higher temperature and martensitic transformation temperatures are brought down to lower temperatures (near room temperature) (Fig. 1). Therefore, the difference between the Curie temperature of austenite and martensitic transformation temperature is notably enhanced and a larger ΔT/μ 0ΔH can be expected in the Ni40Co10Mn40Sn10 alloy according to Ref. [35]. Additionally, this alloy still has a large ΔS tr of 14.1 J kg−1 K−1 determined from the DSC data as shown in Fig. 1. It should be noted that the thermal hysteresis and phase transformation interval of the Ni40Co10Mn40Sn10 alloy are larger than that of the Ni41Co9Mn40Sn10 alloy, as shown in Fig. 1. Similar results were observed in our previous work [35].

In order to determine the value of ΔT/μ 0ΔH and examine the magnetic field-induced phase transformation, we carried out isofield magnetization measurements. The M(T) curves under 0.01 T and 4 T magnetic fields are shown in Fig. 6a and the M(H) curves measured at different temperatures are illustrated in Fig. 6b. It is evident that the high-temperature austenite shows ferromagnetic feature [see the M(H) curve at 350 K in Fig. 6b], while the low-temperature martensite is in a weak magnetic state. Hence, a large magnetization difference between the two phases across martensitic transformation is observed (Fig. 6a). It can be seen from Fig. 6a that application of magnetic fields notably decreases the phase transformation temperatures of the studied alloy. The A s temperature is decreased by 33 K under a magnetic field of 4 T, with the rate of 8.3 K/T. This is much larger than the values reported in other Ni–(Co)–Mn–Sn alloys [13, 23, 35]. We also found that the thermal hysteresis in Ni40Co10Mn40Sn10 increases with the increase of magnetic field. It is generally acknowledged that the hysteresis behavior is related to the nucleation of new phase and the interfacial interaction at the phase boundary during first-order phase transformation. According to previous work [41], the hysteresis is linked to the friction strength of phase boundary motion during the magnetostructural transformation in Ni–Mn–X-based (X = In, Sn, Sb, Ga) Heusler alloys. The increase of hysteresis may suggest that the friction resistance increases with the increase of magnetic field. The value of Δ(μ 0 H)com for this alloy is determined to be about 2.2 T according to Δ(μ 0 H)com = (A f − A s)/(ΔT/μ 0ΔH) and this value of 2.2 T is far smaller than 4 T obtained in the Ni41Co9Mn30Sn10 alloy. This indicates that the transformation in the Ni40Co10Mn40Sn10 alloy can be more easily driven by the magnetic field compared with that in the Ni41Co9Mn40Sn10 alloy. Considering the above-mentioned information, we believe that our Ni40Co10Mn40Sn10 alloy shows large ΔS m with a very broad operating temperature window.

Fig. 6
figure 6

a M(T) curves measured under magnetic fields of 0.01, 2, 4, and 7 T, respectively, for the Ni40Co10Mn40Sn10 alloy. b M(H) curves measured at 100, 200, 240, 270, and 350 K, respectively, for the Ni40Co10Mn40Sn10 alloy. The arrows indicate increasing and decreasing magnetic fields during a cycle. Adapted from [24]

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To evaluate the MCE of the studied Ni40Co10Mn40Sn10 alloy, we performed isothermal magnetization measurements. The M(H) curves at different temperatures close to the austenitic transformation temperature were recorded and the resultant M(H) curves are shown in Fig. 7a. Correspondingly, ∆S m was estimated numerically from the isothermal M(H) curves according to the Maxwell relation [Eq. (1)]. The temperature dependence of ∆S m at different magnetic fields is demonstrated in Fig. 7b. It is apparent that the curves show a broad plateau with the maximum value of ∆S m ≈ 14.9 J kg−1 K−1 under a magnetic field of 5 T, since this magnetic field is large enough to induce complete phase transformation over a wide temperature range. Notably, the plateau covers a broad temperature interval from 267 to 287 K (under 5 T), resulting in an effective operating temperature window of 33 K (determined from the full width half maximum of the ∆S m peak). The maximum value of ∆S m (14.9 J kg−1 K−1) is in good agreement with the ∆S tr (14.1 J kg−1 K−1) determined from DSC. To further validate the ∆S m we achieved, we also carried out estimation with the Clausius–Clapeyron relation [Eq. (2)], and the obtained results for a field of 5 T are shown as solid stars in Fig. 6b. Clearly, the ∆S m values estimated with the Maxwell relation and the Clausius–Clapeyron relation are in good agreement, confirming the reliability of our results.

