First-Principle Calculations to Investigate Structural, Electronic, and Magnetic Properties of Noble Metal-Doped $CdS/Se$

Abstract

This research aims to employ a first-principles approach based on density functional theory (DFT) to predict the structural, electronic, and magnetic attributes of $CdMX$ compounds, where $M$ represents $Ru$, $Rh$, or $Pd$, and $X$ represents either $S$ or $Se$. We utilized the modified Beck-Johnson potential, combined with the generalized gradient approximation ($mBJGGA$), to scrutinize the electronic and magnetic features of these compounds. The results reveal robust magnetic ground states for $M$-doped $CdX$. The analysis of spin-polarized band structures and densities of states indicates that $CdRuX$ and $CdPdX$ compounds exhibit half-metallic ferromagnetism, characterized by complete spin polarization of 100% at the Fermi level. Conversely, $CdRhX$ compounds exhibit the properties of ferromagnetic semiconductors. For $Ru$, $Rh$, and $Pd$-doped $CdX$, an integer-integrated total magnetic moment is observed, corresponding to 4, 3, and 2 ${\mu }_{B}$, respectively, with the primary contribution stemming from the doping atom and its four nearest neighboring $X$ atoms. This ferromagnetic behavior is attributed to the strong $p$-$d$ hybridization occurring between the states of the host $X$ ions and the $M$ impurity ion. Consequently, the outcomes of our study render these alloys as suitable materials for possible spintronic devices.

1 Introduction

Over the past two decades, there has been significant interest in diluted magnetic semiconductors $(DMSs)$, which combine semiconductor properties with magnetic characteristics. This heightened attention is primarily driven by their potential applications in the field of spintronic devices [1, 2]. Among $DMSs$, half-metallic ferromagnets ($HMFs$) have emerged as particularly fascinating materials. They exhibit distinct behavior for each spin channel, with one behaving as a metal and the other as a semiconductor or insulator. This unique property leads to the complete spin polarization of the electronic density of states at the Fermi level, opening up exciting technological applications such as functioning as a source of single-spin electrons and enabling the development of highly efficient magnetic sensors [3,4,5]. Since the pioneering discovery of $HMFs$ in 1983 by de Groot et al. [6] in the context of half-Heusler alloys, specifically $NiMnSb$ and $PtMnSb$, numerous HMFs have been either theoretically predicted or experimentally confirmed in a wide array of materials including half and full Heusler alloys, perovskite alloys, and $DMS$ compounds [7,8,9].

Recently, II–VI semiconductors have been the focal point of extensive research owing to their potential as promising host materials for achieving room temperature $DMSs$. The most commonly employed method to generate room temperature ($RT$) ferromagnetism in II-VI materials centers on the introduction of transition metal ($TM$) elements. This approach has been explored through both experimental studies [10,11,12,13,14] and theoretical investigations, as demonstrated by research involving materials like ${Zn}_{1-x}T{M}_{x}S/Se$ ($TM$ = $Mn$, $Fe$, $Co$, $Ni$) [15], $Cr$-doped $ZnTe$ [16], $Cr$-doped $HgSe$ [17] $V$, $Cr$-, $Mn$-, and $Fe$-doped $SrS$ [18], $Co$-doped $BeS$ [19], $Cr$-doped $CaZ$ ($Z\;=\;S, Se$) [20], and $MgS/Se$ doped with $Ti$, $V$, and $Cr$ [21]. Nevertheless, the origin of the observed ferromagnetism in these alloys remains controversial. It has been observed that dopant materials can segregate, leading to the formation of clusters, secondary magnetic phases, or metal precipitates [22, 23]. Such phenomena have the potential to restrict the efficiency of DMS in practical applications.

