https://doi.org/10.52131/jmps.2022.0301.0023 22 Journal of Materials and Physical Sciences Volume 3, Number 1, 2022, Pages 22 - 28 Journal Homepage: https://journals.internationalrasd.org/index.php/jmps Theoretical Investigation of Ferromagnetism and Optical Properties of CuCr2X4 (X = S, Se) Spinels via Ab-initio Calculations Q. Mahmood1*, Jameelah Alzahrani1, T. Ghrib1 1 Department of physics, College of Science, Imam Abdulrahman Bin Faisal University, P.O. Box 1982, 31441, City Dammam, Saudi Arabia ARTICLE INFO ABSTRACT Article History: Received: March 03, 2022 Revised: April 28, 2022 Accepted: June 29, 2022 Available Online: June 30, 2022 The spintronics technology improve the spin functionality which captivated the existence of ferromagnetism. The control of magnetic properties by electrons spin and transport effect have been illustrated in CuCr2X4 (X = S, Se) spinels DFT through Wien2k and BoltztraP codes. The negative formation of energy established the thermodynamic stability of the examined spinels. The half metallic ferromagnetism in the analyzed spinel’s assures density of states. Magnetic moment (Integer value) and the insulating nature with down spin is the reaction of 100% spin polarization. The Δ(𝑑)>(Δ𝐶𝐹) and negative Δ(𝑝𝑑) attainment of the condition have presented the prevailing part of electrons spin to create ferromagnetism. Keywords: Density Functional Theory Electronic Characteristics Magnetic Properties Crystal Field Energy © 2022 The Authors, Published by iRASD. This is an Open Access article under the Creative Common Attribution Non-Commercial 4.0 *Corresponding Author’s Email: qmmustafa@iau.edu.sa 1. Introduction The half metallic ferromagnetism has been a theme of intense attention due to inherent technologically usage in significant spintronic, ferroelectric, and ferromagnetic applications displaying in spinels (Lunkenheimer, Fichtl, Hemberger, Tsurkan, & Loidl, 2005; Mahmood et al., 2020; C. Sun et al., 2010). Researchers have fascinated in view of the attention of CMR (Colossal Maneto-resistance) between studied spinels due to transition metal ferro-spinels among these spinels (Baltzer, Wojtowicz, Robbins, & Lopatin, 1966; von Helmolt, Wecker, Holzapfel, Schultz, & Samwer, 1993). CdCr2S4 and CdCr2Se4 are technically the two vital transition of temperatures at 84.5K and 129.5K separately in ferromagnetic semiconductors (Hemberger et al., 2005). In these type of materials S ions (in CdCr2S4) or six Se ions (in CdCr2Se4) forms the surrounding and crystallize in cubic spinel structure. In ferro-magnets, electrostriction has been discovered for it (Lunkenheimer et al., 2005; C. P. Sun et al., 2010). By using electric field CMR may be stimulated in these spinels as it has been reported besides it (C. Sun et al., 2010). Magnetic properties of such materials has extended the significance by application view point in the study of field induced electrical characteristics (Kim, Myung, Yoon, Kang, & Sun, 2004). CuCr2S4 has been investigated by Wustrow et al investigated to exploit CuCr2S couple at high voltage which belongs to Cu thiospinels family (Wustrow et al., 2018). In this presumed research work CuCr2S4 comprises of the synthesis, structural and electrochemical examinations.CuCr2S4 testified studies displays that stable compound with normal distribution of cations indicates that compound is stable (Zhang, Stevanović, d’Avezac, Lany, & Zunger, 2012). Pyrochlore lattice created at tetrahedral positions by the combination of Cr ions in which antiferromagnetic interaction among closest neighbors that restricts the spin alignment as well as magnetic prevention (Anderson, 1956). Though, the SOC effect reduces the ferromagnetism by producing balance states and least free energy, but this energy simultaneously helps the magnetic ordering. The least energy creates net magnetic ordering in it. Particularly magnetic frustrations due to Cr bonded by tetragonal contraction which surprised by creating it valuable contender in spintronics and other electronic devices by ZnCr2O4 and CdCr2O4 (Dutton, Huang, Tchernyshyov, Broholm, & https://journals.internationalrasd.org/index.php/jmps mailto:qmmustafa@iau.edu.sa Q. Mahmood, Jameelah Alzahrani, T. Ghrib 23 Cava, 2011; Kumar, Fennie, & Rabe, 2012; Tran & Blaha, 2009). The MgCr2O4 and ZnCr2O4 studied ensure their sensitivity to ferromagnetism. Instead of limiting literature the ferromagnetic ordering and high magnetic moment had been explored in CuCr2X4 (X = S, Se). Furthermore, the insulting band gaps 0.938 eV and 0.638 eV for CuCr2S4 and CuCr2Se4 also reported which make them significant materials for transport applications (Madsen & Singh, 2006). The literature analysis about these materials show the experimental research work is very limiting on CuCr2Se4 but few theoretical reports exist on CuCr2X4 (X=S, Se) which support to analyze them for spintronic applications. Therefore, in the view of above discussion, the theoretical studies of transport and magnetic behaviors of CuCr2X4 (X=S, Se) have been incorporated in this article. For this task, the DFT based Wien2K code, and BoltzTraP code has been practiced exploring the structures of studied spinels (Perdew et al., 2008). These exact band gap structures are run for the transport analysis by BoltzTraP code (Tran, Blaha, & Schwarz, 2007). The existence of structures of spinels reveals their diverse applications in the field of spintronic. Therefore, the results are discussed step by step below for the complete of the studied spinels. 