Fig. 7
figure 7

a M(H) curves measured at different temperatures close to the austenitic transformation temperature, for the Ni40Co10Mn40Sn10 alloy. For clarity, only the curves during increasing magnetic fields are displayed. b The magnetic entropy change (∆S m) as a function of temperature at different magnetic fields, for the Ni40Co10Mn40Sn10 alloy. The solid stars denote the data estimated from the Clausius–Clapeyron relation for a magnetic field of 5 T, while the other solid symbols denote the data calculated using the Maxwell relation for different magnetic fields. Adapted from [24]

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With Eq. (3), the RC value for our Ni40Co10Mn40Sn10 alloy was estimated and it is compared with the values for the most studied magnetocaloric materials [26, 28, 32, 42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62], as shown in Fig. 8a. It can be seen that the RC value for the present Ni40Co10Mn40Sn10 alloy is significantly larger than that of other Heusler-type Ni–Mn-based magnetocaloric materials. With Eq. (4), RCeff for the studied alloy was calculated to be 251 J kg−1 for a magnetic field of 5 T. For comparison, the RCeff values under a field of 5 T for the most studied magnetocaloric materials [26, 28, 32, 42,43,44,45,46,47,48,49,50,51, 63] are schematically illustrated in Fig. 8b. It is clear that our Ni40Co10Mn40Sn10 alloy shows the largest RCeff among the Ni–Mn-based magnetocaloric materials, and its RCeff value is comparable to that of the most promising Gd–Si–Ge and La–Fe–Si magnetocaloric materials. The large RCeff is beneficial for the magnetic refrigeration applications.

Fig. 8
figure 8

Schematic illustration of the magnetic refrigeration capacity (RC) (a) and the effective magnetic refrigeration capacity (RCeff) (b) as a function of temperature under a magnetic field of 5 T for the most studied magnetocaloric materials. Except for the data obtained from the present work (for the Ni40Co10Mn40Sn10 alloy), the other data are taken or deduced from the references, with the numbers denoting: 1-Ni45Co5Mn37In13 [43], 2-Ni45Co5Mn37.5In12.5 [26], 3-Gd5Si2Ge2/Gd5Si2Ge1.9Fe0.1 [28], 4-Fe48Rh52 [42], 5-Ni42Co8Mn30Fe2Ga18 [32], 6-Ni45Co5Mn36.6In13.4/Ni45Co4.75Fe0.25Mn36.6In13.4 [44], 7-Ni50Mn34In16 [45], 8-Ni50Mn37Sn13 [46], 9-Ni52Mn26Ga22 [47], 10-Ni50Mn34In16 [48], 11-La0.7Pr0.3Fe11.5Si1.5C0.2H x (x = 0.6, 1.2) [49], 12-Gd/La1−x Pr x Fe10.7Co0.8Si1.5 (x = 0, 0.2, 0.4, 0.5) [50], 13-Ni2Mn0.75Cu0.25Ga [51], 14-Ni50Mn35.3In14.7 [52], 15-MnAs [53], 16-Ni45Co5Mn37.5In12.5 [54], 17-Mn0.89Fe0.11CoGe [55], 18-Ni2Mn1.36Sn0.4Ga0.24 [56], 19-Ni50Mn35In15 [57], 20-Ni49Fe1Mn37Sn13 [58], 21-Ni44Fe2Mn43Sn11 [59], 22-Ni43Co7Mn31Ga19 [60], 23-Ni41Co9Mn32Ga16In2 [61], 24-Ni43Mn46Sn11C2 [62], 25-Ni50Mn33Cr1In16 [63]. Adapted from [24]