Cadmium sulfide ($CdS$) and cadmium selenide ($CdSe$), belonging to the II-VI semiconductor group, have captured the keen interest of researchers due to their direct energy band gap and remarkable electrical and optical properties. These features make $CdS$ and $CdSe$ highly appealing for a wide range of technological applications, spanning solar cells [24, 25], photocatalysts [26], optoelectronic devices [27], and nonlinear optical materials [28]. Under standard environmental conditions, $CdS$ and $CdSe$ crystals adopt the wurtzite phase. However, when employing the molecular beam epitaxy (MBE) growth technique, these materials can also be stabilized in the zinc blende phases [29,30,31,32]. The introduction of TMs into $CdS$ and $CdSe$ is pivotal to enhance their multifunctionality and attain the desired material characteristics. In addition to the earlier mentioned works supporting the ferromagnetic behavior of $TM$-doped $II$-$VI$ semiconductors, there are reports indicating that $CdS/Se$, when doped with elements like $V$, $Cr$, and $Co$, exhibits a half-metallic ferromagnetic character [33,34,35]. Particularly, $Co$-doped $CdS$ and $CdSe$ have emerged as potential candidates for applications in optoelectronics and spintronics [36]. Besides the mechanism behind the emergence of ferromagnetism remains a subject of debate, the $II$–$VI$ semiconductors encounter difficulty in the doping process to produce p- or n-type devices due to the matching valence of the cation with common magnetic ions. To overcome these obstacles, some scientists have proposed an alternative approach, which involves doping nonmagnetic elements into nonmagnetic host semiconductors to induce ferromagnetism. In this context, $Cu$-doped $CdS$ has demonstrated a half-metallic character, with an estimated Curie temperature predicted to be 400 K above room temperature [37]. Additionally, theoretical predictions have suggested the possibility of ferromagnetism in $CdS$ doped with $Be$, $B$, and $C$ [38]. Recent research highlights the potential of ${Cd}_{1-x}{Ag}_{x}S$ alloys for new optoelectronic applications in the infrared-visible range, as well as potential spintronic application [39]. These exciting findings served as a catalyst for us to investigate new $CdS/Se$-based $DMS$ with unambiguous intrinsic ferromagnetism.

First-principle calculations are essential tools for understanding, predicting, and designing materials with tailored properties for a wide range of applications [40,41,42,43,44,45,46,47,48,49]. Their accuracy, predictive power, and ability to uncover fundamental insights make them indispensable in advancing both fundamental science and technological innovation in materials research. In this current research study, our objective is to investigate the impact of non-magnetic dopants $Ru$, $Rh$, and $Pd$ on the electronic structure and magnetism of zinc blende $CdS/Se$ through first-principle calculations. Theoretical analysis of the electronic structures provides insights into the mechanisms responsible for the ferromagnetism induced by $Ru$, $Rh$, and $Pd$ dopants. The structure of the article is organized as follows: Section 2 briefly outlines our calculation methodology, Section 3 presents a discussion of the diverse outcomes arising from our calculated properties, and finally, Section 4 provides our concluding remarks.

2 Computational Method

The full potential linearized augmented plane wave ($FP$-$LAPW$) method is considered one of the most precise techniques for determining the fundamental properties of crystalline materials. In our current study, we exclusively employed the $FP$-$LAPW$ method within the framework of density functional theory ($DFT$) [50], as implemented in the wien2k package [51]. For treating the exchange and correlation potential, we utilized the generalized gradient approximation of Perdew, Burke, and Ernzerhof ($GGA$-$PBE$) [52]. This choice was made to determine the structural parameters. When it came to calculating electronic and magnetic properties, we turned to the Tran Blaha modified Becke Johnson potential ($TB$-$mBJ$) [53]. The application of the mBJ approach significantly improves the precision when describing the electronic structure and accurately predicting the band gap energies for semiconductors, insulators, and HM systems [53, 54].

The un-doped $CdS$ and $CdSe$ cells exhibit a zinc blende (B3) structure with a space group of 216 $(F\overline{4 }3m)$. Within this structure, the $Cd$ atom resides at coordinates (0, 0, 0), and the atom $S/Se$ is positioned at (0.25, 0.25, 0.25) (refer to Fig. 1a). To simulate $M$-doped zinc blende $CdX$ with $M$ being one of $Ru$, $Rh$, or $Pd$, and $X$ being either $S$ or $Se$, we have generated a cubic supercell ${Cd}_{16}{X}_{16}$ with dimensions of 2 × 2 × 2, containing $16 Cd$ and $16 (S/Se)$ atoms (see Fig. 1b). Introducing a 6.25% doping concentration of M atom involves substituting the $Cd$ atom at (0, 0, 0) in the ${Cd}_{16}{X}_{16}$ supercell with the $M$ atom, resulting in the formation of the ternary alloy ${Cd}_{0.9375}{M}_{0.0625}X$, as depicted in Fig. 1c. The fully relativistic and scalar relativistic approach is used for core and valence electrons, respectively. Atomic sphere radii of $Cd$, $M$, and $X$ atoms were selected to be 2.2, 2.2, and 2.1 Bohr, respectively. The cutoff parameter ${R}_{MT} {K}_{max}$ was set 8, where ${K}_{max}$ represents the length of the maximal reciprocal lattice vector, and ${R}_{MT}$ is the smallest of all atomic sphere radii. Inside the atomic sphere, the maximum value for partial waves was taken as ${l}_{max}$ = 10. Brillouin zone integrations are performed using $14\;\times\;14\times\;14$ k points Monkhorst-pack ($MP$) mesh [55] for binary compounds and $5\;\times\;5\times\;5$ k points $MP$ mesh for ternary alloys. Self-consistency is attained when the maximum force exerted on each atom is below 2.10⁻³ Ry/a.u., and the total energy difference between successive iterations is less than 10⁻⁵ Ry/cell.

