KKR-CPA Study of the Electronic and Magnetic Properties of Transition Metal-Doped AgZnF₃ Perovskites

Abstract

In this work, the electronic, structural, and magnetic properties of Ti-, V-, Cr-, Mn-, and Ni-doped AgZnF₃ perovskites are systematically investigated using the Korringa–Kohn–Rostoker method combined with the coherent potential approximation (KKR-CPA) within the generalized gradient approximation (GGA). Transition metal dopants (Ti and V) at a concentration of 5% substituting the Zn site introduce 3d states that cross the Fermi level in the majority-spin channel, resulting in half-metallic behavior. Ferromagnetic stability is predicted for Ti-, V-, Cr-, and Mn-doped AgZnF₃ at a doping concentration of 5%. The TM-doped AgZnF₃ alloys exhibit noticeable variations in exchange splitting between the t₂g and e_g states of the TM-3d orbitals. In Ti-doped AgZnF₃, the calculated spin magnetic moments follow the expected trend based on crystal-field splitting theory. Furthermore, a clear correlation is observed between the nature of the transition metal dopant (Ti, V, Cr, Mn, and Ni) and the total magnetic moment of the system.

1. Introduction

Perovskite materials have attracted considerable attention in recent years due to their versatile crystal structure and remarkable physical properties. The perovskite family includes a wide range of compounds that share a crystal structure similar to that of the mineral perovskite. Owing to their structural flexibility, these materials exhibit a variety of interesting electrical, optical, and magnetic properties, making them promising candidates for numerous applications in materials science, energy technologies, and electronic devices [1,2,3,4,5]. Perovskites have a kind of structure that is crystal-like. This structure is made up of metal atoms in the middle. These metal atoms are arranged in a cubic shape. The metal atoms are surrounded by atoms that are not metals called non-metal atoms. Perovskites are really interesting because of this structure [6,7], such as the chemical structure of the ABC₃-type [8,9]. Atoms A and B behave like they have a charge because of the way they attract electrons. This is different from atom C, which behaves like it has a charge. Perovskites have an arrangement of atoms that makes them very interesting. The way the atoms are arranged in perovskites gives us a lot of options for what elements we can use in the A and B spots. This means perovskites can have a lot of properties. Perovskites have some interesting properties that can be changed in big ways by doping. This means that doping can affect how perovskites work with light and how well they conduct electricity and the energy levels of their electrons. So, it is very important to understand what happens to perovskites when they are doped. This is because perovskites could be used in a lot of technologies. When perovskites are doped, they become useful materials. They have some properties that have made a lot of people want to study them. People are working hard to find ways to use doped perovskites, in electronic devices [10,11]. Considerable research has focused on the electronic and magnetic characteristics of metal perovskites containing inorganic metal cations [12,13]. Well known for their intriguing optical, electronic, and magnetic properties [14,15], perovskites find extensive use in several fields [16,17,18,19].

Doping materials, particularly perovskites, can induce substantial changes in their properties, including alterations in their electronic, magnetic, and optical properties, as well as in their crystal arrangement [20,21,22,23]. To really get a handle on how semiconductor materials behave, we need to make it clear that density functional theory, or DFT for short, is ideal. DFT approaches are key to figuring out the density of states in semiconductor materials [24,25,26,27]. They also help us understand the properties of semiconductor materials and the magnetic properties of semiconductor materials. Semiconductor materials are pretty interesting. We can learn a lot about them by using DFT approaches to study semiconductor materials [28,29,30,31].

Perovskite materials have recently attracted increasing attention due to their remarkable electrical, dielectric, and magnetic properties, which make them promising candidates for a wide range of technological applications, including spintronics and multifunctional devices. Significant progress has been achieved in understanding and tailoring these properties through compositional engineering and transition metal doping. In this context, recent comprehensive reviews have highlighted the crucial role of structural flexibility and electronic correlations in governing the magnetic behavior of perovskite systems. In particular, Tayari et al. [32] provided an extensive overview of recent advances in perovskite materials, emphasizing the interplay between electrical, dielectric, and magnetic properties and the importance of first-principles approaches in predicting and optimizing these characteristics. Motivated by these developments, the present work focuses on the magnetic and electronic properties of transition metal-doped AgZnF₃ perovskites using a KKR-CPA first-principles framework.