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Large Reversible Magnetocaloric Effect in a Ni–Co–Mn–In Magnetic Shape Memory Alloy with Small Magnetic Hysteresis

For Ni–Mn–X-based (X = In, Sn, Sb, Ga) magnetocaloric materials, as mentioned before, their disadvantage is the presence of thermal and magnetic hysteresis which will make them exhibit small or no magnetocaloric effect during the second and subsequent field cycles [11]. To achieve a reversible magnetocaloric effect, the Ni–Mn–X-based (X = In, Sn, Sb, Ga) magnetocaloric materials should have small ΔT hys, narrow ΔT int, and large ΔT/μ 0ΔH. Among the Ni–Mn–X-based (X = In, Sn, Sb, Ga) alloys, Ni–Mn–In-based alloys are easier to meet these demands due to their very small hysteresis, according to the information in literature [21, 64]. Therefore, we select Ni51Mn33.5In15.5 as an initial alloy and add Co at the expense of Ni in this Ni–Mn–In alloy.

Figure 9a shows the DSC curve of the Ni49.8Co1.2Mn33.5In15.5 alloy. It can be seen that the Curie temperature is 325.7 K, while the martensitic and austenitic transformation start and finish temperatures, M s, M f, A s, and A f, are 248.7, 243.4, 251.1, and 256.8 K, respectively. Correspondingly, the thermal hysteresis is A f − M s = 8.1 K (or A s − M f = 7.7 K) and transformation interval is M s − M f = 5.3 K(or A f − A s = 5.7 K). Additionally, the ΔS tr is determined to be 14.4 J kg−1 K−1 from the DSC data. Figure 9b shows the M(T) curves measured under 0.02 T and 5 T, respectively. From the M(T) curve under 5 T, a large magnetization difference (ΔM ≈ 75.4 emu/g) between the two phases across martensitic transformation can be determined. It can be seen that A s is decreased by 24.5 K by a field of 5 T, with the rate of ΔA s/µ0ΔH ≈ 4.9 K/T. It is reported that a reversible MCE can be obtained in a certain temperature interval when the magnitude of the shift in martensitic transformation temperatures induced by the magnetic field is larger than the sum of the thermal hysteresis and transformation interval [21]. That is to say, a reversible MCE occurs in a certain temperature interval when there is a gap between the M(T) hysteresis loop under magnetic field and that under zero field. We indeed found a gap between the hysteresis loop under 5 T and that under 0.02 T (Fig. 9b), which corresponds to the temperature interval between 225.7 K (the A s under 5 T) and 242.1 K (the M f under 0.02 T). Thus, a reversible MCE could be achieved within this temperature interval in our Ni49.8Co1.2Mn33.5In15.5 alloy.

Fig. 9
figure 9

a DSC curves with cooling and heating rates of 10 K/min, for the Ni49.8Co1.2Mn33.5In15.5 alloy. The horizontal arrows indicate the cooling and heating processes. The determination of the transformation temperatures, M s, M f, A s, A f, and T c, is illustrated on the curves. b M(T) curves measured under magnetic fields of 0.02 and 5 T, respectively, for the Ni49.8Co1.2Mn33.5In15.5 alloy. Adapted from [25]

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To evaluate the reversibility of the magnetic field-induced transformation, we carried out M(H) measurements in the temperature range of 222–240 K at an interval of 3 K during the cyclic increasing and decreasing magnetic field, as shown in Fig. 10a. It can be found that at each temperature, the M(H) curves recorded during the first and second cycles of increasing and decreasing magnetic field almost coincide with each other (Fig. 10a). This suggests that there is no residual field-induced austenite after each cycle and the transformation induced by magnetic field at these temperatures is almost fully reversible, which could lead to a reversible MCE. It can also be found that the magnetic hysteresis (∆H hy) is very small (≈1.1 T) in our Ni49.8Co1.2Mn33.5In15.5 alloy, which is marked by the horizontal arrow in Fig. 10a. In order to compare the magnetic hysteresis in the present Ni49.8Co1.2Mn33.5In15.5 alloy with that in other magnetocaloric materials in literature [14, 19, 24, 26, 43, 64,65,66,67,68,69,70,71,72,73], the magnetic hysteresis of Ni–(Co)–Mn–X (X = In, Sn, Sb) Heusler alloys is shown in Fig. 10b. Obviously, our Ni49.8Co1.2Mn33.5In15.5 alloy shows the minimum magnetic hysteresis (≈1.1 T) among the Ni–Mn–X-based (X = In, Sn, Sb, Ga) magnetocaloric materials. The small magnetic hysteresis is important for reducing the energy loss during magnetic field cycling and attaining a large reversible MCE.

