All-d-Metal Heusler Alloys: A Review

Abstract

Heusler alloy research has increased considerably in recent years. This is mostly due to their strong desire to develop future smart device applications. However, many limiting variables remain for researchers to overcome in order to enhance their functional properties. The poor mechanical properties of these alloys restrict their use as solid-state cooling materials in magnetic refrigeration devices. A promising strategy, resulting in novel compounds with better mechanical properties and substantial magnetocaloric effects, is favoring the d–d hybridization with transition-metal elements to replace p–d hybridization. The term given to these materials is “all-d-metal”. In light of recent experimental results of the magnetocaloric effect and the increased mechanical characteristics in these alloys (with complex crystallographic behavior due to off-stoichiometry and disorder), a review of this advanced functional behavior is offered. Moreover, the impact of the substitution of transition metal for the p-group to increase mechanical ductility and considerable magnetocaloric effects has also been addressed. These Heusler alloys are a potential new class of materials for technological applications because of their optimum functional behavior. Finally, we highlighted the potential challenges and unsolved issues in order to guide future studies on this topic.

1. Introduction

Most research funding organizations across the globe prioritize energy efficiency and sustainability, and these issues are often discussed in the media. According to statistics from the Lawrence Livermore National Laboratory, the expected US energy consumption until 2021 corresponds to rejected energy was to be 61%, while only 39% was used in energy services. Other developed countries have similar statistics, such as the United Kingdom and Spain, where 63% rejected energy was detected in 2011. These findings demonstrate the need to focus on the primary energy source and avoid dependency on non-renewable energy sources, as well as devoting major research resources to improving energy conversion efficiency. Most renewable energy sources must be converted, in particular, into electricity before being used, with 67% of the conversion process resulting in lost energy in the United States in 2015 [1]. In many cases, magnetic materials play a vital role in the conversion of energy into electricity. This is a driving force behind the development of magnetic materials for energy applications [2]. Air conditioning and refrigeration consume a significant amount of electricity in both the residential and industrial sectors, with quantities varying from country to country due to climatic differences. In fact, specific effects appear when ferromagnetic shape memory alloys (FSMAs) are subjected to external magnetic fields (magnetocaloric (MCE)), hydrostatic pressure (barocaloric (BCE)), and uniaxial stress (elastocaloric (eCE)), this technology is dependent on thermal processes [3,4,5,6,7]. Due to its important role in improving refrigeration system functionality, exploring good materials based on caloric impacts has progressively grown to be a hot research topic. The exceptional multi-magnetofunctional features of Ni−Mn-based Heusler alloys, connected to their tightly coupled ferromagnetic (FM) martensitic transition (MT) around transition temperature (T_t), have received growing interest. Moreover, Ni−Mn-based alloys generally display the first-order phase transition (FOPT) related to the magnetic transition because of the strong coupling between lattice structure transition and magnetism [8]. Furthermore, a significant MCE is caused by a rapid shift in magnetization from a weak-magnetic to a ferromagnetic (FM) state when the magnetic field is applied or removed. Therefore, during MT and under uniaxial stress, the eCE would be created by the FOPT. Due to the coexistence of MCE and eCE, these alloys are being evaluated as potential prospects for industrial uses. The Ni–Mn–Ga [9], Ni–Mn–Ga–Co [10], Co–Ni–Al [11], Ni–Mn–Sn–Cu [12], and Ni–Co–Mn–Sn [13] shape memory alloys have been examined as exhibit both properties. Because of their excellent magnetic properties and tunable MT temperatures, Ni–Mn-based alloys have been regarded as improved alloys among these noted [14]. In addition, the brittleness of most of these alloys restricts their applications and causes cracking under repetitive stress cycling [15]. Moreover, to reduce the hysteresis behavior associated with MT and improve the mechanical performance, several methods, such as introducing a second phase into grain boundaries, alloying with additional elements, and micro-alloying with boron, are proposed [16,17,18]. However, the covalent character of this orbital has recently been linked to the poor mechanical performance of Heusler alloys, a disadvantage that limits practical use [19]. Due to their mechanical response, Heusler alloys’ useful life as cooling materials and/or mechanical actuators is reduced, which causes structural fatigue when subjected to repeated thermo-mechanical/magnetic cycles. It is well-known that intrinsic brittleness is one of the largest and most pressing concerns to be solved in terms of appropriateness for technology applications [20].

