Unveiling the Robust Struct-Electromagnetic Characteristics of CdAB 2 Chalcopyrite (A = Cr, Mn, Fe; B = P, As): A Comprehensive Ab-Initio Study

We present a comprehensive investigation of the electromagnetic properties of CdAB 2 compounds, where A represents Cr, Mn, or Fe, and B denotes P or As. To investigate the spin-polarized behavior of these compounds the A atoms were substituted at the Group IV (Ge) position in CdGeB 2 in the chalcopyrite crystal structure. Our results reveal that all the CdAB 2 compounds exhibit compelling spin-splitting of energy states near the Fermi level ( E F ). Notably, CdAB 2 materials with A = Cr and Mn exhibit intriguing half-metallic ferromagnetic (HMF) characteristics, with the calculated total magnetic moments of 2.00 and 3.00 µ B /f.u., respectively. The HMF properties originated in CdAB 2 (A = Cr and Mn; B = P, As) these compounds owing to the hybridization of partially ﬁ lled -3d(t 2g ) states of A atoms with the p-states of B (P, As) atoms, with minor contributions from Cd ’ s-like states. In contrast, CdFeB 2 displays distinct behavior, demonstrating spin-splitting of energy levels around the E F indicative of a stable ferromagnetic (FM) state and the absence of HMF at their equilibrium volume. The calculated total magnetic moments for CdFeP 2 and CdFeAs 2 are about 1.83 (1.64 µ B /f.u.) and 1.94 µ B /f.u. (1.84 µ B /f.u.) under generalized gradient approximation (GGA) (local spin density approximation (LSDA)) approximations, respectively. Perhaps these CdAB 2 compounds (A = Cr and Mn; B = P, As) with HMF characteristic within both LSDA and GGA formalisms makes them highly promising candidates for spin injectors in the spintronic device applications. Furthermore, their semiconducting nature renders CdCrB 2 and CdMnB 2 materials compatible with silicon and other semiconducting lattices, enhancing their potential practical applications in the spintronic technologies. In conclusion, this study presents a thorough exploration of the robust electronic and magnetic properties of CdAB 2 chalcopyrites, offering exciting prospects for their utilization in the future spintronic applications.

For practical spintronic applications, materials displaying room-temperature ferromagnetism (FM) are highly preferred.
Ternary II-IV-V 2 semiconductors, crystallizing in the bodycentered tetragonal (BCT) chalcopyrite structure with the space Group I-42d, have emerged as promising candidates for various technological applications [10][11][12][13].By replacing a small fraction of constituent atoms with TM ions such as Cr or Mn, II-IV-V 2 materials can be engineered for spintronic purposes.The doping of TM ions induces a strong spin splitting of energy levels around the Fermi level (E F ) with relatively high T C [10][11][12][13][14]. The appearance of HMF property relies on the concentration of magnetic ions and temperature.Experimental results have revealed room temperature FM (T C = 320 K) in Mn-doped CdGeP 2 due to the high-carrier solubility of Mn atoms in CdGeP 2 , where Mn 2+ easily occupies the divalent Cd site without altering electrical neutrality.
The substitutional site of TM ions in ternary compounds plays a crucial role in determining FM or antiferromagnetic (AFM) properties.When M (A = Mn, Cr, or V) atoms are substituted at the Group II (divalent) site of Ternary II-IV-V 2 chalcopyrite, AFM spin arrangement is favored.Conversely, when the same M atoms are substituted at the tetravalent (Group IV) site, FM configuration with hole formation is observed [15].Notably, stable FM states have been achieved with T C = 355 K by substituting Mn at the Ge site in CdGeP 2 , making the experimental fabrication of such materials feasible.Moreover, TM-doped or replaced chalcopyrite (II-IV-V 2 ) semiconductors have been shown to exhibit FM above room temperature, drawing attention in the field of spintronics [13,14,16,17].
Building on the previous research, [19,20] which explored spin-polarized calculations on ZnMX 2 (A = Sc, Ti, V, Cr, Mn, Fe; X = P, As) and CdAB 2 (A = Sc, Ti, V; X = P, As) compounds, revealing the possibility of FM upon M atom substitution at the Ge site of II(Zn/Cd)IV(Ge)-VI(P/As) 2 compounds, our present work extends this study by substituting M atoms (A = Cr, Mn, Fe) at the Ge site of CdGeX 2 .Utilizing the fullpotential linearized augmented plane wave (FP-LAPW) method with two correlation functionals, generalized gradient approximation (GGA) [21] and local spin density approximation (LSDA) [22,23], we investigate the introduction of deep levels by TM impurities in the band gap of CdGeB 2 semiconductors, resulting in attractive electronic and magnetic properties in these chalcopyrite's.To understand the magnetic states of CdAB 2 compounds, we perform total energy vs. volume calculations for NM, FM, and AFM phases.Additionally, we present spin-dependent band structures, charge density plots, and density of states (DOS) at equilibrium conditions for all the compounds.
This study contributes to the growing understanding of robust room temperature ferromagnetism in CdAB 2 chalcopyrite through transition metal substitution, offering valuable insights for the potential spintronic applications.