2. Method of Calculation The thiospinels CuCr2X4 (X=S, Se) magnetism and transport characteristics have been done by FP-L(APW+lo) method through the Wien2K code. The structural analysis and ground state study has been done by PBE-GGA (Koller, Tran, & Blaha, 2011). The optimizations of studied structures done until the all the strain forces becomes zero. In addition, for true electronic structures and band gap analysis, the TB-mBJ has been done through exchange and correlation configuration. The TB-mBJ improve the band gaps this high precision and less time (Blaha, Schwarz, Madsen, Kvasnicka, & Luitz, 2001; Rashid et al., 2019; Scheidemantel, Ambrosch-Draxl, Thonhauser, Badding, & Sofo, 2003). By using TB-mBJ exchange potential results achieved from thermoelectric as well as electronic band structures conveyed. The K-mesh of order 12 × 12 × 12 have been selected in first Brillion zone. Furthermore, the product RMT×Kmax= 8, Gmax = 16 and lmax are adjusted in the in put of the software. 3. Analysis Section 3.1. Electronic Characteristics The spinel's CuCr2X4 (X=S, Se) with cubic structure and and space group Fd- 3m#227 are optimized to in ferromagnetic state and compared its energy released with nonmagnetic state. The energy is taken the default units (Ry) in both the FM and NM states. The relative investigation depicts that the more energy released in FM state than NM states, which approve the FM state is much stable than the NM states. The thermodynamic stability of the deliberate spinel's, and also associated with the enthalpy formation which has been computed and reported in the Table 1.The thermodynamic stability guarantees the negative establishment of energy that declines from -1.46 eV to - 0.34 eV as S is changed with Se. The stability, decreasing trend as we go down the group the exit of energy lessens by the substitution of S with Se. When structures optimized the lattice constantsa0 (Å) by Murnaghan equation of states and shown in Table 1. Bulk modulus decreases by increasing the S/Se size and distance among atoms whereas the lattice constant increase from CuCr2S4 to CuCr2Se4. The computed magnetic and electronic and electronic characteristics are illustrated to see the effect of electrons spin. Thorough explanation of band structures (BS) is essential to recognize the electronic behavior. Hence, the examined compounds are plotted in Fig.2. For the computation of band structures. At Γ- symmetry point direction the valence band maxima exist, and conduction band minima exists at Χ direction having EF on VB in up spin (↑) which depict the indirect band gap. Journal of Materials and Physical Sciences 3(1), 2022 24 Figure 1: Optimized Energy Versus Volume Plots of (a) CuCr2S4, and (b) CuCr2Se4 in FM and NM States Figure 2: The Band Structures for Spin Up and Spin Down of (a, b) CuCr2S4 and (c, d) CuCr2Se4 While in down spin (↓) medium, both VBM and CBM exist at the Γ direction having Fermi level inside them which persuades the insulting gap because of exchange mode. Hence, the formation of ferromagnetic semiconductors results as the incorporation of up spin (↑) and down spin (↓) medium by insulting properties. Q. Mahmood, Jameelah Alzahrani, T. Ghrib 25 Table 1 The calculated lattice constant a0 (Å), bulk modulus B0 (GPa), Ground state energy difference (ΔE = ENM-EFM), enthalpy of formation ∆H(eV) for CuCr2X4 (X = S, Se, Te). aRef (Tran & Blaha, 2009), Ref (Mahmood, Hassan, et al., 2019)b The density of states (DOS) shows identical functioning and shown in Figs.3 The 𝑆𝑃 = 𝑁↓−𝑁↑ 𝑁↓+𝑁↑ 𝑋100 is the equation computed for spin polarization in which N↑ showing the total density of states in the up-spin mode while N↓ is the total density of states in the down spin mode? Densities of states exist at Fermi level in up spin (↑) mode however energy gaps are forbidden inside the Fermi level. Consequently, SP has been found hundred percent (Choi, Shim, & Min, 2006; Walsh et al., 2007). The SP can be maintained by the integer value of total MM of the studied compounds is 100% as presented in Table 2. Partial density of states (PDOS) Cu, Cr and S/Se demonstrates further the exchange mechanism and ferromagnetism and are examined thoroughly as shown in Fig.3. The hybridize in the energy interval -4.0 to -0.5 eV between 3d states of Cr/Cu and O-2p