Many transition elements can be incorporated into AgZnF₃ compounds, which belong to the halide perovskite family [33,34]. Owing to their remarkable optical, electronic, and structural characteristics, these materials have attracted considerable research interest [35,36]. Their stability is supported by experimental evidence showing that they crystallize in a cubic structure that remains unaffected by variations in temperature and pressure [37,38,39]. This robustness opens new avenues for investigating fundamental physical phenomena and uncovering unexpected behaviors. Furthermore, doping strategies can be employed to tailor key properties of perovskite materials, including electrical conductivity and band gap.

The interesting thing about perovskites is that doping perovskites is currently being investigated by researchers. They are interested in knowing the effects that can be achieved by doping perovskites. They are also interested in knowing the methods by which these effects can be managed within perovskites. This is quite helpful for discovering applications for perovskites as well as improving perovskites.

Despite the growing interest in fluoroperovskites, the magnetic properties of transition metal-doped AgZnF₃ remain largely unexplored from a first-principles perspective. In this work, we present a systematic KKR-CPA investigation of the electronic and magnetic properties of AgZn_1-xTM_xF₃ (TM = Ti, V, Cr, Mn, and Ni). The main objective is to clarify the role of transition metal substitution in generating magnetic moments and to analyze the correlation between crystal-field splitting, exchange interaction, and spin polarization. This study provides new insight into the design of fluoroperovskite-based magnetic materials for potential spintronic applications.

This particular project aims at synthesizing a perovskite of a certain type named perovskite AgZn_1−xTM_xF₃ alloy. The perovskite AgZn_1−xTM_xF₃ alloy makes use of transition metals, including Ti, V, Cr, Mn, and Ni. The individuals working on this particular project are attempting to synthesize perovskites with transition metals, which are perovskites as well, and are analyzing what happens as a result of this attempt. They use a technique named DFT, which allows them to analyze how a certain amount of transition metals affects the formation of a certain structure of electrons and the magnetic properties of AgZnF₃ perovskites. The addition of transition metals into perovskites makes them possess some fascinating magnetic properties. The perovskites with transition metals possess certain moments that belong to different electronic bands in perovskites. The particular class of alloys provides a very useful platform that allows them to explore ferromagnetic properties as well as different magnetic properties, including itinerant and localized magnetic properties. The parallel alignment of magnetic moments in ferromagnetic structures gives rise to complex exchange interactions, resulting in a wide range of magnetic properties in this class of compounds.

2. Model and Method

The ferromagnetic properties of AgZnF₃ doped with Ti, V, Cr, Mn, and Ni were investigated using the Korringa–Kohn–Rostoker (KKR) method combined with the coherent potential approximation (CPA) within the framework of density functional theory (DFT) [40]. Exchange–correlation effects were treated using the generalized gradient approximation (GGA) [41,42,43,44], which accounts for both the local electron density and contributions from neighboring regions. All calculations were performed within the DFT–CPA formalism. Within the CPA framework, the disordered alloy system is described by a set of effective sites characterized by a common coherent potential, with an appropriate ε(CPA) energy assigned to each site. The CPA approach is particularly suitable for describing substitutional disorder in diluted magnetic systems. Instead of modeling a specific atomic configuration as in supercell calculations, CPA provides configurationally averaged electronic and magnetic properties that represent a random distribution of dopant atoms in the lattice [45,46]. This approach has been widely used to study transition metal-doped semiconductors and perovskites, where the magnetic behavior arises from the averaged interaction between localized TM-3d states and the host electronic bands.

The Green’s functions and density of states (DOS) were evaluated using a mean-field approximation for the effective sites [47,48], enabling an efficient solution of the Kohn–Sham equations within DFT. Computational modeling was carried out using Akai’s MACHIKANEYAMA-2002 (V09) package [49] to investigate the AgZn_0.95TM_0.05F₃ (TM = Ti, V, Cr, Mn, and Ni) alloy system. In the electronic structure calculations performed with the Akai-KKR code, Green’s functions were evaluated within the GGA framework. This approach provides a flexible and reliable means of analyzing the effects of chemical disorder, including cation and anion vacancies, on the electronic and magnetic properties of the material. Furthermore, it enables precise control over the dopant concentration in the host lattice, which is essential for tailoring the resulting material properties [47].