Fig. 1

Conventional cell configurations for a $CdS/Se$, b ${Cd}_{16}{(S/Se)}_{16}$, c ${Cd}_{0.9375}{M}_{0.0625}S/Se\;\left(M=Ru, Rh, Pd\right)$  

3 Results and Discussions

Based on the computational method presented in Section 2, we first describe the ground state structural properties of $CdS/Se$ based DMS. Figure 2 shows the optimization plots of $CdMS/Se$ in two distinctive magnetic states: paramagnetic ($PM$) and ferromagnetic ($FM$). The total energy as a function of the unit cell volume is fitted with Murnaghan’s equation of state [56]. This equation characterizes the relationship between the variables (E, V) and is expressed as follows [57, 58]:

$$E\left(V\right)\;=\;{E}_{0}\;+\;\frac{BV}{{B}^{\prime}}\left[\frac{{({V}_{0}/V)}^{{B}^{\prime}}}{{B}^{\prime}\;-\;1}\;+\;1\right]-\frac{B{V}_{0}}{{B}^{\prime}\;-\;1}$$

(1)

Fig. 2

Volume optimization plots of ${Cd}_{0.9375}{M}_{0.0625}S/Se\;\left(M\;=\;Ru, Rh, Pd\right)$ in $PM$ and $FM$ phases

Here, ${V}_{0}$ represents the equilibrium volume, while ${E}_{0}$, $B$, and ${B}{\prime}$ denote the total energy, bulk modulus, and the pressure derivative of the bulk modulus at the equilibrium volume, respectively. The obtained equilibrium lattice parameters a, the $B$ and ${B}{\prime}$ are stated along with existing theoretical and experimental data in Table 1. The lattice constants of $CdS/Se$ were determined to be 5.94 Å/6.22 Å, which align well with previous theoretical findings [59, 60], but they are slightly larger than the experimental measurements [60]. This overestimation is a general norm of $GGA$-$PBE$ functional. Importantly, to the best of our knowledge, there are no published data available to make any comparison of zinc blende $CdS/Se$ doped with noble metals $Ru$, $Rh$, and $Pd$. To ascertain the stable $FM$ state in these ternary compounds, we have computed the difference between the minimum energies of $PM$ and $FM$ states ($\Delta E\;=\;{E}_{PM}\;-\;{E}_{FM}$). Both our volume-optimized calculations (see Fig. 2) and the $\Delta E$ values (as detailed in Table 1) imply that $FM$ phase is energetically more stable than $PM$ phase for all the six compounds.

Table 1 Calculated optimized parameters and energy of spin polarization $\Delta E$ for $CdS/Se$ and ${Cd}_{0.9375}{M}_{0.0625}S/Se\;\left(M=Ru, Rh, Pd\right)$

