稀有金属(英文版) 2015,34(08),527-539

收稿日期：14 April 2015

基金：financially supported by the National Natural Science Foundation of China (Nos. 51371105, 51071023, and 51101047);

Recent progress in Heusler-type magnetic shape memory alloys

Guang-Hua Yu Yun-Li Xu Zhu-Hong Liu Hong-Mei Qiu Ze-Ya Zhu Xiang-Ping Huang Li-Qing Pan

Department of Materials Physics and Chemistry, University of Science and Technology Beijing

College of Science, China Three Gorges University

Department of Physics, University of Science and Technology Beijing

Abstract：

Magnetic shape memory alloys(MSMAs), both in condensed matter physics and in material science, are one of the most extensive research subjects. They show prompt response to the external magnetic field and give rise to large strain and have fine reversibility. The well-known example is Heusler-type MSMAs, which possess excellent multifunctional properties and have potential applications in energy transducer, actuator, sensor, microelectromechanical system, and magnetic refrigerator. In this paper, it is shown the recent progress in magnetostructural transformation, magnetic properties, shape deformation, magnetocaloric effect as well as magnetic field-induced shape memory effect in Ni–Mn–Ga, Ni Mn Z(Z = In, Sn, Sb),and Ni Co Mn Z(Z = In, Sn, Sb, Al) Heusler-type MSMAs.The remaining issues and possible challenges are briefly discussed.

Keyword：

Heusler alloy; Magnetic shape memory alloy; Martensitic transformation; Magnetocaloric effect;

Author： Li-Qing Pan,e-mail: lpan@ctgu.edu.cn;

Received： 14 April 2015

1 Introduction

In the past decades, magnetic shape memory alloys (MSMAs) with Heusler structure have attracted considerable attention due to their multifunctional properties which include giant magnetoresistance (MR) [1, 2], shape recovery [2–5], metamagnetic properties [6, 7], and large magnetocaloric effect (MCE) [8, 9]. Among these attracting properties, the shape memory with strains as large as 10 % under applying magnetic fields is a focus for concern [10], in which there are two primary mechanisms leading to the field-induced strain in MSMAs: magnetic field-induced phase transformation and magnetic field-induced twin boundary motion. In the former, the materials undergo a structural transformation from a high-symmetric cubic austenite to a low-symmetric martensite upon cooling. The structural transformation is diffusionless and displacive. In the latter, the energy needed for a martensite twin boundary motion is lower than the magnetocrystalline anisotropy energy of a martensite variant in the mechanism, and then, the variant will grow and result in a field-induced macroscopic shape change [11]. As to the external stimulation, the application of field, temperature change, and chemical or hydrostatic pressure can adjust the properties of MSMAs, in which many works were involved.

Heusler alloys are a famous kind of intermetallic compounds with 1:1:1 (usual called half-Heusler alloys) or 2:1:1 (usual called full-Heusler alloys) composition containing more than 1500 members [12], which discovered by Fritz Heusler in 1903. Nowadays, they are still a hot research field [13]. New characteristics and potential technology applications arise continually [14]. The fullHeusler alloys have a general stoichiometric formula X₂YZ in which all the components occupy inequivalent crystallographic positions in the cubic structure of the L2₁type as shown in Fig. 1a [13]. But the half-Heusler alloys form in a non-centrosymmetric cubic structure (F-43m, C1_b) as shown in Fig. 1b. The large class of magnetic X₂YZ and XYZ compounds demonstrates various magnetic behaviors and functional magnetic properties, such as half-metallic ferromagnetic (Co₂Fe Si, Ni Mn Sb, etc.), magneto-optical effect (Mn Pt Sb, etc.), superconductivity (Yb Pd₂Sn, Ni₂Zr Sn, etc.), shape memory effect (Ni₂Mn Ga, Mn₂Ni Ga, etc.), topological insulators (REPt Bi, RE = rare earths, etc.), and magnetocaloric and magnetostructural characteristics (Ni Mn In, Ni Mn Sb, etc.) [15–20]. All these properties indicate that the Heusler alloys are the potential candidates for the applications in spintronics, solar cells, high-energy photoemission, superconductivity, and thermoelectric fields [13].

Fig.1 Crystal structure of Heusler alloys X2YZ (structure type L21) a and crystal structure of half-Heusler alloys XYZ (structure type C1b) b

Since Ullakko et al. [21] discovered large magnetic field-induced strains (MFISs) in Heusler alloy Ni₂Mn Ga single crystal in 1996, many Heusler alloys have been investigated extensively such as Ni Mn Z (Z = In, Sn, Sb, Al) [22–24], Ni Co Mn Z (Z = In, Sn, Sb, Al, Ga) [6, 25, 26], Ni₂Fe Z [27–31], Mn₂Ni Z [32, 33], Fe₂Mn Z [34, 35], and Co₂Ni Z [36–38]. This kind of MFISs exhibit many merits, such as large strain, high work output, high response frequency, and tunable working temperature. Here, it is focused on the Ni–Mn–Ga, Ni Mn Z (Z = In, Sn, Sb), and Ni Co Mn Z (Z = In, Sn, Sb, Al) systems. This class of functional materials exist potential technological application in mechanical sensing, magnetic field-induced actuation, energy harvesting, and magnetic refrigeration [11, 39, 40].