Several approaches have been employed to restrict the macroscopic effects of the intrinsic brittle nature of these alloys, as briefly discussed in reference [21]. However, significant findings of a distinct class of Heusler alloys generated by substituting the p-group atom with a third transition metal, i.e., alloys made entirely of transition metal elements, have been found in recent years. In these alloys, considerable p–d hybridization among the elements is replaced by d–d hybridization, resulting in increased mechanical properties [19,22] associated with the MT and intense MCEs.

This review examines the basic and functional features of full Heusler alloys, with a particular focus on the impact of p–d orbital hybridization. Following that, we discuss the basic and functional features of all-d-metal Heusler alloys, with a focus on the effect of d–d orbital hybridization. Then, we examine some of the most current research on these unique families. Finally, we provide an outlook on the issue, as well as some perspectives for future research.

2. Heusler Alloys

2.1. Composition

Heusler alloys are magnetic intermetallic with face-centered cubic structure and composition of XYZ (half-Heusler) or X₂YZ (full-Heusler), where X and Y are transition metals, and Z is in the p-group [23]. In a few cases, the Y atom can be replaced by alkaline earth metal or rare earth (lanthanide family) [24]. In the molecular formula, the transition metal element with the most atoms is placed first, followed by the p-group atom.

2.2. Crystalline Structure

Full Heusler alloys crystallize in a face-centered cubic structure that belongs to the Fm3m space group and includes Cu₂MnAl as the prototype structure at room temperature (RT). This crystallographic structure is referred known as L2₁. Heusler alloys X₂YZ typically have an ordered cubic structure. The four Wyckoff positions in the lattice are A (0, 0, 0), B (¼, ¼, ¼), C (½, ½, ½), and D (¾, ¾, ¾). These alloys obey the site preference rules where X and Y are d-group atoms, and Z is a p-group atom [25], which determines the site occupancy for X₂YZ stoichiometry, as shown in Figure 1. De Paula et al. [26] and Burch et al. [27] proposed empirical site occupancy rules decades ago, indicating that the atoms of the p-group prefer (D) sites, whereas the (A, C) sites are occupied by the transition metals with more valence electrons, resulting in the highly ordered L2₁ structure. According to these rules, the (B) site was occupied by the other transition metal. Usually, the site preference of different 3d elements in Heusler alloys is determined by the number of their valence electrons [28]: elements with more valence electrons tend to enter the (A, C) sites and form a Cu₂MnAl type of structure, while elements with fewer electrons prefer the B sites and form a Hg₂CuTi type of structure; the main group elements usually occupy the D sites. We draw attention to the fact that these principles explain why individual atoms’ electronic valences are p or d [29]. Another possible order is that an inverse Heusler structure is created when the valence of the Y atom is larger than that of the X atom, with the Y atom occupying the (A) site and one of the X atoms being reallocated to the (B) site. A multitude of disordered alternate forms is associated with this L2₁ structure. The XA inverse Heusler structure is a cubic structure that belongs to the space group F43m and has CuHg₂Ti as its prototype structure. It is a common occurrence in Mn₂-based compounds.

For the purposes of this review, it is useful to present two types of distinct disordered structures. The B2-type disorder is created when the Y and Z atoms indistinctly occupy B and D sites. Thus, in the figure, green and red sites are equivalent, resulting in a symmetry-reduced cubic structure with the space group Pm3m.

Finally, a completely disordered structure named A2-type disordered structure can arise when all X, Y, and Z sites are equivalent, resulting in a body-centered cubic lattice with decreased symmetry and space group Im3m. Thus, in the crystallographic phase, a unique color can be used to draw all atoms. By way of summary, Table 1 shows the sites (A, B, C, and/or D) of the atoms of X, Y, and Z (for a stoichiometric composition).