The spin-polarized band structures of ferromagnetic ${Cd}_{0.9375}{M}_{0.0625}X (M\;=\;Ru, Rh,Pd, X\;=\;S, Se)$ compounds at their predicted equilibrium lattice constants along the high symmetry directions of the Brillouin zone with the corresponding total density of state (TDOS) are calculated using the modified Becke-Johnson ($mBJ$) approach, as illustrated in Figs. 3 and 4. Upon preliminary examination, it is evident that the band structures of both majority spin (spin up) and minority spin (spin down) in each compound display asymmetry. This means that the incorporation of dopant atoms into nonmagnetic $CdS/Se$ results in the emergence of magnetic ordering within these systems. Furthermore, it can be observed that $CdMS/Se$ $(M\;=\;Ru \;{\text{and}}\; pd)$ compounds demonstrate a half-metallic nature, characterized by semiconducting behavior in the majority spin channel and metallic behavior in the minority spin channel, leading to 100% carrier spin polarization at Fermi level. As a result, an energy band gap $({E}_{g})$ is present in the majority of spin bands, along with the presence of a half-metallic gap. In contrast, $CdRhS$ and $CdRhSe$ exhibit energetic band gaps for both majority and minority spins, indicating their semiconducting nature, and thus, they are classified as ferromagnetic semiconductors ($FMSs$). In a zinc blende structure, the noble metals are surrounded by the closest chalcogen ions, giving rise to a tetrahedral crystal field. This field induces a splitting of the $4d$ states into two-fold lower energy states $4d$-${e}_{g}$ (${d}_{{x}^{2}-{y}^{2}}$ and ${d}_{{z}^{2}}$) and three-fold higher energy states $4d$-${t}_{2g}$ (${d}_{xy}$, ${d}_{xz}$, and ${d}_{yz}$). This occurrence finds a comprehensive explanation within the framework of crystal field theory. The upper valence bands primarily exhibit $M$-$d$ and $X$-$p$ characters, with distinctions between majority and minority spin states. Specifically, for the three-filled majority spin bands situated at approximately − 0.5 eV, ${E}_{f}$, and − 0.8 eV for $CdRuS/Se$, $CdRhS/Se$, and $CdPdS/Se$, respectively, there is a dominance of the $4d$-${t}_{2g}$ orbitals of the $M$ atom. These bands display dispersion compared to the $4d$-${e}_{g}$ bands. Conversely, the two very narrow minority spin bands, appearing as a sharp peak in the TDOS, positioned at − 0.4 eV for $CdRhS/Se$ and crossing the Fermi level for $CdRuS/Se$, are primarily characterized by $M$ $d$-${e}_{g}$ character, resulting in their flat nature. The ${e}_{g}$ states, unable to bond symmetrically, remain relatively unperturbed within the solid, existing as non-bonding states that are well-localized in both space and energy [61]. The degree of localization associated with these states increases from $Pd$ to $Rh$ and then to $Ru$.

Fig. 3

Spin-dependent band structure and TDOS of ${Cd}_{0.9375}{M}_{0.0625}S\;\left(M\;=\;Ru, Rh,Pd\right)$ calculated using $mBJGGA$. The solid black (red) lines represent the majority (minority) spin channel. Fermi level is set to 0.0 eV

Fig. 4

Spin-dependent band structure and TDOS of ${Cd}_{0.9375}{M}_{0.0625}Se\;\left(M\;=\;Ru, Rh, Pd\right)$ calculated using $mBJGGA$. The solid black (red) lines represent the majority (minority) spin channel. Fermi level is set to 0.0 eV

In our study, we have provided the computed values of the minority spin gap $({E}_{g}^{dn})$, majority spin gap $({E}_{g}^{up})$, and half-metallic gap ${(E}_{HM})$. The results presented in Table 2 indicate that the calculated ${E}_{g}^{dn}$ is an indirect gap for $Rh$-doped $CdX$. Conversely, for all studied alloys,${E}_{g}^{up}$ has a direct nature, as both the highest point of the valence band and the lowest point of the conduction band are situated at the Γ point of the Brillouin zone. Notably, the ${E}_{g}^{up}$ increases as the doped elements range from $Ru$ to $Pd$, while it decreases when passing from $S$ to $Se$. The ${E}_{HM}$ is a crucial parameter for evaluating the suitability of DMS materials for spintronic devices. It specifically measures the energy gap between the Fermi level and the nearest energy level between the conduction band’s bottom and the valence band’s top. A substantial half-metallic gap is of utmost importance to realize the potential of half-metallic spintronic devices. Based on the findings presented in Table 2, the half-metallic gaps obtained for $CdPdS/Se$ are larger than those observed for $CdRuS/Se$, suggesting that $CdPdS/Se$ may possess higher Curie temperature [62], making them more attractive candidates for spin injection in spintronic applications compared to $Ru$ doped $CdS/Se$.