2 Properties of Ni–Mn–Ga systems

2.1 Structure and shape deformation of Ni–Mn–Ga systems

The structure of the stoichiometric Ni₂Mn Ga is cubic L2₁type (space group: Fm3m) with the lattice constant a = 0.5825 nm. At room temperature (RT), it is ferromagnetic and the Curie temperature (T_C) is slightly higher than RT, T_C& 376 K [41]. Upon the cooling of the alloy, the high-temperature cubic phase passes into a quasi-cubic modulated phase 3M (i.e., called a premartensitic phase) with a modulation period equal to three atomic planes. Upon further cooling of the alloy, there occurs a structural transition from the quasi-cubic phase 3M into a tetragonal martensitic phase 5M with a modulation period equal to five atomic planes at the martensitic transformation temperature (T_M) of about 200 K. A further increase in pressure along the [001] axis leads to the transition of the tetragonal phase 5M into an orthorhombic phase 7M, which is also modulated with a period of seven atomic planes (Fig. 2) [42].

In Ni–Mn–Ga systems, the values of T_Mand T_Cvary obviously with the stoichiometric composition. Many factors play an important role in the magnetic and structural properties of Ni₂Mn Ga, such as interatomic spacing, composition, 3d electron numbers, and d–d exchange interactions [43].

Systematic experiments and theoretical investigations of nonstoichiometric ferromagnetic alloys Ni_2?xMn_1–xGa were carried out during the last years. It is confirmed that the magnetic and structural transitions take place not only in the stoichiometric alloy but also in alloys with a significant deviations from stoichiometry [10, 44–46]. The phase diagram is shown in Fig. 3 [42] in the T–x–e/ a (where e/a is the concentration of valence electrons per atom) coordinates.

Fig.2 Crystal structure of Ni2Mn Ga alloy: a structural transition from phase with a cubic lattice of L21type into a phase with a tetragonal structure of L10type; b, c lattice distortions in 5M and 7M phases, respectively (schematic)

Fig.3 Phase diagram of Ni2?xMn1-xGa alloys in T (temperature)– x (concentration of excess Ni atoms)–e/a (concentration of valenceelectrons per atom). Tm, temperature of structural transition; TC, temperature of magnetic transition; Tp, temperature of premartensitic transition; FMferromagnetism; PMparamagnetism

Fig.4 Field-induced strain of a single-variant sample of orthorhombic seven-layered phase in Ni48.8Mn29.7Ga21.5alloy at 300 K measured perpendicular to magnetic field applied along [100] direction

Since the first observation of 0.2 % MFIS in a single crystal of Ni₂Mn Ga in 1996 [21], a lot of work were developed. Murray et al. [44] reported MFIS of 6 % in ferromagnetic martensitic Ni49.8Mn28.5Ga21.7alloy at room temperature. Sozinov et al. [10] declared that they acquired giant MFIS of *9.5 % in Ni48.8Mn29.7Ga21.5orthorhombic seven-layered martensitic phase in the field of less than 1 T at ambient temperature (Fig. 4; [10]). Wang et al. [47] obtained a large reversible MFIS of -0.6 % in [001] direction of the Ni₅₃Mn₂₂Ga₂₅single crystal at 300 K with a field of 1194 k A m^-1(Fig. 5; [47]). In addition, they found a net MFIS of 1.8 % by rotating the field around the sample from the [001] to [100] directions. These works stimulate numerous investigations on Ni–Mn–Ga shape memory alloys [41, 45, 48–58].

Fig.5 Longitudinal MFIS of Ni52Mn23Ga25single-crystal sample as a function of magnetic field (H) applied along [001] and [100]directions of sample at 300 K. Arrows indicating directional change of magnetic field. Inset displaying relative orientation of sample, strain gauge, and applied field for MFIS measurements

Karaman et al. [54] reported that in Ni₂Mn Ga single crystals, the magnetic field-induced structure transformation (MIST) is feasible by stress-assistant under low field. Moreover, if cyclic field is loaded, this effect will be repeatable. Under a low value of magnetic field, a reversible MFIS of 0.5 % accompanied with an actuation stress (*20 MPa) was acquired due to the magnetocrystalline anisotropy energy (Fig. 6; [53–56]). Experiments confirmed that the one-way MFIS can reach up to 3.1 % when loading different stress magnitudes (less than 110 MPa) in Ni₂Mn Ga single crystals [54, 56].