2.3. Influence of p–d Hybridization

The creation of hybrid orbitals may be understood in light of traditional molecular orbital theory, which is responsible for defining the various forms of chemical bonding in solids [30]. The macroscopic mechanical behavior of materials is described by C_i,j elastic constants [31], which are directly dependent on the atomic chemical bonds. The correlation between the degree of p–d hybridization and mechanical properties of Ni₂MnZ (Z = Al, Ga, In, Si, Ge, and Sn) has been recently investigated via first-principle calculations by Yan et al. [32]. This study illustrates how the choice of the p-group atom strongly affects the three elastic constants (C11, C12, and C44) characteristic of a cubic lattice. Typical X₂MnZ Heusler specimens show a distinct structural phase transition, resulting in multi-functional characteristics. Winterlik et al. [33] reported the electronic structure calculations for Heusler alloys to investigate candidates for superconductivity and identified several Ni₂-based Heusler alloys that become superconducting in the low-temperature region. The superconductivity aspect appears in the system (Eu_1−xPr_x)BCO [34]. As part of this MT, the material transitions from a high-temperature austenite phase with cubic symmetry to a low-temperature martensitic phase with decreasing symmetry. The fact that the atoms actively rearrange themselves using a shear-like process while keeping their relative positions is its most distinctive feature [35]. When it comes to controlling the MT temperature range, the level of the p–d orbital hybridization process between the p states of Z atoms and the d states of X atoms is also significant [36,37,38]. Moreover, the enhancement of mechanical properties of all-d-metal full Heusler alloys is the main achievement caused by the suppression of p–d hybridization, as depicted in Table 2. The lower values of Young’s elastic modulus exhibited by all-d-metal Heusler in comparison to conventional ones are related to its higher ductility since it is a quantitative parameter of the resistance to elastic deformation upon mechanical load [39,40,41,42,43].

From a practical standpoint, stoichiometric variation or partial atomic replacement can be used to tailor MT for specific applications. Both situations have a different number of electrons available for this interaction. The valence electron concentration per atom (e/a) measures this distinct property and is expressed as [39]:

(e/a) = ½[N_Xf_X + N_Yf_Y+ N_Zf_Z]/100,(1)

where N_X, N_Y, and N_Z are the number of valence electrons of each element, and f_X, f_Y, and f_Z stand for their corresponding atomic percentages.

A linear dependency of MT versus the (e/a) ratio for many common X₂MnZ Heusler compounds is usually found [22]. Likewise, the austenite (AS) to martensite (MS) structural transformation can be accompanied by the ferromagnetic (FM) to paramagnetic (PM) magnetic transformation. Depending on alloy and composition, this magnetic transformation can appear in the austenite or in the martensitic regions. Thus, all the combinations are possible: AS-FM, AS-PM, MS-FM, and MS-PM. Figure 2 shows a temperature transformation diagram. The slope of the martensitic start temperature (Ms) is influenced by choice of the p-element. Obviously, some of these alloys present another magnetic behavior as supermagnetism or spin glass [40].