The substitutional doping in AgZn_1−xTM_xF₃ (TM = Ti, V, Cr, Mn, and Ni) was implemented using the CPA within the KKR formalism. A doping concentration of x = 0.05 was introduced by treating the Zn sublattice as a random alloy consisting of 95% Zn atoms and 5% TM atoms. In this approach, each Zn site is represented by an effective coherent medium that statistically accounts for the presence of both Zn and TM atoms, allowing an accurate description of substitutional disorder without imposing artificial periodicity. Given the dilute doping level and the focus on configurationally averaged electronic and magnetic properties, no explicit supercell calculations were performed to validate the CPA assumptions.

The KKR-CPA was employed to study the system. Within this framework, the atomic sphere approximation (ASA) was adopted, which is justified by a volume-filling ratio exceeding 95%, ensuring the validity of the approximation for the present system.

The atomic sphere radii were systematically tested to evaluate their influence on the results. It was found that small variations in the atomic sphere radii do not significantly affect the magnetic or electronic properties obtained within the KKR-CPA framework.

All KKR-CPA calculations were carried out until self-consistency in total energy was achieved, with a convergence criterion better than 10⁻⁵ Ry, ensuring high numerical accuracy. The Brillouin zone was sampled using a dense Monkhorst–Pack scheme with 1000 k-points to guarantee reliable results. Scalar relativistic effects were included in the calculations, and the potential was expanded in real spherical harmonics up to an angular momentum cutoff of ℓ_max = 2 at each atomic site, allowing for an accurate treatment of both the Brillouin zone and the atomic environments.

Exchange–correlation effects were described within the generalized gradient approximation (GGA), using the Perdew–Wang parameterization (GGA91), as implemented in the Akai-KKR code. This methodological approach enables precise control of the doping concentration and provides the flexibility to investigate structural modifications, including the effects of anion and cation vacancies, on the electronic and magnetic properties of the system [47].

The perovskite compound (ABX₃) has a cubic crystal structure in the space group of Pm$\overline{3}$m, as in zinc blende (no. 221). This work is based on the pure and doped AgZnF₃ compounds by (TM = Ti, V, Cr, Mn, and Ni), collectively denoted as (ABX₃ = AgZnF₃), with lattice parameters of a₀ = b₀ = c₀ = 3.972 Å [50], with α = β = γ = 90° [50]. The AgZnF₃ compound has an ordered filled octahedral configuration of the A (Ag), B (Zn), and X (F) atoms in an fcc lattice with three atoms (Figure 1). Their corresponding Wyckoff positions in AgZnF₃ are (0, 0, 0), (0.5, 0.5, 0.5), and (0, 0.5, 0.5). We studied the pure compound and the doped samples with Ti, V, Cr, Mn, and Ni atoms at a concentration of 5% in the Zn position for the calculations [37].

The DOS of TM alloys with larger dimensions is calculated using the Green’s function formalism within the KKR-CPA framework. Compared with the LDA, the GGA offers a significantly more reliable description of the ground state properties of atoms, molecules, and light elements. In this work, the GGA scheme corresponds to the Perdew–Wang functional (GGA91), which is well known for its improved accuracy in predicting structural and electronic properties [31,51]. According to the DOS shown in Figure 2, AgZnF₃ exhibits a total spin magnetic moment of zero, as evidenced by the symmetry between the majority and minority spin bands, indicating a non-magnetic ground state.

3. Results and Discussion

As shown in Figure 3, the magnetic moments mainly originate from the 3d orbitals of the transition metals, namely titanium, vanadium, chromium, manganese, and nickel. These transition metals play a crucial role in determining the magnetic behavior of the system through their contribution to the local magnetic moments.