Method of Calculation and Crystal Structure
In this study, we conducted first-principal calculations using the Full-Potential Linearized Augmented Plane Wave (FP-LAPW) method [22], known for its accuracy in electronic structure calculations of the periodic solids.The WIEN2k code [24] was employed for the calculations of the structural, electronic, and magnetic properties of CdAB 2 compounds.Both GGA [24] and LSDA [22] were used for the exchangecorrelation functions in these calculations.
The FP-LAPW technique employs a muffin-tin potential to represent the crystal potential.This assumes that the crystal potential is spherically symmetric within the muffin-tin sphere and remains constant in the interstitial space.The core electrons within the atomic sphere are treated with full relativistic considerations and self-consistency using a spherical approximation.Meanwhile, the valence electrons in the interstitial region are treated as self-consistently as possible, but with a semi-relativistic approach.Inside the atomic sphere, the crystal potential, electronic wave functions, and charge density are expanded using spherical harmonics up to a maximum angular momentum quantum number of l max = 10.In the interstitial region, a Fourier series of plane waves is employed, with a cutoff defined as the product of the muffin-tin radius (RMT) and the maximum wave vector (K max ), set to 7.0.For specific elements like Cd, Cr, Mn, Fe, P, and As, atomic sphere radii are designated as 2.08, 2.23, 2.24, 2.17, 2.20, and 2.09, respectively.The charge density is expanded in a Fourier series up to a maximum reciprocal lattice vector denoted as Gmax = 12.To integrate over k-points in the irreducible wedge of the first Brillouin zone, an 8 × 8 × 4 k-mesh is used.Through an iterative process, the crystal's self-consistent total energy is brought to convergence, achieving a value lower than 0.01 m Ry.