2.4. MCE in Heusler Alloys

In 1983, Wachtel et al. [45] and Maeda et al. [46] produced the first studies on MCE of Heusler Ni₂(Mn_1−xM_x)Sn with M = V and Nb(x = 0.1, 0.2, 0.3 and 0.4), Mn_3-y-zCr_yAlC_1+z (z = 0.1 and y = 0, 0.06, 0.15 and 0.26), and (y = 0 and z = −0.16, −0.08, 0 and 0.1) alloys. They discovered that Curie temperature (T_C) values drop linearly from room temperature (RT) to around 200 K, and M_salsodecreases linearly. The biggest maximum values of magnetic entropy change (ΔS_M) found in the system at x = 0.1 to 0.2 and in the latter one at y = 0 and z = 0.9 are roughly half of Gd, while (ΔS_M)_Max steadily declines with increasing x or y. Later, in 2000, at moderate fields (ΔS_M = +4 Jkg⁻¹K⁻¹ at 0.9 T), Hu et al. [47] observed an inverse MCE attributed to MT (thermal hysteresis 10 K. Due to the substantial uniaxial magneto-crystalline anisotropy of the martensitic phase, inverse MCE arises when both phases are FM, and the high-temperature phase (austenite) has a stronger magnetization than the low-temperature phase (martensite) at low fields [48]. However, for fields larger than 1 T, inverse MCE is replaced with direct MCE [49,50]. A giant MCE [51] was discovered in the compositional area where the magnetostructural transition occurs. Zhou et al. [52,53] studied magnetic and structural transitions, as well as MCE, in Ni₂MnGa alloys. Because Ni-rich alloys have a lower T_C than Mn-rich alloys, their MT is closer to RT. By using neutron diffraction on Ni₂MnGa and Ni_1.75Mn_1.25Ga systems, Singh et al. [54] recently showed that the inverse MCE is caused by the antiferromagnetic (AFM) contact between Mn atoms at in-equivalent sites. Figure 3 depicts the ΔS_M values’ field dependency in two examples: adapted from reference Ni₂MnGa and Ni₂MnGa_0.95Sn_0.05 [55].

Sasso et al. [56], whose results are consistent with those of Khovaylo et al. [57], who attributed differences in field-applied and field-removed curves to magnetostructural hysteresis, also highlighted MCE’s historical dependence on the field and thermal sequence. Porcary et al. [58] established the convergence of direct and indirect methodologies in the analysis of Ni(Co)–Mn–Ga alloy. There are various arguments against using Heusler alloys as magnetic refrigerants, including the irreversible nature of the magnetic field-driven MT and the considerable hysteresis found [54]. As a result, researchers in MCE for Heusler alloys are presently focusing their efforts on removing hysteresis. Inverse giant MCE in Ni₅₀Mn₃₇Sn₁₃ was reported by Krenke et al. [59] in 2005, while Han et al. [60] reported inverse giant MCE in In-containing Heusler alloys in 2006. Later, in 2007, Khan et al. [61] and Du et al. [62] indicated a good correlation for Ni₂Mn_1+xZ_1−x (Z = In, Sn, and Sb) and Ni_50-xMn₃₇Sb₁₃ alloys close to stoichiometric composition (x = 0.3) showing a cubic L2₁ austenitic phase and a typical FM/PM magnetic transition preserving this austenitic phase. However, alloys with a higher divergence from 2:1:1 stoichiometry show MT. In contrast to Ga-containing Heusler alloys, AFM coupling between Mn atoms is enhanced (martensitic state) in these alloys, resulting in a metamagnetic transformation from AFM to FM, which may be adjusted to be a meta-magneto-structural transition from AFM to FM austenitic phase. It has been proposed that the existence of both (direct and inverse) MCE is a mechanism for increased refrigeration cycle performance [63].

Due toits MCE, several Heusler alloy families have been studied. Temperatures surrounding the second-order phase transition (SOPT) of Ni–Mn–Ge have been observed [64], with T_C decreasing as the Ni/Mn ratio increases. Ni–Fe–Ga [65], Ni–(Fe,Co)–Ga [66], and Co–Ni–Ga [67] are examples of Mn-free systems discovered in the literature. Due to its higher ductility, Ni–Fe–Ga has been advocated as a superior MCE material than Ni–Mn–Ga. Its MCE effect is field dependent, similar to Ni–Mn–Ga, and at low fields, it switches from inverse to conventional MCE. Co helps to align the Curie temperatures of martensite and austenite phases with the transition temperature of MT by shifting to higher levels. Moderate MCE values were reported: ΔS_M (5 T) = 2.4 Jkg⁻¹K⁻¹ at 360 K [63]. On the other hand, the higher MCE values of Co₅₀Ni₂₂Ga₂₈ alloy were reported: ΔS_M (5 T) = 10.5 Jkg⁻¹K⁻¹ at 313.5 K, which was attributed to the MT between FM martensite and FM austenite [64]. On the other hand, its sharp ΔS_M(T) curves are full width at half maximum (FWHM < 2 K), and the considerable thermal hysteresis of the MT (20 K) must be taken into account. Vivas et al. [68] studied the effects of the number of valence electrons on the MCE of half-metal Fe₂MnSi(Ga) alloys and found a phenomenological linear relationship between ΔS_M and this parameter. In summary, Figure 4 shows the ΔS_M values at 5 T as a function of the transition temperatures of various Heusler alloys.