2.2 Properties of element doping in Ni–Mn–Ga systems

To improve the ductile strength of Ni–Mn–Ga alloys, some scholars studied the magnetic properties and shape memory effect of Fe-doped Ni–Mn–Ga [1, 28, 29, 31, 51, 52, 59]. Wu et al. [52] observed that by partly substituting Fe for Mn in Ni52Mn24Ga24, the alloy (Ni52Mn16Fe8Ga24) shows a large moment of 3.91 l_B/f.u. and a higher T_Cof 381 K compared with T_C= 348 K of undoped sample Ni₅₂Mn₂₄Ga₂₄. Liu et al. [51] reported that iron doping increased T_Cfrom 351 to 429 K in Ni50.4Mn28-xFexGa21.6, while dropped TMfrom 220 to 140 K in Ni50.5Mn25-xFexGa24.5, and the thermal hysteresis was expanded from about 7 to 18 K in Ni50.5Mn25-xFexGa24.5with x varying from 0 to 17, respectively. The intense coupling between Fe and Mn and the large moment of Fe atoms may be the main factors that caused the increase in T_C[59]. Subsequently, they observed a large MR up to -9 % at 136 K and 5 T during the martensitic transformation in Ni₅₀Mn₈Fe₁₇Ga₂₅ribbon [1], where the martensite and austenite phase coexist (Fig. 7; [1]). The magnetoresistance(MR = [R(H) - R(0)]/R(0),where R(H) is the resistance of sample in magnetic field H, R(0) is the resistance of sample in zero field) is mainly associated with the local magnetic disorders, heterogeneity, and magnetic clusters.

Fig.6 Schematic of magneto-thermo-mechanical (MTM) setup with an electromagnet and a capacitive displacement sensor used in study a; a plot of representative data obtained during MTM experiments b. Stress applied and temperature keeping constant, magnetic field being ramped,and strain response being measured

Fig.7 Longitudinal magnetoresistance (MR) versus magnetic field (H) at different temperatures. Inset (1) showing temperature dependence of MR at 5 T. Inset (2) plotting temperature dependence of resistance (R) during heating

In order to increase the difference of the saturation magnetization between the martensite and austenite, and acquire large MCE, or increase the Curie temperature (T_C), many researchers attempt to improve the properties by Co doping into Ni–Mn–Ga systems. Kanomata et al. [58] observed that T_Cincreases while T_Mdecreases with the increase in Co concentration (x) in Co-doped Ni_2-xCo_xMn Ga, and the magnetic moment per formula unit at 5 K shows a broad maximum of 4.7 l_Baround x = 1.0. The doping of Co into Ni Mn Ga can stabilize the austenite, weaken the stability of martensite, and give rise to the large MCE simultaneously. So the reverse martensitic transformation may be enhanced by appropriate Co doping in Ni Mn Ga [60]. High values of DM, the difference of magnetization during the martensitic transformation, up to 49.3 Am²kg^-1at the martensitic transformation in the samples of Ni₄₁Co₉Mn₃₂Ga₁₈were obtained, assuring the possibility to strongly drive the transformation by applying an external magnetic field (|d T/d H| up to *3 K T^-1) [61]. Fabbrici et al. [60] reported that the MCE value increased from (-9.1 ± 4.5) J kg^-1K^-1for the Co-free sample of Ni50Mn30Ga20up to (17.8 ± 3.6) J kg^-1K^-1for the sample of Ni41Co9Mn32Ga18.

For the Ni–Mn–Ga alloys with large magnetostrain tend to be broken after certain magnetizing circles because of the brittleness, Li et al. [62] investigated the substitution of Cu for Ni in Ni50-xCuxMn31Ga19(x = 2–10) alloys. They observed the magnetic field-induced reverse martensitic transformation in the Ni Mn Ga Cu alloys and the T_Mreduced 40 K with per Cu atom addition. The substitution of Cu for Ni in Ni Mn Ga could improve the ductility obviously.

Khan et al. [43] discussed the structure, magnetization, and electrical resistivity in In-doped Ni–Mn–Ga samples of Ni₂Mn Ga_1-xIn_x(0 \ x \ 0.25) alloys. The lattice parameters enlarge with x increasing due to the larger radii of In ion, while the negative volume change (*-0.1 %) is shown following the martensitic transformation. T_Mand T_Cshow a linear decrease with In concentration increasing. Albertini et al. [61] reported a high value of DM up to 73.5 Am²kg^-1and a high decrease (closer to RT) of the T_M(|d T_M/d H| up to *5 K T^-1) in Ni41Co9Mn32Ga16In2alloy. Zhang et al. [63] reported that by the partial substitution of In for Ga, the paramagnetic austenite phase is well stabilized, and the magnetostructural transition can be tailored around RT.

Barton et al. [64] investigated the Heusler alloys Ni₂Mn Ga_1-xZ_xwith Z = Sn (0 \ x \ 1) and Z = Zn (0 \ x \ 0.1). T_Mdecreases with a rate of 25 K per Sn addition. To the contrary, T_Mincreases rapidly with the substitution of Zn for Ga. With certain Zn content, the martensitic transition occurs at RT. The replacement of Ga with Sn suppresses the martensitic transition intensively. However, owing to the easily evaporation of the metallic zinc at low temperature, the sample preparation of Zn substitution is difficult.