Results and Discussion
Before delving into electronic and magnetic properties, we performed full structural optimization for the CdAB 2 Advances in Condensed Matter Physics (A = Cr, Mn, Fe; B = P, As) compounds.The chalcopyrite structure (BCT phase) with space group I-42d (# No. 122) was described using unit cell lattice parameters (a o , c o ) and one internal parameter (u).Structural optimization was carried out for all compounds within both the GGA and LSDA for the nonmagnetic (NM), ferromagnetic (FM), and antiferromagnetic (AFM) phases.Since the results obtained under GGA and LSDA schemes were found to be identical, the calculated total energy as a function of the lattice parameter for GGA is represented in Figure 1.
To determine the equilibrium values of u, a o , c o , and bulk modulus (B o ) of CdAB 2 , the total energies were fitted to Birch-Murnaghan's equation of state [26] as a function of relative volume within GGA and LSDA for the NM, FM, and AFM states of each compound.The calculated values of u, a o , c o , and B o for CdGeB 2 and CdAB 2 compounds are presented in Tables 1 and 2. Remarkably, the calculated ground state properties of CdGeB 2 are in excellent agreement with the experimental and previously reported results [27].However, it is noted that the calculated lattice constants are overestimated by GGA and underestimated by LSDA, as expected.The internal parameter u was found to vary from 0.268 to 0.306, as observed from the tables.
Figure 1 showcases the total energy-volume curves of CdAP 2 and CdAAs 2 (A = Cr, Mn, Fe) compounds under GGA approximation.The energy-volume curves for CdAB 2 (A = Cr, Mn, Fe; B = P, As) compounds indicate that the FM phase exhibits the minimum energy, signifying their ferromagnetic stability at equilibrium.To further assess the stability of the magnetic state, we calculated the spinpolarized energy differences ΔE 1 (ΔE 1 = E FM − E NM ) and ΔE 2 (ΔE 2 = E FM − E AFM ), i.e., the energy gains due to the formation of magnetic moments in the systems.The negative values of total energy differences ΔE 1 and ΔE 2 for CdAB 2 (M = Cr, Mn, Fe) compounds indicate the desirability of the FM state in these materials.The calculated total energy differences ΔE 1 and ΔE 2 under GGA and LSDA can be found in Tables 1 and 2.
The equilibrium bulk modulus (B o ) values of CdAB 2 (A = Cr, Mn, Fe; B = P, As) compounds were calculated for their NM, FM, and AFM phases using Equation (1) [28].The calculated B o values are presented in Tables 1 and 2 under the GGA and LSDA schemes.
Bulk modulus is a crucial mechanical property that characterizes a material's resistance to volume changes during expansion or compression.With the substitution of transition metal (TM) atoms in the host CdGeB 2 compounds, the lattice parameters (a o , c o ) may increase or decrease, leading to corresponding changes in the B o values due to the displacement of the electric charge of core electrons via valence electrons.Notably, GGA tends to yield larger lattice parameters and smaller bulk modulus values compared to the LSDA.
The chalcopyrite crystal structure is a superlattice of the zinc blende (ZnS) structure.Doubling the unit cell of ZnS results in a change in the anion As/P position along the z-direction.This leads to tetragonal distortion in CdAB 2 compounds, forming different bond lengths.The relaxed anion-cation bond lengths (R Cd-X and R M-X ) for the host CdGeB 2 and CdAB 2 compounds were calculated for the NM, FM, and AFM states using Equations ( 2) and (3) [29] under GGA and LSDA and are presented in Tables 3 and 4.
In CdAB 2 compounds with M = Cr and Mn, the calculated bond length R M-B is shorter than R Cd-B due to the larger electronegativity of B [22] atoms.Consequently, the M atoms move closer to the B atom, resulting in decreased R M-B in these compounds with u values > 0.25.Conversely, for u < 0.25, R Cd-B becomes reduced compared to R Fe-B in CdFeB 2 , where R Fe-B increases due to the decrease in the electro-positivity of Fe atoms.In this case, the Cd atom moves toward the B atom.It is important to highlight that bond lengths exhibit a reduction in the GGA method as opposed to the LSDA approach.This reduction in bond lengths intensifies the rigidity among Cd, M, and B atoms and amplifies the electron concentration in the valence area.In order to enhance our comprehension of electron behavior within the valence region, additional calculations were performed to determine the compounds' band structure, density of states (DOS), and electron charge density.
Additionally, the heat of formation (ΔH) for all the CdAB 2 compounds in the NM, FM, and AFM phases were calculated using Equation (4) [29], and the results are provided in Tables 3 and 4.
The computed ΔH (enthalpy) values were discovered to be negative using both the LSDA and GGA methodologies.This signifies that all the compounds are expected to be thermodynamically stable in the chalcopyrite structure.These findings provide valuable insights into the mechanical and thermodynamic stability of CdAB 2 chalcopyrite, contributing to a deeper understanding of their potential applications in various fields of materials science.
The spin-resolved electronic band structures of CdAB 2 compounds (where A = Cr, Mn, Fe, and B = P, As) were computed along high-symmetry directions within the first Brillouin zone at their equilibrium volume using both the GGA and LSDA.Electronic band structures for CdAB 2 compounds (A = Cr, Fe; B = P, As) are depicted in Figures 2 and  3 for the GGA approach.These figures illustrate the overall profile of the band structure, which remains quite similar for all CdAB 2 compounds under both approximations.The introduction of -d states near the Fermi level (E F ) due to the substitution of elements A = Sc, Ti, V, Cr, Mn, and Fe in the ZnGeB 2 structure leads to a crystal field resonance.This resonance causes a splitting of the -d states into Advances in Condensed Matter Physics suborbitals labeled as "eg" and "t 2g ".As a result of the hybridization between -d states and -p states from the nearest neighboring B atom, an indirect band gap emerges in the spin-down channel.Meanwhile, the, eg and t 2g states within the majority spin channel intersect the Fermi level, indicating a HMF characteristic within these compounds.Figure 2 illustrates the spin-polarized band structure of CdCrP 2 , highlighting the noticeable spin polarization of energy states in the vicinity of the Fermi level (E F ). Specifically, the bonding -3d, eg states and the anti-bonding t 2g states associated with the Cr atom is notably concentrated near the EF.This arrangement results in the formation of an indirect band gap between the valence band maximum (VBM) and the conduction band minimum (CBM) within the spin-down channel.In contrast, in the spin-up channel, the e g , t 2g states of the -3d Cr atom and -3p states of P atoms extend and cross the E F , leading to HMF nature in this compound.Similar phenomena were observed in CdCrAs 2 and CdMnB 2 (B = P, As) compounds.The calculated HMF gap (E HM ) and spin-splitting energy gaps (E g ↓) of CdAB 2 (A = Cr, Mn; B = P, As) are listed in Table 5 for both GGA and LSDA.
On the other hand, CdFeP 2 (Figure 3) shows spinsplitting of energy levels around the E F , indicating the occurrence of stable ferromagnetism.However, the VBM crosses the E F in both the spin-up and spin-down channels, signifying   TABLE 5: Calculated half-metallic gap (E HM ) in eV, minority spin gap (E g ↓) in eV, partial, interstitial, and total magnetic moments in μ B for CdAB 2 (M = Cr, Mn, Fe; B = P, As) compounds at their equilibrium volume using generalized gradient approximation (GGA) and local spin density approximation (LSDA).Note.The integer magnetic moment shows the characteristic of half-metallic ferromagnetism which is indicated in bold.