3. All-d-Metal Heusler Alloys

3.1. Background of These Kinds of Alloys

Recently, Wei et al. [22] suggested the notion of an all-d-metal Heusler based on d–d orbital hybridization. The authors of this seminal work established the term “all-d-metal” after discovering that the Heusler phase could be formed without the p-group atom. Experiments on the crystal structure of Zn₂AuAg and Zn₂CuAg compounds [69,70] may be traced all the way back to the 1960s. Both compounds have L2₁ organized and B2 disordered structures, according to these ancient publications. The Zn₂AuAg, in particular, shows a B2 to L2₁ order-disorder transition, as evidenced by changes in structural order characteristics. On the other hand, their applications as FSMAs are limited due to the absence of FM ordering in these alloys, and no further research on these alloys has been conducted as far as we know. Both alloys now belong within the category of Heusler alloys since the notion of all-d-metal Heusler is widely known.

3.2. Crystalline Structure

In the recently found Ni₂Mn_2-yTi_y and Ni_2−yMn₂Ti_y systems, Ti atoms have the fewest valence electrons (3d²4s²) compared to Ni (3d⁸4s²) and Mn (3d⁵4s²), and Wei et al. [22] predicted that Ti would occupy the D site. Both systems crystallize in a B2-type disordered structure, with the Mn excess atoms sharing the D site with Ti atoms in the Ni₂Mn_2-yTi_y system, resulting in a strong AFM coupling due to the Mn(B)–Mn(D) interaction (Figure 5). The main difference with conventional Heusler alloys is the competence between the L2₁ and the inverse XA phases.

The Ni_2−xCo_xMn_1.4Ti_0.6 quaternary series was discovered by Wei et al. [19], who employed the strategy of introducing Co atoms at Ni sites to impose FM long-range ordering on the Ni–Mn–Ti system, resulting in the first FSMAs among all-d-metal Heusler alloys. Partially replacing Co atoms in Ni₂MnZ systems has previously been investigated [71], resulting in a strong local Mn(B)–Co(A/C)–Mn(D) exchange coupling with FM ordering [72], overcoming the Mn(B)–Mn(D) AFM coupling inherent in the B2-type disordered lattice. Moreover, some experimental results observed that strong ferromagnetism provides direct evidence of this probable atomic configuration and of the ferromagnetic activation effect in the Ni(Co,Fe)–Mn–Ti all-d-metal Heusler alloys. For example, in Ni_50−xCo_xMn₃₅Ti₁₅ alloys, Co atoms that have been substituted for Ni atoms will also share the (A,C) sites with Ni atoms, leaving Mn and Ti with fewer valence electrons at the B/D sites. With the aid of the strong FM exchange interactions between nearest-neighbor Co-Mn atoms, the original AFM exchange coupling between Mn-Mn atoms in Ni-Mn-Ti alloys is converted into FM one, resulting in parallel alignment of the Mn-Co-Mn moments [19]. This phenomenon is known as the “ferromagnetic activation effect of the Co atom” [72]. FM ordering in Ni_2−xFe_xMn_1.4Ti_0.6 alloys [73], in which Fe substitutes Co in the exchange coupling, is generated via a similar mechanism. Co (3d⁷4s²) and Fe (3d⁶4s²) atoms are considered to share the (A/C) sites with Ni (3d⁸4s²) atoms in both series since their valence numbers are greater than those of Mn and Ti. Feng [74] used theoretical calculations on the X₂MnTi (X = Pt and Pd) series to study the impact of Ti as a p-group atom replacement. The findings show that the L2₁ crystallographic structure is energetically stable for both compositions, with high valence Pd (4d⁸5s²) and Pt (5d⁸6s²) filling the (A/C) sites and Mn (3d⁵4s²) occupy the (B) site, respectively. Ti prefers to remain in the D site. Han et al. [75] developed research for all-d-metal Heusler alloys X_2−xMn_1+xV (X = Pd, Ni, Pt, Ag, Au, Ir, Co; x = 1, 0). They looked at the atomic occupancy of these alloys in the cubic phase and discovered that the well-known site preference criterion does not apply to all of them. Han et al. [76,77] and Wang et al. [78] studied other Zinc-based all-d-metal Heusler ZnCdTMn combinations by theoretical calculations on the Zn₂YMn series. As a result of its complete 3d occupied state, the Zn atoms behave as a major group element, and Zn atoms prefer to occupy the D site rather than replacing Pd atoms at site A. The phenomenon of this process is the whole 3d shell of the Zn atom.