Dong et al. [65] reported that Ti alloying is an effective method to increase the ductility of Ni Mn Ga alloy after proper aging treatment, for the Ti-rich precipitates which form during aging hinder the movement of dislocations.

2.3 Magnetocaloric effect of Ni–Mn–Ga systems

The magnetocaloric effect (MCE) is also significant in the Ni–Mn–Ga systems. An important parameter of MCE is the entropy change that accompanies the martensitic transformation. Ingale et al. [55] reported that the magnetic entropy change (DS) is about -7.0 J kg^-1K^-1at 332 K in the magnetic field of 1.2 T in Ni54.8Mn20.3Ga24.9. Meanwhile, the entropy change can be enhanced by Co doping. In Ni₄₁Co₉Mn₃₂Ga₁₈, the entropy change (DS) reaches (17.8 ± 3.6) J kg^-1K^-1contrast to (-9.1 ± 4.5) J kg^-1K^-1in the Co-free alloy Ni50Mn30Ga20[60]. Cherechukin et al. [45] investigated magnetic entropy change in Ni_2?xMn_1-xGa (x = 0.16,0.18,0.19,0.20,0.21) alloys. The largest entropy change of (20.7 ± 1.5) J kg^-1K^-1in the magnetic field of H = 1.8T is acquired in the Ni_2.18Mn_0.82Ga alloy at a magnetostructural phase transition temperature of T = 333.2 K.

In a word, Ni–Mn–Ga alloys have an excellent MFIS effect with large strain of 10 % and large MCE effect, although they are brittle and tend to fracture easily after cycle running. The properties of Ni–Fe–Ga alloys are less prominent, and the c phase of Ni–Fe–Ga easily grows up during the fabrication.

3 Properties of Ni Mn Z(Z 5 In, Sn, Sb) systems

The magnetic field-induced strain caused by martensite variant reorientation in Ni–Mn–Ga systems is of crystal orientation dependent, so the work output and actuation stress are limited to the magnetocrystalline anisotropy energy. Researchers explore new Ga-free MSMAs instead of Ni–Mn–Ga systems, such as Ni Mn Z (Z = In, Sn, Sb) systems.

3.1 Structure and phase transformation of Ni Mn Z(Z = In, Sn, Sb) systems

The magnetostructural transition is observed in Ni–Mn–Z alloys (Z = In, Sn, Sb), which is accompanied by giant inverse MCE and MR [8, 24, 42, 66–74].

Theexperimentalinvestigationsshowthat Ni₂Mn_1?xZ_1-xalloys (Z = In, Sn, Sb) close to stoichiometry (x B 0.3) have a cubic L2₁-type Heusler structure [42]. Ni0.5Mn0.5-xInxalloys undergo martensitic transformations in the range of 0.05 B x B 0.16, while in the range of 0.16 B x B 0.25, the alloys are maintaining the cubic phase. When x = 0.16, MIST occurs, and T_Mshifts by 42 K in the field of 5 T [67]. In Ni0.5Mn0.5-xSnx alloys, the structure of the martensite is of 10M (the same as 5M), 14M (the same as 7M), or L1₀relying on the Sn composition, while the one for austenite is of L2₁type. It is observed that both the martensite and austenite are ferromagnetic in Ni0.5Mn0.5-xSnx[66]. Khan et al. [75] investigated the Ni50Mn25?xSb25-xwith 0 B x B 12.5 and 13 B x B 14 alloys, and observed that the martensitic transition occurred above 150 K with 7 B x B 10. The austenitic phases of Ni50Mn25?xSb25-xare L21cubic structure at room temperature, while the martensitic phases show orthorhombic structure (space group: Pmm2). With the increase in Mn concentration, T_Mincreases rapidly while T_Cof the austenitic phase decreases slightly from 370 K (x = 0) to 340 K (x = 12.5).

The phase diagrams of the Ni–Mn–Z alloys (Z = In, Sn, Sb) were studied systematically in Refs. [24, 66, 67, 76], which are shown in Fig. 8 [75, 76]. In the phase diagram, the magnetic and structural transitions depending on the composition of the alloy are depicted.

3.2 Magnetoresistance and magnetocaloric effect of Ni–Mn–Z(Z = In, Sn, Sb) systems

The distinction in magnetic exchange interaction between the austenite and martensite phases in Ni–Mn–Z (Z = In,Sn, Sb) alloys results in the appearance of magnetization jumps, which manifest themselves in the possible occurrence of the magnetostructural transition, giant MR, and inverse MCE.