In the pristine AgZnF₃ compound, the electronic structure is spin symmetric, leading to a non-magnetic ground state. However, when Zn atoms are substituted by transition metals, partially filled 3d orbitals are introduced into the system. These 3d states interact with the surrounding fluorine 2p orbitals and create spin-polarized electronic states near the Fermi level. As a result, local magnetic moments develop on the transition metal atoms and induce ferromagnetic ordering in the doped systems.

In Figure 3a, the electronic configuration closely resembles that expected for a Ti²⁺ ion. In this case, two electrons occupy the spin-up t_2g states above the Fermi level, which is characteristic of half-metallic behavior in transition metal-based systems. This indicates that titanium significantly contributes to the observed magnetic moment. As illustrated in Figure 3b, the electronic configuration is consistent with a V²⁺ charge state, where three electrons occupy the spin-up t_2g⁺ states above the Fermi level. For the AgZn_0.95Cr_0.05F₃ alloy, ferromagnetic behavior is predicted, as the spin-up e_g⁺ states lie close to the Fermi energy. In this configuration, three electrons occupy the t_2g⁺ states, while the remaining electron occupies the e_g⁺ state, as shown in Figure 3c.

As illustrated in Figure 3d, the supposed charge state of the AgZn_0.95Mn_0.05F₃ alloy is Mn^2+, in which three electrons will be found in t_2g⁺, where two electrons are occupied e_g⁺ above the Fermi level, which is adequate for ferromagnetic stability. In the AgZn_0.95Ni_0.05F₃ system, the ferromagnetic behavior is further supported by the difference between the disordered local moment energy (E_DLM) and ferromagnetic energy (E_ferro), as expressed by the equation: ΔE = E_DLM − E_ferro where ΔE represents the total energy difference. The total energy differential (ΔE), or the difference between the E_Ferro and the E_DLM, can be computed to assess the magnetic stabilization of the AgZn_0.95Ni_0.05F₃ alloy and confirm the ferromagnetic stability. Since ΔE > 0, the alloy AgZn_0.95Ni_0.05F₃ is in a ferromagnetic (FM) state, according to the value that was found. It is predicted that this behavior, as shown in Figure 3e, is the result of the hybridization of the Ni-3d and F-3p orbitals, suggesting an indirect coupling [52].

The substitution of Zn by transition metal atoms (Ti, V, Cr, Mn, and Ni) modifies the local electronic structure of the AgZnF₃ lattice. In the cubic perovskite environment, the 3d orbitals of the transition metal split into t2g and eg states due to the crystal field created by the surrounding fluorine octahedron. The calculated density of states indicates that these TM-3d states strongly hybridize with the F-2p orbitals near the Fermi level. This hybridization induces exchange splitting between the spin-up and spin-down channels, which leads to the formation of local magnetic moments on the transition metal sites [53]. As the number of 3d electrons increases from Ti to Mn, the magnetic moment increases accordingly, following the crystal-field splitting mechanism typical of transition metal-doped perovskites.

The origin of ferromagnetism induced by transition metal substitution at the Zn site in AgZnF₃ can be understood within the framework of diluted magnetic semiconductors, as extensively discussed in the literature for Zn-based compounds. When a transition metal (TM) replaces Zn, localized TM-3d states are introduced inside or close to the host electronic bands, giving rise to strong exchange interactions with the anion p states. Sato and Katayama-Yoshida [53] demonstrated through ab initio calculations that ferromagnetism in ZnO-, ZnS-, ZnSe-, and ZnTe-based systems originates from the exchange coupling between localized TM-3d electrons and the surrounding anion p orbitals, leading to carrier-mediated or double-exchange-like magnetic interactions depending on the dopant electronic configuration and concentration. A similar mechanism is observed in the present AgZn_0.95TM_0.05F₃ alloys, where a pronounced hybridization between TM-3d and F-3p states near the Fermi level is evidenced by the calculated density of states, resulting in spin polarization and ferromagnetic stabilization.

