Recently, Wei et al. ^[1][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 ^[2][3][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.

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. ^[1][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 1). 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. ^[4][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 ^[5][71], resulting in a strong local Mn(B)–Co(A/C)–Mn(D) exchange coupling with FM ordering ^[6][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 ^[4][19]. This phenomenon is known as the “ferromagnetic activation effect of the Co atom” ^[6][72]. FM ordering in Ni_2−xFe_xMn_1.4Ti_0.6 alloys ^[7][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 ^[8][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. ^[9][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. ^[10][11][76,77] and Wang et al. ^[12][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 12, 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 23.

Theoretical calculations revealed that stoichiometric Ni₂MnTi displays mechanical properties superior to those of conventional Heusler systems. Yan et al. ^[13][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) ^[14][80] and Ni_2.0Mn_1.11Ga_0.89 (unloading 100 MPa of uniaxial stress, ΔT_ad = −6.1 K) ^[15][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 ^[16][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. Researchers see that Ni₂MnTi is more ductile than Ni₂MnGa ^[17][83] and Ni₂MnIn ^[18][84], two of the most promising FSMAs among Heusler systems, according to theour results. Furthermore, Ni₂MnTi ^[19][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.

Until recently, only a few investigations have focused on Heusler alloys of this type. Wei et al. ^[1][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. ^[20][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. ^[11][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. ^[13][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. ^[4][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. ^[13][79] and Wei et al. ^[4][19]. Therefore, some researchers have attempted to improve its MCE by means of doping elements. Li et al. ^[21][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 ^[15][81] and Ni–Co–Mn–Ti ^[7][73] Heusler alloys, a giant MCE was observed. Recently, Aznar et al. ^[22][23][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.

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. ^[24][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 ^[25][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) ^[19][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 ^[26][91]. These materials can also have high magnetoresistance ^[27][92] and spintronic properties ^[28][93].

ResWearchers 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 ^{[24][25][26][27][28][29]}[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 ^[30][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.