Fig.8 Phase diagram of a T–x showing different magnetic regions of Ni50Mn25?xSb25-xsystem and b Ni2Mn1?xIn1-xshowing transition temperature as a function of e/a. AFM, antiferromagnetism; FM, ferromagnetism; PM, paramagnetism; EB region, where AFMand FMregions exist; TM, temperature of martensitic transition; TCA, ferromagnetic transition temperature of austenitic phase; TCM, ferromagnetic transition temperature of martensitic phase; TB, exchange bias blocking temperature; Ms, saturation magnetic moments

Fig.9 Magnetoresistance (MR) dependence of field strength at various temperatures for a Ni50Mn34In16(TM= 190 K) and b Ni50Mn35In15. Arrows indicating direction of field variation

Yu et al. [77] observed large MR of over 70 % in Ni₅₀Mn₃₄In₁₆(T_M& 190 K) single crystal in a wide temperature range of 100–180 K at a low magnetic field of 3.0 T (Fig. 9a; [77]). While at the proximity of the transition temperature 190 K, MR recovered only a value of 30 % since the sample cannot fully recover to the martensitic phase at zero field. For the MR associated with martensitic structure, it would be favorable to get a smaller entropy change in martensitic transformation by changing the composition in order to gain a larger MR with a lower field.

Krenke et al. [78] reported that the maximum value of inverse MCE in Ni50.3Mn33.8In15.9(TC= 305 K) calculated from the Maxwell relation is DS_M= 12 J kg^-1K^-1which is acquired at about 190 K in a magnetic field of 4 T. It is reported in Ref. [42] that the maximum isothermal magneticentropychangeinNi50Mn35In15is DS_M& 35.8 J kg^-1K^-1in the region of the martensitic transition (T & 311 K) at a change of magnetic field of DH = 5 T, while isothermal change in the magnetic part of entropy (DS_mag) is equal to *15 and *20 J kg^-1K^-1for Ni50Mn35Sn15and Ni50Mn37Sn13, respectively, at the magnetic field change of DH = 5 T. Du et al. [8] investigated Ni₅₀Mn_50-xSb_x(x = 12, 13 and 14) and observed a largepositivemagneticentropychangeof DSM= 9.1 J kg^-1K^-1in Ni50Mn37Sb13at 287 K for a magnetic field change of DH = 5 T in the vicinity of the martensitic transition. Manosa et al. [23] reported the value for the barocaloric effect of 24.4 J kg^-1K^-1in Ni49.26Mn36.08In14.46under the stress of 2.6 k Pa at ambient temperature (Fig. 10; [23]). This effect is 20 times larger than the value caused by elastic heating. Nayak et al. [79] observed significant improvement in MCE upon Co doping in Ni50-xCoxMn38Sb12near RT. The value of magnetic entropy change in Ni45Co5Mn38Sb12is 29 J kg^-1K^-1at RT, while this value reaches 34 J kg^-1K^-1at 262 K in a magnetic field of 5 T. Sharma et al. [73] reported that the theoretical adiabatic temperature change (DT_ad) in Ni₅₀Mn₃₄In₁₆can reach up to -9 K under the field of 8 T.

Fig.10 Barocaloric effects in Ni–Mn–In system as a function of temperature, associated with isothermal application of selected hydrostatic pressures (from p = 0.2 k Pa up to indicated value)

The alloying of Ni–Mn–Z alloys (Z = In, Sn, Sb) with Co leads to a substantial change in the magnetic properties, in particular on the value of the magnetization.

4 Properties of Ni–Co–Mn–Z(Z 5 In, Sn, Sb, Al) systems

4.1 Properties of Ni–Co–Mn–In systems

In Ni–Mn–Z alloys, the magnetic coupling between the nearest neighbor Mn atoms is likely to be antiferromagnetic, but by doping Co to replace part of Ni atoms, the magnetic coupling of Mn–Mn should be activated to be ferromagnetic. Therefore, the doping of Co will not only enhance the magnetization of the magnetic phase of the Ni–Mn–Z, but also improve greatly the metamagnetic properties. Except the tremendous properties of metamagnetic shape memory effects, giant MCE, and large magnetoresistivity,Ni–Co–Mn–Inalloyshavemany advantages for application, such as the composition not containing rare earth or toxic elements, easy fabrication and easy machining, high superelastic strain, high adiabatic temperature change in low field, and good oxidation resistance [9].

The nature of Ni–Co–Mn–In alloys is sensitive to their composition, such as the addition of Co resulting in an increase in T_Cand a decrease in the martensitic transformation starting temperature, while the martensitic transformation starting temperature decreases with In content increasing [7, 80]. Ni45Co5Mn36.6In13.4single crystal has cubic L2₁structure with a = 0.5978 nm [3], and the Curie temperature is T_C= 382 K. Upon cooling, a martensite phase transformation occurs at a specific temperature T_Maround RT, accompanied by large magnetization change (DM). Monroe et al. [4] report that the maximum DM & 115 m A m²g^-1was obtained in Ni45Co5Mn36.5 In13.5 single crystal at 3 T when the martensitic transformation occurred. The martensite structure is a 14M modulated structure with a = 0.4349 nm, b = 0.2811 nm, c = 2.9892 nm, and b = 93.24° [3].