In addition, Pham et al. [54] reported that ferromagnetism in ZnO:Co systems can be reinforced by indirect exchange mechanisms mediated by anion bridges, such as Co–O–Co complexes, particularly in the presence of defects. Although explicit defect states are not considered in the present work, the KKR-CPA approach inherently accounts for chemical disorder at finite dopant concentrations. The observed exchange splitting and positive magnetic stabilization energy in TM-doped AgZnF₃ suggest that an indirect p–d exchange mechanism mediated by F-3p orbitals plays a dominant role in establishing long-range ferromagnetic ordering, in close analogy with previously reported Zn-based diluted magnetic semiconductors.

To further clarify the nature of the magnetic interactions in AgZn_0.95Ni_0.05F₃, we analyze the projected density of states (PDOS) of the Ni-3d and F-2p orbitals. As shown in the PDOS results, a pronounced overlap between Ni-3d and F-2p states is observed in the energy range extending from approximately −0.3 Ry up to the Fermi level. This energy overlap provides clear evidence of strong hybridization between these orbitals. The hybridization leads to a redistribution of electronic states near the Fermi level, which plays a crucial role in mediating the indirect exchange interaction between localized Ni magnetic moments through the fluorine anions. Consequently, this Ni-3d–F-2p hybridization contributes significantly to the stabilization of the ferromagnetic ground state in the Ni-doped AgZnF₃ system. These results confirm that the magnetic behavior of AgZn_0.95Ni_0.05F₃ is governed by orbital hybridization effects rather than purely localized Ni-3d states.

Notably, interestingly, Figure 4 shows a notable variance in the exchange splitting ${∆}_{\mathrm{E}\mathrm{x}}^{Ni}$ of Ni-3d with relation to (t_2g⁺, e_g⁺) in comparison to Ti, V, Cr, up and spin-down electrons, exceeding ${∆}_{\mathrm{E}\mathrm{x}}^{Ti}$, ${∆}_{\mathrm{E}\mathrm{x}}^V$, ${∆}_{\mathrm{E}\mathrm{x}}^{Cr}$, and ${∆}_{\mathrm{E}\mathrm{x}}^{Ni}$ thereby permitting nearly full spin polarization of the current. These findings collectively demonstrate that the magnetic and electronic properties of AgZnF₃-based compounds can be effectively tuned through targeted transition metal doping. Each dopant introduces distinct magnetic configurations and spin splitting patterns, which opens promising avenues for the design of spintronic and magneto-optoelectronic materials.

To sum up, the elements Ti, V, Cr, Mn, and Ni are considered as potential possibilities in the field of magnetism and play important roles in it. Some observations about the doped elements included here are worth mentioning. In particular, the transition metals’ spin moment trend is in line with the crystal-field splitting prediction (see Figure 5). That is to say, the magnetic moment follows the sequence $\Vert M^{Ti}\Vert <\Vert M^{Ni}\Vert <\Vert M^V\Vert <\Vert M^{Cr}\Vert <\Vert M^{Mn}\Vert$.

Furthermore, a correlation between Ti, V, Cr, Mn, and Ni may be seen in their total magnetic moments $\Vert M^{Tot}\Vert$ with the trend being $\Vert M_{{\mathrm{A}\mathrm{g}\mathrm{Z}\mathrm{n}}_{0.95}{Ti}_{0.05}{F}_3}^{Tot}\Vert <\Vert M_{{\mathrm{A}\mathrm{g}\mathrm{Z}\mathrm{n}}_{0.95}{Ni}_{0.05}{F}_3}^{Tot}\Vert <\Vert M_{{\mathrm{A}\mathrm{g}\mathrm{Z}\mathrm{n}}_{0.95}{V}_{0.05}{F}_3}^{Tot}\Vert <\Vert M_{{\mathrm{A}\mathrm{g}\mathrm{Z}\mathrm{n}}_{0.95}{Cr}_{0.05}{F}_3}^{Tot}\Vert <\Vert M_{{\mathrm{A}\mathrm{g}\mathrm{Z}\mathrm{n}}_{0.95}{Mn}_{0.05}{F}_3}^{Tot}\Vert$ as showed in

Table 1. Moments of AgZn_0.95TM_0.05F₃ in µ_B.