Table 2 Calculated spin-up gap $({E}_{g}^{up})$, spin down gap $({E}_{g}^{dn})$, and half-metallic gap ${(E}_{HM})$ for ${Cd}_{0.9375}{M}_{0.0625}S/Se\;(M\;=\;Ru, Rh, Pd)$  

Various models have been employed to elucidate the ferromagnetic behavior in diluted magnetic semiconductors. These models encompass a range of explanations, such as the Zener’s $p$-$d$ hybridization [63], the Zener’s double exchange [64], the super-exchange [65], the spin-split donor impurity band [66], the bound magnetic polaron [67], and the phenomenological RKKY exchange [68]. In order to provide a deeper understanding of the magnetic exchange coupling that has given rise to magnetism in $CdS/Se$ material upon the introduction of non-magnetic dopants, the partial density of states (PDOS) has been computed for ${Cd}_{0.9375}{M}_{0.0625}S/Se$ compounds at their equilibrium lattice constant, and the results are presented in Figs. 5 and 6. The PDOS for both spin channels reveals that the valence band is predominantly governed by the $M$-$d$ and $X$-$p$ states with a minor contribution of $M$-$p$ states in all the compounds under investigation. It can be seen that $4d$-${e}_{g}$ minority spin states of the doped systems are shifted from higher to lower energies when passing from $Ru$ to $Pd$. Moreover, in the spin-down channel, the Fermi level is crossed by the $4d$-${e}_{g}$ and $4d$-${t}_{2g}$ states for $CdRuS/Se$ and $CdPdS/Se$, respectively. Similar patterns are noted in the case of $Fe$ and $Ni$-doped $MgS$ [69]. As depicted in Figs. 5 and 6, it is evident that there is a clear overlap between the impurity cation $M$-$4d$ states and the anion $S$-$3p/Se$-$4p$ states in the vicinity of the Fermi level. This points to a strong exchange interaction between these states, particularly between the $M$-${t}_{2g}$ and $X$-$p$ orbitals. To elaborate, the spin-up states of $M$-${t}_{2g}$ orbitals exhibit a higher degree of hybridization with the $X$-$p$ orbitals compared to the spin-down states. This hybridization is more significant when considering the situation of $PdCdS/Se$. Hence, the mechanism of $p$-$d$ exchange governs the emergence of ferromagnetism in our systems, a phenomenon analogous to the ferromagnetism found in $Pd$-doped $ZnS$ [70] and $Pd$-doped $ZnO$ [71].

Fig. 5

Partial DOSs of ${Cd}_{0.9375}{M}_{0.0625}S\;\left(M\;=\;Ru, Rh, Pd\right)$ calculated using $mBJGGA$

Fig. 6

Partial DOSs of ${Cd}_{0.9375}{M}_{0.0625}Se\;\left(M\;=\;Ru, Rh, Pd\right)$ calculated using $mBJGGA$

In our quest to visually depict the magnetic characteristics of the investigated alloys, we have chosen $CdPdS$ as a case study to analyze the spatial distribution of spin-charge density. This is illustrated in Fig. 7 where the spin density is concentrated around the $Pd$ atom and its four nearest neighboring $S$ atoms, while the remaining $S$ atoms situated farther from the $Pd{S}_{4}$ tetrahedron display negligible magnetic effects. Nevertheless, for $Pd$-doped wurtzite cadmium sulfide ${Cd}_{35}Pd{S}_{36}$ [72], it is not just the four nearest $S$ atoms that exhibit magnetic moments; the next nearest neighboring $S$ atoms also contribute to the overall magnetic properties. This suggests an extension of the magnetic orbital coupling’s influence to include the next nearest neighboring $S$ atoms to the $Pd$ atom.

Fig. 7

A 3D representation of the isosurface for the spin-charge density $(\rho\;=\;{\rho }_{{\text{up}}}-{\rho }_{{\text{down}}})$ in $CdPdS.$ The isosurface is highlighted in red, with $\rho$ value of 0.017 $e/{A}^{3}.$ The $Cd$, $Pd$, and $S$ atoms are depicted in yellow, blue, and gray, respectively

In Table 3, we have tabulated the computed total and partial magnetic moments for $CdXM$ compounds using the $mBJ$-$GGA$ method. In all cases, the global magnetic moment per $M$ atom is found to be an integer value, a characteristic often associated with $HMFs$. However, it is essential to underscore that this integer magnetic moment, by itself, does not offer conclusive confirmation of half-metallicity. This is particularly evident when we examine the cases of $Rh$-doped $CdS$ and $CdSe$, which are recognized as $FMSs$ and also exhibit integer magnetic moments. Therefore, it becomes clear that relying solely on the integer magnetic moment is insufficient to establish half-metallicity, as highlighted by other authors in earlier theoretical investigations [73, 74].