Fig.11 Recovery strain at 298 K (Tt= 298 K) induced by a magnetic field for Ni45Co5Mn36.7In13.3. A compressive pre-strain of about 3 % (e0= 3 %) being applied to alloy, with magnetic field applied in parallel to compressive direction of specimen and length change in same direction

Large output stress level may be generated in magnetic field-induced transformation, which is larger than that originated from the variant rearrangement in the martensite phase. In Ni45Co5Mn36.7In13.3alloy, it has recently been found that the parent phase is ferromagnetic, while its martensite phase has weak magnetism. The large Zeeman energy difference between the two phases results in the transformation induced by applying magnetic field. When applied magnetic field changes from 1 to 7 T at zero tension, T_Mdecreases from 260 to 170 K, while the temperature hysteresis increases from 18.5 to 56.2 K, respectively [4]. T_Mdecreases with the increase in magnetic field in Ni Co Mn In alloys. The transformation temperature change (DT) caused by magnetic field change (DB) is approximately described by the Clausius–Clapeyron relation [3]:

where B is the applied magnetic field, T is the absolute temperature, DS and DM are the differences in entropy and magnetization between austenite and martensite phases, respectively. According to Eq. (1), it is obvious that both a small DS and a large DM are required to enhance the magnetic field-induced transformation. Kainuma et al. [3] observed that DT & 30 K is given by DB & 7 T and DM & 100 m A m²g^-1. They firstly observed a recovery strain of about 2.9 % in the pre-strain of 3 % in Ni45Co5Mn36.7In13.3single crystal with a magnetic field of 8 T at 298 K (Fig. 11; [3]). Karaca et al. [11] demonstrated that fully reversible MIST of Ni45Co5Mn36.5In13.5single crystal oriented along the [100] orientation at different temperatures (Fig. 12; [11]). At 220 K, the sample undergoes a completely reversible MIST with a magnetic hysteresis of about 1.5 T. It is confirmed that magnetic hysteresis increases with temperature decreasing at zero tension, while it increases with the increase in external tension during isothermal test [11].

Fig.12 Change in magnetization of Ni45Mn36.5Co5In13.5single crystals oriented along [100] orientation as a function of applied magnetic field at different temperatures demonstrating fully reversible magnetic field-induced phase transformation a; superelastic response of Ni45Mn36.5Co5In13.5single crystals along [100] orientation under compression at 273, 293, and 333 K b

However, experimental results confirm that MIST cannot create large strains unless a bias stress is loaded to the material [4]. Therefore, many researches focus on the stress-assisted MIST [11, 81].

Monroe et al. [4] tested the relationship between compressive strain and magnetic field for Ni45Co5Mn36.5In13.5 single crystal under 75 and 125 MPa bias stress at several testing temperatures (100, 150, 200, and 250 K). Fully recoverable MFISs were obtained except for the 125 MPa testing at 250 K, and the maximum MFIS is 3.1 %, while the critical field for austenite finish and magnetic hysteresis increases with the decrease in test temperature [4]. Karaca et al. [11] discussed the superelastic response of the Ni45Co5Mn36.5In13.5single crystal along [100] orientation, acquiring a transformation strain of about 6.3 % at 273 K. Theoretical calculations show that the maximum transformation strain can reach up to 6.61 % and 6.74 % for compression and tension along the [100] orientation, respectively. The magnetic work output of Ni₄₅Co₅Mn36.5In13.5single crystal was determined to be 1620 k J m^-3under 1.6 T [11]. When load stress was up to 100 MPa, a compressive strain of about 7 % was obtained at T = 298 K in Ni45Co5Mn36.6In13.4, but the deformed strain still remained after the stress was unloaded [3]. The critical transformation stress to drive martensitic transformation in Ni45.7Co5.1Mn36.5In13.3polycrystal at 300 K is about 80 MPa, which is lower than that of Ni45Co5Mn36.5In13.5 [001] single crystal (about 150 MPa at 300 K) [3, 82].

Recently, the mechanocaloric effect (including elastocaloric effect and barocaloric effect) and MCE in shape memory alloys, originated from superelasticity or giant volume change on martensite transformation or structure transformation, have been increasingly attracting attention [82–85]. A reversible elastocaloric adiabatic temperature change (DT_ad) of ?3.5 K was observed at room temperature by applying a uniaxial compressive stress of 100 MPa in a [001]-oriented Ni45.7Co5.1Mn36.6In13.3single crystal [82]. While it should be pointed out that the stress-induced temperature change behavior of Ni–Co–Mn–In has the difference from that driven by magnetic field. The Ni45.2Co5.1Mn36.7In13sample exhibits large inverse MCE during the MIST, for the temperature change is as large as DT_ad= -6.2 K at 317 K in DH = 1.9 T [9]. Whereas the giant DT_adis obtained only in the first loading of field, but it sharply decreases after the cycle runs of the field. The hysteresis in the first-order transition is the main factor that causes the reduction in DT_ad. The irreversible energy loss caused by the hysteresis significantly reduces the efficiency in applications of the magnetic refrigeration. Therefore, the primary issue in Heusler-type MSMAs is how to reduce the hysteresis. Liu et al. [9] discussed that the hysteresis can be controlled by employing any other stimulation such as hydrostatic pressure. They proved that the magnetic hysteresis can be sharply reduced only by applying a low hydrostatic pressure of 1.3 k Pa during the process of demagnetizing [9]. By means of loading pulsed fields up to 15 T (duration: 36 ms), a maximum DT_addecrease of -12.8 K was gained in Ni45Co5Mn36.7In13.3(Fig. 13; [85]). The entropy change at the martensitic transformation is associated with the external magnetic field and the thermal treatment methods. For Ni–Co–Mn–In, experimental results confirmed that after proper aging treatment, the magnitude of entropy change can reach up to 40 J kg^-1K^-1for a single alloy [86].