Fig. 10
figure 10

a Two cycles of isothermal M(H) curves with minor difference between the first and second cycles at constant temperatures from 222 to 240 K with an interval of 3 K, for the Ni49.8Co1.2Mn33.5In15.5 alloy. b Schematic illustration of the magnetic hysteresis as a function of temperature for Ni–(Co)–Mn–X (X = In, Sn, Sb) Heusler alloys. Except for the data obtained from the present work (for the Ni49.8Co1.2Mn33.5In15.5 alloy), the other data are taken or deduced from the references, with the numbers denoting: 1-Ni50.3Mn33.8In15.9 [71], 2-Ni50Mn35In15 [66], 3-Ni50Mn34In16 [72], 4-Ni45Co5Mn36.7In13.3 [14], 5-Ni45Co5Mn37In13 [43], 6-Ni50Mn35In15 [73], 7-Ni51Mn33In16 [64], 8-Ni45Co5Mn37.5In12.5 [26], 9-Ni43Co4Mn42Sn11 [19], 10-Ni43Co7Mn39Sn11 [70], 11-Ni43.5Co6.5Mn39Sn11 [69], 12-Ni40Co10Mn40Sn10 [24], 13-Ni45Co5Mn38Sb12 [68], 14-Ni45Co5Mn38Sb12 [67], 15-Ni50Co5Mn39Sb11 [65]. Adapted from [25]

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The temperature dependence of the reversible magnetic entropy change (∆S m) under 5 T, estimated with the Maxwell relation [see Eq. (1)] based on the M(H) data shown in Fig. 11a, is depicted in Fig. 11b. It can be seen that the maximum value of ΔS m under 5 T is about 14.6 J kg−1 K−1. To further verify the validity of our data, we also estimated the ΔS m values with the Clausius–Clapeyron relation which applies to the first-order phase transformation [see Eq. (2)], and such values are shown in Fig. 11b as solid stars. A good agreement between the values estimated with the Clausius–Clapeyron relation and the Maxwell relation is observed, confirming the reliability of the data. The reversible magnetic refrigeration capacity (RC) is estimated with Eq. (3) to be 125.0 J kg−1. Thanks to the small magnetic hysteresis, the present Ni49.8Co1.2Mn33.5In15.5 alloy only exhibits a low average magnetic hysteresis (\(\overline{HL}\)) of 48.4 J kg−1. Therefore, according to Eq. (4), the reversible magnetic refrigeration capacity RCeff is determined to be 76.6 J kg−1. Actually, this is a large reversible RCeff, beneficial for practical magnetic refrigeration applications.

Fig. 11
figure 11

a M(H) curves measured at different temperatures from 222 to 240 K with an interval of 3 K, for the Ni49.8Co1.2Mn33.5In15.5 alloy. For clarity, only the curves recorded during increasing magnetic fields are shown. b The reversible magnetic entropy change (∆S m) under a magnetic field of 5 T shown as a function of temperature, for the Ni49.8Co1.2Mn33.5In15.5 alloy. The solid stars denote the data estimated from the Clausius–Clapeyron relation. Adapted from [25]