Table 3 Total and partial magnetic moments of ${Cd}_{0.9375}{M}_{0.0625}S/Se\;(M=Ru, Rh, Pd)$

Also, as demonstrated in Table 3, it is evident that as we move from ruthenium to palladium, two distinct trends emerge. Firstly, the ratio between the magnetic moment of the doping atom and the total magnetic moment decreases. Secondly, the ratio of the magnetic moment contributed by the four nearest $X$ atoms to the overall magnetic moment increases. This scenario can be attributed to the increasing hybridization between the $M$-$4d$ states and the $S$-$3p/Se$-$4p$ states, leading to the formation of covalent bonds. In this context, it is noteworthy that the $M$ atom in each ternary alloy donates two electrons in the host semiconductor to form bonds with the surrounding $X$ atoms. As a result, the electronic configurations of $Ru$, $Rh$, and $Pd$ become ${Ru}^{+2}({4d}^{6})$, ${Rh}^{+2}(4{d}^{7})$, and ${Pd}^{+2}({4d}^{8})$, respectively.

Due to Hund’s rule, the 4 $d$ orbitals of $Ru$, $Rh$, and $Pd$ in the respective compounds $CdRuS/Se$, $CdRhS/Se$, and $CdPdS/Se$ exhibit distinct spin configurations as outlined below:

• In the case of $Ru$, the $4d$ orbitals adopt the configuration ${({e}_{g}^{\uparrow })}^{2}{({e}_{g}^{\downarrow })}^{1}{({t}_{2g}^{\uparrow })}^{3}$. One of the $4d$-${e}_{g}$ states is empty, while the three spin-up electrons partially occupy the $4d$-${t}_{2g}$ states. Consequently, the $Ru$ atom contributes a magnetic moment of 4 ${\mu }_{B}$ in the $CdRuS/Se$ compound.

• For $Rh$, its $4d$ orbitals assume the configuration ${({e}_{g}^{\uparrow })}^{2}{({e}_{g}^{\downarrow })}^{2}{({t}_{2g}^{\uparrow })}^{3}$, with three spin-up electrons filling the high-lying triple degenerate ${t}_{2g}$ states. This electron arrangement results in a magnetic moment of 3 ${\mu }_{B}$ per $Rh$ atom in $CdRhS/Se$.

• In the case of $Pd$, the $4d$ orbitals have the configuration ${({e}_{g}^{\uparrow })}^{2}{({e}_{g}^{\downarrow })}^{2}{({t}_{2g}^{\uparrow })}^{3}{({t}_{2g}^{\downarrow })}^{1}$. Two of the $4d$-${t}_{2g}$ states remain unoccupied. This electron configuration gives rise to a magnetic moment of 2 ${\mu }_{B}$ per $Pd$ atom in $CdPdS/Se$.

As indicated in Table 3, the primary source of the total magnetic moment primarily originates from the $M$ element and its adjacent $X$ atoms, with a noteworthy magnetic moment also found in the interstitial region. However, the contributions from $Ru$, $Rh$, and $Pd$ atoms fall short of our prior predicted values based on Hund’s rule, which were 4, 3, and 2 ${\mu }_{B}$, respectively. This reduction can be attributed to the strong $p$-$d$ hybridization occurring between the $S$-$3p/Se$-$4p$ states and the $M$-$4d$ states.

4 Conclusion

In this study, we have explored the structural, electronic, and magnetic properties of $CdMS/Se$ alloys (where $M$ = $Ru$, $Rh$, and $Pd$) through ab-initio calculations employing the $FP$-$LAPW$ method. The $mBJGGA$ functional was chosen to assess electronic and magnetic traits, using equilibrium lattice parameters initially estimated with $PBE$-$GGA$. Across all doped systems, it was found that the ferromagnetic state is the most energetically favorable configuration. In terms of electronic characteristics, $CdRhS/Se$ materials were identified as ferromagnetic semiconductors, while $CdRuS/Se$ and $CdPdS/Se$ exhibited a half-metallic ferromagnetic behavior, featuring 100% spin polarization at the Fermi level. Interestingly, we have demonstrated the achievement of stable ferromagnetism with integer total magnetic moment values of 4, 3, and 2 ${\mu }_{B}$ in $Ru$, $Rh$, and $Pd$-doped $CdX$ systems, respectively. The predominant source of these magnetic moments is the doping atom and its four closest neighboring X atoms. The origin of the ferromagnetism in these compounds can be attributed to the robust $p$-$d$ hybridization occurring between the states of the host $X$ ions and the $M$ impurity ion. Given the absence of a magnetic element, $Ru/Rh/Pd$-doped $CdS/Se$ appears to be promising dilute magnetic semiconductors, free from magnetic precipitate and may hold potential applications in the field of spintronics.