In Figure 5, as the content of Ti was usually lower than 25 at.%, some Mn atoms are located on D sites by substituting Ti atoms. However, the martensitic crystallographic structure can be more complex, including modulation, as shown in Figure 6.

3.3. Influence of d–d Hybridization

Theoretical calculations revealed that stoichiometric Ni₂MnTi displays mechanical properties superior to those of conventional Heusler systems. Yan et al. [79] later discovered that the Ni_2.0Mn_1.27Ti_0.73 composition has a significant eCE (under 600 MPa of uniaxial stress, adiabatic temperature change ΔT_ad = −20.4 K). Many Ni–Mn-based systems, such as Ni_1.80Mn_1.76Sn_0.44 (ΔT_ad = −11.6 K unloading 600 MPa of uniaxial stress) [80] and Ni_2.0Mn_1.11Ga_0.89 (unloading 100 MPa of uniaxial stress, ΔT_ad = −6.1 K) [81], have lower values. Changing the chemical bonding character of the Ni_2.0Mn_1.27Ti_0.73 all-d-metal Heusler alloy by substituting high p–d hybridization with somewhat weaker d–d hybridization among transition metals increases its ductility, according to further examination of the electron localization function. Pugh’s ratio [82] is a popular metric for determining solid ductility. It is defined as the ratio of the bulk modulus B to the shear modulus G of a material. Values greater than 1.75 indicate ductile behavior. For different X₂MnZ compositions, Figure 7 illustrates Pugh’s ratio as a function of Cauchy pressure, a parameter that describes the dominant kind of chemical bonding. We see that Ni₂MnTi is more ductile than Ni₂MnGa [83] and Ni₂MnIn [84], two of the most promising FSMAs among Heusler systems, according to our results. Furthermore, Ni₂MnTi [85] also has the highest Cauchy pressure, indicating that chemical bandings are weakly covalent. As a consequence, reducing covalent p–d hybridization in Ni₂MnZ Heusler alloys is connected to enhanced ductility.