Compounds
Advances in Condensed Matter Physics the absence of HMF property in these compounds.The decrease in exchange spin-splitting energy is attributed to the coupling of magnetic t 2g and e g suborbital of -3d states of Fe atoms and the repulsion between the -3d (t 2g and e g ) states of Fe and -p states of P atoms in the VBM.This leads to an increase in the VB width, reducing the localization of the electron in the VB region and increasing the spin-polarization around the E F .The charge density contour plots (Figures 4 and 5) offer insight into the chemical bond nature in CdAP 2 (A = Cr, Fe) compounds.The plots provide evidence of charge transfer involving valence electrons shifting from Cd to P and from M to P ions.This transfer signifies a blend of both ionic and covalent attributes in the atomic bonds between Cd-P and M-P, holding for both spin channels across all compounds.An examination of the electronic charge distribution surrounding the P atom reveals the establishment of Cd-P and M-P bonds.Particularly strong p-d exchange interactions between Cr (d) and P (p) states are evident, driving a substantial covalent character between P and Cr within CdCrP 2 .Likewise, the compounds CdCrAs 2 and CdMnB 2 (where B = P, As) showcase pronounced charge transfer between M and P ions.This results in a robust p-d(t 2 g) interaction between the band carriers and localized spins, leading to a HMF nature in these compounds.
Total and partial density of states (PDOS) calculations (Figures 6 and 7) for CdCrP 2 and CdFeP 2 within GGA reveal significant changes in the DOS near the E F , leading to spinpolarization of the valence bands (VBs).In CdCrP 2 , the e g orbitals are well-localized and form an indirect band gap between the VB and CB in the spin-down channel.In the spin-up channel, the t 2g states cross the E F , leading to HMF behavior.A similar phenomenon was observed in CdCrAs 2 and CdMnB 2 (B = P, As), where the p-d (t 2g ) states of B and A (Cr, Mn) atoms play a dominant role in the formation of the gap between valence and conduction bands in the spin-down channel.
Conversely, CdFeP 2 and CdFeAs 2 do not exhibit HMF behavior, as the strong overlapping and repulsive reaction between -3d states of Fe (e g and t 2g ) and -p states of P/As reduce the magnetic moment of Fe, resulting in spin-splitting of energy states around the E F without an observed band gap in the minority spin channel.
Using the spin-polarized calculations, the total and local magnetic moments of CdAB 2 compounds (where A = Cr,   Advances in Condensed Matter Physics Mn, Fe and B = P, As) have been computed within both the LSDA and GGA methods.These results are summarized in Table 5.It is evident from the findings that the primary source of the total magnetic moments stems from the partially filled -3d states of the M atoms.For instance, in CdCrB 2 , the Cr atom contributes some of its valence electrons to the majority spin band during bond formation, resulting in a total magnetic moment of 2.00 µB/f.u., as shown in Table 5.
Similarly, the Mn atom in CdMnB 2 contributes three unpaired d electrons for a total magnetic moment of 3.00 µ B per formula unit.However, in CdFeB 2 , the Fe atom's magnetic moment gets reduced due to hybridization and repulsion, resulting in stable ferromagnetism without HMF behavior.The magnetic moments calculated by GGA and LSDA significantly differ, with GGA yielding higher values.Our obtained spin-resolved electronic band structures and charge density analysis provide valuable insights into the electronic and magnetic properties of CdAB 2 chalcopyrites, revealing their potential for applications in various fields of materials science.