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The reversibility of phase transformation is especially crucial for a magnetic refrigerant like Ni–Mn–X-based (X = In, Sn, Sb, Ga) Heusler alloys which undergo first-order magnetostructural transformation. Because of the large hysteresis or the very small sensitivity of transition temperature to the applied magnetic field in many of the Ni–Mn-based Heusler alloys reported in literature, the austenite induced by the magnetic field cannot transform back to the initial martensite when the magnetic field is removed. Fortunately, we achieved a large reversible MCE in our Ni49.8Co1.2Mn33.5In15.5 alloy by tuning its magnetostructural transformation parameters. Nevertheless, it should be noted that this large reversible MCE was achieved under a magnetic field of 5 T. From the practical application point of view, large reversible MCE should be achieved at relatively low fields that could be provided by permanent magnets. In order to achieve this goal, it is essential to further reduce the thermal hysteresis and phase transformation interval and enhance the sensitivity of phase transformation temperature to applied magnetic field. Recently, barocaloric effect and elastocaloric effect have also been reported in Ni–Mn-based magnetic shape memory alloys [74]. The multicaloric effects observed in these alloys may imply that the MCE can be tailored by uniaxial stress or hydrostatic pressure. We expect that large reversible MCE could be obtained under low magnetic fields via a dual-stimulus multicaloric cycle.

Conclusions and Extension Remarks

Investigation on MCE is of great significance for not only fundamental interests but also technological applications. Recently, we have investigated the MCE in Ni–Mn–Sn-based and Ni–Mn–In-based magnetic shape memory alloys. In these alloys, thermal hysteresis, phase transformation interval, and the sensitivity of phase transformation temperature to applied magnetic field are not only interdependent but also increase simultaneously with the decrease of phase transformation temperature caused either by magnetic field or by composition variation. It is difficult to optimize the magnetocaloric properties due to the interdependence of these magnetostructural transformation parameters. In this paper, we demonstrated our recent work on developing high-performance magnetocaloric materials in Ni–Co–Mn–Sn and Ni–Co–Mn–In magnetic shape memory alloy systems. By systematically tuning the magnetostructural transformation parameters via Co substitution in Ni–Mn–Sn-based and Ni–Mn–In-based alloys, a variety of novel magnetocaloric properties have been developed. A large magnetic entropy change of 31.9 J kg−1 K−1 under 5 T was obtained in the Ni41Co9Mn40Sn10 alloy. A giant effective magnetic refrigeration capacity of 251 J kg−1 under 5 T and a broad operating temperature window of 33 K near room temperature were achieved in the Ni40Co10Mn40Sn10 alloy. A large reversible magnetic entropy change of 14.6 J kg−1 K−1 and a broad operating temperature window of 18 K were achieved under 5 T in the Ni49.8Co1.2Mn33.5In15.5 magnetic shape memory alloy. Furthermore, a large reversible effective refrigeration capacity of 76.6 J kg−1 was obtained under 5 T in this alloy. Additionally, these alloys only consist of inexpensive and non-toxic elements. All these merits make the above-mentioned magnetic shape memory alloys attractive candidates for magnetic refrigeration. In the future, further reducing the critical field required for complete and reversible field-induced transformation to the field range that can be generated by permanent magnets would greatly benefit the practical magnetocaloric refrigeration applications of these materials. To achieve this goal, further increasing the magnetization difference between the two phases (∆M) and decreasing the thermal hysteresis and phase transformation interval would be required. ∆M may be increased by enhancing the ferromagnetic exchange interaction to increase the Curie temperature and thus enlarge the difference between Curie temperature and phase transformation temperature. The thermal hysteresis and phase transformation interval may be reduced by improving the geometric compatibility between the two phases [75] and/or employing the minor hysteresis loops [17]. THERMAG VI held in 2014 at the Victoria Conference Centre, Canada announced an enhanced scope that includes all magnetocaloric materials and applications, regardless of temperature range [76]. This allows for coverage of new applications such as gas liquefaction systems as well as thermally driven magnetic heat engines. From this point of view, magnetic cooling techniques will be advanced in much wider application fields [76]. Thus, we expect that the balanced tuning of magnetostructural transformation parameters of magnetocaloric alloys provides an instructive reference to the magnetic refrigeration community. The exploration of the multicaloric effect in magnetic shape memory alloys will be a future research trend for solid-state refrigeration.