Although the strain, work output, and actuation stress of Ni Co Mn In alloys are highly promising, the quite high critical magnetic field for phase transformation and large field hysteresis may act as an obstacle for their applications.

Fig.13 Magnetic field (H) versus temperature of Ni45Co5Mn36.7In13.3sample during adiabatic magnetization processes in pulsed magnetic fields. Inset: directly measured adiabatic temperature change (DTad) (15 T) and that calculated from isothermal magnetization curves (DTMH) shown as a function of temperature

4.2 Properties of Ni–Co–Mn–Sn systems

Ni–Co–Mn–Sn systems are another MSMAs system following the Ni Co Mn In system. It is confirmed that the magnetic shape memory effect occurs not only in a singlecrystalline samples, but also in a polycrystalline samples [6, 87, 88]. Ni–Co–Mn–Sn alloys generally have high transformation temperature and low thermal hysteresis, but they are likely to be brittle under pressure.

The study shows that the austenite phases of Ni₄₃Co₇Mn₃₉Sn₁₁have the ordered L2₁structure with a = 0.5965 nm, and the martensite phase shows a mixture of 6M and 10M modulated structures, and T_Mis close to 470 K [6]. Kainuma et al. [6] presented that T_Mshifts to lower temperature with magnetic field increasing. With the magnetic field change of DH = 7 T, the martensitic transformation starting temperature decreases about 28 K, but the thermal hysteresis has no obvious change of less than 10 K. They also found that Ni₄₃Co₇Mn₃₉Sn₁₁undergoes magnetic fieldinduced reverse phase transformation from antiferromagnetic-like martensite to ferromagnetic parent phase between 280 and 300 K, with a magnetic hysteresis of 1.5 T [6].

It is well known that the substitution of Co for Ni should raise the magnetization value of the alloys since Co has higher magnetic moment (*1.0 l_B) than Ni (*0.31 l_B). In Ni–Co–Mn–Sn alloys, Co substitution for Ni decreases the martensitic transformation starting temperature and increases the Curie temperature of martensite (T_CM ) and the Curie temperature of austenite (T_CA ) with the increase in Co content, while decreases the change in magnetization during the martensitic transition [88], and excessive substitution of Co for Ni may form the c phase [87]. Chen et al. [88] reported that tuning Co and Mn composition properly resulted in high entropy change of *32 J kg^-1K^-1near room temperature in Ni₄₈Co₂Mn₃₈Sn₁₂alloys, and adjusted T_Mto room temperature.

Emre et al. [89] discussed that small quantities of Nb substitution can drastically shift T_Mto lower temperatures, and T_Mdecreased 68 K per 1 % Nb atom doping in Ni-CoMn-Sn alloys, which is needed for household refrigeration. In Ni45Co5Mn40Sn10, TMdecreases from 400 to 300 K for 1.5 % Nb substitution. Simultaneously, the thermal hysteresis is about 6 K in 50 m T, and the magnetization change between martensite and austenite phases reaches 70 m A m²g^-1. The maximum entropy change (DS) in a magnetic field of 5 T is about 48 J kg^-1K^-1for 1 % Nb substitution [89]. However, with Nb substitution, a decrease in the latent heat of the martensitic transition is observed, which negatively affects the adiabatic temperature change induced by magnetic field.

Chen et al. [90] observed martensitic transformation in Ti-doped Ni43-xTixCo7Mn43Sn7. It is confirmed that TM decreases and the mechanical properties are obviously improved by adding an appropriate amount of Ti. Experimental results confirm that the compressive strength and compressive strain of Ni42.5Ti0.5Co7Mn43Sn7alloy reach a maximum value of 1760 MPa and 23 %, respectively [90]. Although the addition of Ti may improve the ductility to some extent, the substitution of Ti for Ni does not change the brittle nature of Ni Co Mn Sn alloy.

In contrast to the studies on the MCE in Ni–Co–Mn–Sn alloys, electrical and thermal transports were scarcely investigated. Chen et al. [88] studied the resistivity and thermopowervaluesinzeromagneticfieldfor Ni47.5Co2.5Mn37Sn13samples. It is found that the electrical transport is metallic, but in the case of the paramagnetic and ferromagnetic austenite phases, a change of slope occurs at the onset of the ferromagnetic transition.