Conclusion
In pursuit of new HMF materials, we conducted comprehensive first-principles calculations on CdAB 2 compounds in the chalcopyrite structure within the GGA and LSDA schemes.Ground state properties were evaluated from the energyvolume relation.The CdAB 2 compounds were found to be ferromagnetically stable from the total energy calculations.The structural parameters of CdGeB 2 host compounds agreed well with existing experimental and theoretical data, no comparative data were available for CdAB 2 compounds.The negative formation energies (ΔH) indicated that these compounds are energetically favorable when A occupies the Group IV (Ge) position in CdGeB 2 .
The spin-polarized calculations unveiled intriguing spinsplitting of energy states near the Fermi level (E F ) upon the substitution of A atoms at the Group IV (Ge) position in CdGeB 2 .For CdAB 2 compounds with A = Cr and Mn, a distinct energy gap was observed around the E F in the spin-down channel, while the VB crossed the E F in the spin-up channel, confirming the presence of HMF nature with 100% spin polarization around the E F .Therefore, the HMF property in CdAB 2 (A = Cr, Mn; B = P, As) arose due to the hybridization of A -3d (t 2g ) and B -3/4p states, with a minor contribution from Cd -s states and their corresponding calculated total magnetic moment were found to be 2.00 µ B and 3.00 µ B per formula unit, respectively.
Conversely, in CdFeB 2 compounds, the overlapping of wave functions of -3d (t 2g and e g ) states of Fe and repulsion   with B -np states were more pronounced, leading to a reduction in the space charge density of the Fe atom.This effect diminished the possibility of HMF due to the broadening of VBs.The calculated total magnetic moments for CdFeP 2 and CdFeAs 2 were determined to be 1.83 (1.64 µ B /f.u.) and 1.94 µ B /f.u.(1.84 µ B /f.u.), respectively, under GGA (LSDA) approximations.Consequently, the ground state of CdFeB 2 compounds did not exhibit significant HMF characteristics when using LSDA and GGA functionals.However, considerable magnetic properties, such as stable ferromagnetism, were observed in these compounds.In conclusion, our firstprinciples study sheds light on the potential HMF nature in CdAB 2 (A = Cr, Mn; B = P, As) chalcopyrites.These findings hold significance in the ongoing search for novel HMF materials, offering promising avenues for the future spintronics applications.

2 FIGURE 6 :
FIGURE 6: Spin-dependent total and partial density of states of CdCrP 2 using the generalized gradient approximation (GGA).

FIGURE 7 :
FIGURE 7: Spin-dependent total and partial density of states of CdFeP 2 using the generalized gradient approximation (GGA).

TABLE 4 :
Calculated heat of formation (ΔH) in eV and bond length in Å for CdAB 2 (M = Cr, Mn, Fe; B = P, As) compounds using local Spin Density Approximation (LSDA).