	$\Vert {\mathit{M}}^{\mathit{T}\mathit{o}\mathit{t}}\Vert$	$\Vert {\mathit{M}}^{\mathit{A}\mathit{g}}\Vert$	$\Vert {\mathit{M}}^{\mathit{Z}\mathit{n}}\Vert$	$\Vert {\mathit{M}}^{\mathit{T}\mathit{M}}\Vert$	$\Vert {\mathit{M}}^{\mathit{F}}\Vert$
AgZnF3	0.0000	0.00000	0.00000	-	0.00000
AgZn0.95Ti0.05F3	0.0569	0.00185	0.00039	0.76864	0.00014
AgZn0.95V0.05F3	0.1121	0.00097	0.00016	1.89319	0.00042
AgZn0.95Cr0.05F3	0.1636	0.00128	0.00032	2.87408	0.00060
AgZn0.95Mn0.05F3	0.2361	0.00335	0.00081	3.94794	0.00410
AgZn0.95Ni0.05F3	0.1001	0.00008	0.00223	1.54726	0.00660

. Comparably, in AgZn_0.95TM_0.05F₃ alloys, the crystal-field splitting (t_2g, e_g) shows the following trend among the doped elements: ${\mathsf{\Delta }}_{(t_{2g},e_g)}^{Ti}<{\mathsf{\Delta }}_{(t_{2g},e_g)}^{Ni}<{\mathsf{\Delta }}_{(t_{2g},e_g)}^V<{\mathsf{\Delta }}_{(t_{2g},e_g)}^{Cr}<{\mathsf{\Delta }}_{(t_{2g},e_g)}^{Mn}$. As Figure 6 illustrates, increasing the concentration also raises the magnetic moment. A double-exchange magnetic coupling can be expected based on the doping of AgZnF₃ with those elements at concentrations of 5%, 6%, 8%, and 10%, respectively (Figure 7). This behavior shows the transition metal TM-3d band at different doping concentrations and exhibits a significant drop in the DOS of the (3d) band. Notably, the band widens and its amplitude decreases with increasing doping concentration. This characteristic could be explained by double-exchange magnetic coupling (see Figure 7).

4. Conclusions

The electronic and magnetic properties of the AgZn_0.95TM_0.05F₃ alloys (TM = Ti, V, Cr, Mn, and Ni) were systematically investigated using the Korringa–Kohn–Rostoker method combined with the coherent potential approximation (KKR-CPA). The calculated magnetic moments indicate that the transition metal dopants (Ti, V, Cr, Mn, and Ni) contribute dominantly to the total magnetization, exhibiting significantly larger magnetic moments than those of the host Ag, Zn, and F atoms. Among the investigated systems, the AgZn_0.95Ti_0.05F₃ and AgZn_0.95V_0.05F₃ alloys exhibit clear ferromagnetic behavior. In particular, the Ti-doped compound displays half-metallic character, characterized by a fully spin-polarized Ti-3d state in the vicinity of the Fermi level. The electronic configuration of AgZn_0.95Ti_0.05F₃ is consistent with a Ti²⁺ charge state, where two electrons occupy the majority-spin t₂g⁺ orbitals above the Fermi level. Similarly, the AgZn_0.95V_0.05F₃ alloy is well described by a V²⁺ charge state, with three electrons occupying the majority-spin t₂g⁺ orbitals above the Fermi level. Overall, the evolution of the magnetic moments across the transition metal series follows the crystal-field splitting scenario, yielding the sequence $\Vert M^{Ti}\Vert <\Vert M^{Ni}\Vert <\Vert M^V\Vert <\Vert M^{Cr}\Vert <\Vert M^{Mn}\Vert$, which correlates directly with the increasing exchange splitting between the majority- and minority-spin t₂g states, ${\mathsf{\Delta }}_{(t_{2g}^{+},t_{2g}^{-})}^{Ti}<{\mathsf{\Delta }}_{(t_{2g}^{+},t_{2g}^{-})}^{Ni}<{\mathsf{\Delta }}_{(t_{2g}^{+},t_{2g}^{-})}^V<{\mathsf{\Delta }}_{(t_{2g}^{+},t_{2g}^{-})}^{Cr}<{\mathsf{\Delta }}_{(t_{2g}^{+},t_{2g}^{-})}^{Mn}$ sequence.