3.4. MCE in All-d-Metal Heusler Alloys

Until recently, only a few investigations have focused on Heusler alloys of this type. Wei et al. [22] recently discussed the creation of all-d-metal alloys that exclusively include 3d transition metal components. They found that adding Ti to Ni–Mn aids in the B2 phase creation and stability. Cong et al. [6] achieved a massive elastocaloric impact in Ni–Mn–Ti alloys, with a ΔT_ad = 31.5 K and ΔS_M = 45 Jkg⁻¹K⁻¹, at a pressure of 700 MPa. Yan et al. [77] also discovered that the bulk Ni₅₀Mn_31.75Ti_18.25 alloy has outstanding mechanical characteristics, with a stress of 1.1 GPa and a convincing compressive strain of 13%, respectively. Despite its exceptional elastocaloric sway, the Ni–Mn–Ti combination has a modest MCE when compared to Heusler alloys. The absence of magnetic contrast between the austenite and martensite phases is largely responsible for this. Yan et al. [79] examined the austenite phase’s antiferromagnetic condition in Ni–Mn–Ti alloys. As a result, some thought has been given to doping the elements to improve the magnetocaloric impact. Furthermore, according to Wei et al. [19], cobalt doping in the Ni₅₀Mn₃₅Ti₁₅ alloy affects the transition from AFM to FM in the austenite phase. They created the Mn–Co–Mn configuration by replacing Co for Ni sites in the austenite phase, resulting in the ferromagnetic activation effect. Additionally, the AFM state of austenite in Ni–Mn–Ti alloys was confirmed by Yan et al. [79] and Wei et al. [19]. Therefore, some researchers have attempted to improve its MCE by means of doping elements. Li et al. [86] indicated that under a magnetic field of 3 T, Fe and Co doping in the Ni–Mn–Ti alloy could produce the refrigeration capacity (RC) of 79.5 Jkg⁻¹ and ΔS_M of 8.4 Jkg⁻¹K⁻¹. In addition, taking into account the magnetostructural coupling in the Ni_2−xFe_xMnTi [81] and Ni–Co–Mn–Ti [73] Heusler alloys, a giant MCE was observed. Recently, Aznar et al. [87,88] revealed the B-doped Ni₅₀Mn_31.5Ti_18.5 all-d-metal Heusler alloy. These alloys created an excellent BCE with an RC up to 1100 Jkg⁻¹ and ΔS_M of 74 Jkg⁻¹K⁻¹ under the pressure of 3.8 kbar, undergoing MT with an enormous volume change (ΔV) in its PM. Due to the eCE and MCE coexisting near RT, these alloys must be candidates for magnetic refrigeration.

3.5. Perspectives

Recently, experimental efforts targeted at increasing the MCE of all-d-metal Heusler alloys are worth emphasizing. One option is to add more elements to analyze multicomponent specimens and the effect of the combination of four or fifth elements in the functional response in a similar pathway to the applied to conventional Heusler alloys. Taubel et al. [89] revealed that an ideal annealing technique sharpened the phase transformation in the quaternary Ni_2−xCo_xMn_2−yTi_y series, while the Co content governs the transition’s sensitivity to the external magnetic field. The direct MCE is particularly strong in the Ni_1.40Co_0.60Mn_1.48Ti_0.25 Heusler alloy (ΔT = 4.0 K and ΔS_iso = −20.0 Jkg⁻¹K⁻¹ under an applied magnetic field of 20 kOe). Li and coworkers [90] made a significant addition to the field by investigating the Ni_1.4Co_0.6−xFe_xMn_1.4Ti_0.6 series experimentally. The partial replacement of Fe atoms with Co atoms decreases the d–d hybridizations, in this case, changing the Curie temperature and MT temperatures of the system. The maximum direct MCE value (ΔS_iso = −20.0 Jkg⁻¹K⁻¹ under a field of 50 kOe) was found for the x = 0.024 composition. By applying hydrostatic pressure (0.35 GPa), the functional response is improved, achieving values of ΔS_iso = −24.20 Jkg⁻¹K⁻¹ and RC = 347.26 JK⁻¹ (under a field of 50kOe) [85]. Because this system has both direct and inverse MCE, both demagnetization and magnetization processes may be investigated for solid-state refrigeration.

It should be remarked that these materials are also under study for applications such as catalysis with chemically diverse surface configurations [91]. These materials can also have high magnetoresistance [92] and spintronic properties [93].

We advocate focusing future research on the atomic site occupancy rules of these kinds of alloys. First principles and density functional theory (DFT) studies will be useful in understanding atomic site influence on the total magnetic moment per formula unit [89,90,91,92,93,94]. It is known that a large reversible magnetocaloric effect and high magnetoresistance were achieved by improving the crystallographic compatibility between the austenitic and martensitic phases [95]. Likewise, the influence of d–d hybridizations on atomic ordering may be shown by evaluating structural and magnetic properties when the quantity of the p-atom group decreases. Furthermore, the impact of thermal annealing, applied pressure as well as several synthesis methods on the creation of the L2₁ phase should be further investigated. Finally, because of the increased mechanical ductility and high induced strain values observed, the shape memory impact of ternary Ni_2xMn_1+xTi_xand Mn_2xNi_1+xTi_x series should be further investigated.