states exist near EF in up spinel mode. Whereas in down spin mode the range is from -3.0 to -1.0 eV for Cr-3d states, Cu-3d and S-3p states. Moreover, in the hybridization range for Cr-3d states, Cu-3d states and S-3p states in the conduction band in the range of 1.5 to 2.4 eV and 2 to 3.2 eV for spin up and down modes. Consequently, ferromagnetic semiconducting nature, generated by the interaction inside the valence band and separating of states in the down spin mode. Figure 3: The total and Partial DOS for spin up and spin down of (a, b) CuCr2S4 and (c, d) CuCr2Se4 Compound a0 (Å) B0(GPa) ∆E (eV) ∆H(eV) CuCr2S4 10.22 82.74 5.74 -1.46 Exp. 10.24a, 10.1b CuCr2Se4 10.76 65.35 6.74 -0.84 Exp. ----- Journal of Materials and Physical Sciences 3(1), 2022 26 Table 2 The Total and The Local Magnetic Moments (in Bohr Magneton) Calculated for MgCr2X4 (X = S, Se, Te) Total (µB) Int. ( µB) Mg (µB) Cr (µB) (XµB) CuCr2S4 3.0000 0.43 0.006 3.02 -0.06 CuCr2Se4 3.0000 0.54 0.002 3.05 -0.09 3.2. Magnetic Properties The materials structures elaborated in this material generates crystal field and exchange energies by hybridization in distinct states. Tetrahedral arrangement of S/Se atoms effect the Cu site with valency +2, whereas Cr site having +3 valency is captured by the octahedron of S/Se atoms. The repulsive effect of 3d-Cr creates the octahedral of S/Se which in the near octahedron is powerful and weaker as move away. The increasing energy eg of states as associated to t2g states that extend the octahedron medium of S/Se atoms separate the 3d- Cr into high energy (eg) and low energy (t2g) (Kumar et al., 2012; Mahmood, Rashid, et al., 2019) [30]. Energies of the crystal field energies in both spin modes described by )( 2  −= ggCF et and )( 2  −= ggCF et are shown in Table 3.Furthermore the correlation of crystal energy with the exchange separating of 3d states of Cr determined by the relation ))(  −= dd d Ferromagnetism domination results in the larger value of exchange energy besides the crystal field energy. By the measurement of indirect exchange energy )( pd another kind of energy is produced by 3d states of Cr and p states of S/Se. Lower energy support ferromagnetism when )( pd is negative. CuCr2S4 to CuCr2Se4 the value of )( pd and )(d increases presented in Table 3 where CF decreases that clearly indicates that later one is more promising for ferromagnetism. Ferromagnetism can be elaborated by exchange constant that calculated by the relations = SxEN C  0 and , 0 = SxEN V  where )(  −= VVV EEE and )(  −= CCC EEE and the energies at valence band as well as on conduction bands, where x is the absorption of Cr and S is MM of Cr atom. In usual cases the 0 ( )N  retain positive values and )( 0 N negative. Therefore, the similar effect of studied FM has been seen in Table 3. Table 3 The calculated values spin down gap (Eg (eV)), crystal field energy (ΔEcrystal), direct exchange Δx(d) and indirect exchange Δx(pd) and the exchange constants (Noα and Noβ) for CuCr2X4 (X = S, Se, Te). Compounds Eg (ΔEcrystal) Δx(d) Δx(pd) Noα Noβ CuCr2S4 1.45 3.70 3.98 -0.20 0.33 -0.14 CuCr2Se4 0.85 2.94 4.10 -0.25 0.52 -0.16 Zenger’s exchange model supports the attraction of down spin mode whose energy reduces and shows the magnetic impurity operated have negative value )( 0 N (Hassan, Arshad, & Mahmood, 2017; Kant, Deisenhofer, Tsurkan, & Loidl, 2010; Mahmood, Yaseen, Haq, Laref, & Nazir, 2019). Therefore, the source of ferromagnetism confirm that this is due to exchange energies. The examined compounds of magnetic moments and partial MM are reported in Table 2. The transporting of magnetic moment towards nonmagnetic sites indicates that the exchange interaction Cr-3d states and S/Se p states causes the decrease of magnetic moment of Cr. Because of unlike exchanges included in the structures may be due to transition of MM from magnetic to nonmagnetic sites. 4. Conclusion In short, the present article, ensure the detailed analysis of electronic and magnetic characteristics of CuCr2X4 (X=S, Se) by Wien2k code. The examined compounds are ferromagnetic semiconductors, that validates the electronic band structures and density of Q. Mahmood, Jameelah Alzahrani, T. Ghrib 27 states. The optimization analysis confirms the more energy release in FM states than in NM states ensures the stability of FM states. The FM is elaborated in terms of electrons spin which show strong hybridization. The FM is favorable because Δ(𝑑) has higher values as compared to (Δ𝐶𝐹). The energy decreases in down spin mode have -Ve value of pd- exchange energy which is also the justification of FM and electrons spin. The p-d hybridization/exchange interaction is due to the growth of μCr and shifting of MM on nonmagnetic sits. Therefore, the complete analysis of magnetic characteristics ensures importance of studied materials for spintronic applications. 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