4.3 Properties of Ni–Co–Mn–Sb systems

Nayak et al. [91] studied the effect of stress on the magnetic properties and the MCE in Ni Co Mn Sb Heusler alloy. The temperature dependence of magnetization under various pressure (0–9 k Pa) shows that T_Mshifts to higher temperature with the increase in the stress, and the martensitic phase is enhanced under stress, while the isothermal magnetic entropy change reduces with the increase in the stress. The field dependence of resistivity (q(H)) in Ni₄₅Co₅Mn₃₈Sb₁₂at different temperatures illustrates that the martensitic phase which transforms to parent phase could not completely recover to its original state without external magnetic field. It is confirmed that the austenite phase would be apt to be pinned and the transformation could not be fully reversible in the field dependence of magnetization, resistivity, and heat capacity [92]. When repeated temperature/field cycling is applied in Ni₄₅Co₅Mn₃₈Sb₁₂, the resistivity significantly increases and the magnetization decreases due to the microstructural deformation and lattice disorder [93]. Sahoo et al. [94] compared the magnetic properties, MR, and MCE of asspun ribbon with the annealed ribbon and the bulk alloy of Ni46Co4Mn38Sb12, and observed that TMof as-spun ribbon is higher than that of the bulk sample, while the magnetization of as-spun ribbon is lower. Si substitution for Sb stabilizes the austenite phase in Ni46Co4Mn38Sb12-xZx (Z = Si, Ga), whereas Ga substitution stabilizes the martensite phase. With x = 1 for Si, T_Mdecreases to 254 K, and a large MCE of 70 J kg^-1K^-1is acquired [95].

4.4 Properties of Ni–Co–Mn–Al systems

Xuan et al. [96] observed a unique martensitic transformation from the ferromagnetic austenite to the weak magnetic martensite phase in Ni50-xCoxMn32Al18(x = 6, 8). A magnetization difference up to 45 m A m²g^-1was measured across the martensitic transformation for Ni₄₂Co₈Mn₃₂Al₁₈alloy. In the same quaternary alloy, the large MR effect of 67 % at 225 K was observed through this field-induced magnetic phase transition. Rios et al. [97] discussed Ni Co Mn Al thin films which show a MIST after heat treatment, while the MIST of the films is irreversible due to the large thermal hysteresis. The change rate of T_Minduced by magnetic field was measured to be *2.1 K T. Xu et al. [98] studied the Ni44.3Co5.1Mn31.4Al19.2metamagnetic shape memory alloy under a pulsed magnetic field up to 35.5 T, in which the magnetic field-induced reverse martensitic transformation was directly observed. By systematic study on Ni Co Mn Al alloys, Xu et al. [99] observed that the thermal transformation arrest temperature increased up to 190 K in the Ni Co Mn Al alloy systems. Singh et al. [100] reported that the ferromagnetic–paramagnetic transition occurred at T_Cof 200 K in the Ni₄₈Co₆Mn₂₆Al₂₀polycrystalline ribbons which have B2 structure at room temperature.

In summary, most of the properties of the quaternary systems surpass those of the ternary systems. Ni Co Mn In alloy has superb metamagnetic properties in which the difference of magnetization is larger than 100 m A m²g^-1when undergoing the martensitic transition. It reveals the biggest magnetocaloric entropy change among the quaternary systems. The adiabatic temperature change is as large as 12.8 K, but the largest strain during MFIS is 7 %, smaller than that for Ni–Mn–Ga. Ni Co Mn Sn alloy has low thermal hysteresis and magnetic hysteresis, 10 K and 1.5 T, respectively. Ni Co Mn Sb alloy shows a great magnetoresistance of larger than 70 %. The fabrication of Ni Co Mn Al single crystal is relatively easy, but it has large thermal hysteresis.

5 Conclusion

Since Heusler-type MSMAs were investigated systematically for decades, their physical properties, characteristic of phase transformation, and strain mechanism have been known clearly. These materials exhibit lots of excellent properties, such as metamagnetic properties, shape memory effect, giant MCE, and giant MR. The nature of large recovery strain, high stress output, high response frequency, and precise control make themselves have a broad prospect in scientific research and engineering applications.

However, there are still some issues and possible challenges as follows. Some of the Heusler-type MSMAs are brittle and tend to fracture easily after cycle running. Though the researchers want to improve the properties by changing the composition and doping of other elements in MSMAs, the results are not highly satisfied. To induce magnetostructural transition, the Heusler-type MSMAs require high critical magnetic fields and/or high critical stress. The problem hinders their industrial application. How to reduce the critical magnetic field or stress for the transition, as well as not to suppress their properties, is still a challenge. The existence of the hysteresis in magnetostructural transition brings up waste of energy. The refrigerating efficiency will increase, while the hysteresis is reduced effectively. The methods used for reducing hysteresis are decreasing grain, stress assisted during the transition, or to search for new material systems.

The development of the Heusler-type MSMAs is still at the laboratory stage, and the application area is limited. New applications, for example, in the fields of magnetic sensor and actuator, need to be explored. In short, the investigations into the fundamental physics and applications of Heusler-type MSMAs are still in the beginning.