4. Conclusions

By removing the p-group atom from the X₂YZ composition, novel functional all-d-metal Heusler alloys are developed. These findings contribute to our knowledge of the role of orbital hybridization in the fundamental and functional features of X₂YZ Heusler alloys. According to the current study, despite the lack of a p-group atom, the martensitic transition with adjustable MT by chemical composition occurs. Finally, substituting a transition metal for the p-group enhances mechanical ductility and results in considerable reversible MCE. The suppression of p–d hybridization and the growth of d–d hybridizations is the key physical process that combines remarkable mechanical features with huge MCE. Because of their optimal functional behavior, these alloys are a possible new class of materials for technological applications. We advocate focusing future research on the atomic site occupancy rules of these kinds of alloys. The influence of d–d hybridizations on atomic ordering may be shown by evaluating structural and magnetic properties when the quantity of the p-atom group decreases. Furthermore, the impact of thermal annealing techniques, as well as several synthesis methods on the creation of the L2₁ phase, should be further investigated. Finally, because of the increased mechanical ductility and high induced strain values observed, the shape memory impact of ternary Ni_2xMn_1+xTi_xand Mn_2xNi_1+xTi_x series should be further investigated.

Author Contributions

Conceptualization, T.B.; methodology, T.B. and J.-J.S.; writing—original draft preparation, T.B.; writing—review and editing, J.-J.S. and T.B. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

Data can be requested from the authors.

Acknowledgments

The authors acknowledge A. Carrillo for the MAUD crystallography images support.

Conflicts of Interest

The authors declare no conflict of interest.

Footnotes

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Figures and Tables

Figure 1. Crystallographic structure of X2YZ Heusler alloys is shown in this diagram. Blue (A sites), green (B sites), yellow (C sites), and red (D sites).

Figure 2. Temperature (martensitic start Ms) transformation diagram topic of Heusler alloys (Reprinted with permission from ref. [44]. Copyright 2022 MDPI).

Figure 3. Field dependence of ΔSM for Ni2MnGa1−xSnx (x = 0 and 0.05) alloys. Reproduced from reference [55]. Copyright 2012 Elsevier.

Figure 4. ΔSM values for several Heusler alloys as a function of peak temperatures (Tpeak) at 5 T. Reprinted with the permission from refs. [65,66,67,68]. Copyrights 2008, 2009 and 2016 Elsevier.

Figure 5. Schema of the L21 Heusler crystallographic structure (left) indicating with red lines the cell of the L10 tetragonal martensite (right) for stoichiometric Ni50Mn25Ti25 alloy.

Figure 6. (a) Cell of the seven-layer modulated martensite phase (14M) of an arbitrary composition sample seen in 3D and laterally. (b) Cell of the five-layer modulated martensite phase (10M) of an arbitrary composition sample seen in 3D and laterally (generated with MAUD-free software, version 2.08, Luca Lutterotti, Trento, Italy).

Figure 7. Ductile-brittle diagram of some conventional Ni–Mn–Z (Z = Ga, Al, In and Sn) and stoichiometric Ni2MnTi alloys. The horizontal dashed and the vertical dashed dot lines indicate Pettifor’s and Pugh’s brittleness–ductility criteria, respectively. The inhibition of covalent p–d hybridization obtained by removing the p-group atom is supported by this result. Reproduced with permission from ref. [79]. Copyright 2019 Elsevier.

Table 1

Sites associated withX, Y, and Z atoms for the different austenitic phases of Heusler-type stoichiometry alloys.

Structure	X Atoms (Sites)	Y Atoms (Sites)	Z Atoms (Sites)
L21	A, C	B	D
Inverse XA	B, C	A	D
Disordered B2	A, C	B, D	B, D
Disordered A2	A, B, C, D	A, B, C, D	A, B, C, D

Table 2

Young’s elastic modulus E for some representative conventional (p–d) and all-d-metal (d–d) Heusler alloys.

Composition	Ni2MnAl	Ni1.48Co0.52Mn1.4Ti0.6	Ni2MnGa
Type	p–d	d–d	p–d
E (Gpa)	192.00	54.81	124.61
Refs.	[39]	[40]	[41]

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