Tuning Magnetic and Semiconducting Properties of Cr-Doped CaTiO₃ Perovskites for Advanced Spintronic Applications

Abstract

The physical properties of perovskite-type materials are sensitive to their chemical composition and crystallographic structure, which makes them highly versatile for various advanced technological applications. In this theoretical study, density functional theory (DFT) is employed to investigate the electronic properties of the perovskite-like material CaTiO₃, focusing on the substitution of Ti⁴⁺ with the magnetic transition metal Cr⁴⁺. The results reveal a systematic increase in the effective magnetic moment and a gradual decrease in the bandgap with increasing Cr⁴⁺ content in the CaTi_1−xCr_xO₃ system (x = 0.0, 0.25, 0.5, 0.75, 1.0). The interactions between electronic orbitals associated with Ti-O-Cr inter-octahedral bonds modify the magnetic response of the material, leading to hybridizations between valence and conduction states that alter its semiconductor character. This tunability in electronic and magnetic properties underscores the potential of these materials for applications in spintronics. This study offers novel insights into the design of new magnetic semiconductor materials with tailored functionalities, contributing to the development of next-generation spintronic devices.

1. Introduction

The physical properties of perovskite-type materials are notably sensitive to their chemical composition and crystallographic structure. This characteristic makes them a focal point of research due to their versatile applications in various fields, including electronics, photonics, and spintronics [1,2,3]. Perovskites are promising candidates for advanced technologies because their properties can be finely tuned through chemical substitutions, which significantly alter their electronic, magnetic, and optical behaviors [4,5,6]. Specifically, the substitution of transition metals in these materials can lead to substantial modifications, making them ideal for developing materials with tailored functionalities [7,8,9].

Extensive research has been conducted on the impact of doping and substituting different elements in perovskite structures. Hassen et al. [10] demonstrated the effects of substituting Ti with Cr in CaTiO₃, revealing significant changes in structural, dielectric, and optical properties due to the doping process. Wang et al. [1] analyzed ferromagnetism in Cr and Mn co-doped 3C-SiC using density functional theory (DFT). Their study highlighted a significant increase in energy levels and magnetic properties due to the doping of these transition metals, which is crucial for developing spintronic materials. Similarly, Dar et al. [4] studied the structural, electronic, magnetic, and optical properties of various doped perovskite materials, emphasizing the role of dopants in altering their band structure and magnetic moments, which are essential for tailoring material properties to specific applications. Rizwan et al. [7] examined the electronic and optical behavior of lanthanum-doped CaTiO₃. Their findings showed that doping significantly affects the material’s band structure and optical properties, further illustrating the broad impact of doping on perovskite materials. Al-Qhtani [8] explored the half-metallic ferromagnetism and transport properties of zinc chalcogenides, which are relevant for understanding similar effects in Cr-doped perovskites. Alsobhi et al. [11] used first-principles calculations to study the electronic, structural, optical, thermoelectric, and elastic properties of CeXO₃ (X = Ti, V, Cr) perovskites, revealing significant effects of doping on these properties. Zhang et al. [12] investigated the electronic structure and high magnetic properties of (Cr, Co)-codoped 4H-SiC using first-principles calculations. This study revealed high magnetic moments and the potential for spintronic applications, emphasizing the role of co-doping in enhancing material properties. Chang et al. [13] examined the effect of Cr substitution on the structure and electrical properties of BiFeO₃ ceramics, finding significant changes in resistivity and dielectric properties with Cr doping. Gong et al. [14] focused on the structural, electronic, and magnetic properties of double perovskite Pb₂CrMO₆ (M = Mo, W, Re) using a first-principles investigation, highlighting the potential of the materials for spintronics due to their high Curie temperatures and magnetic properties.

Further studies have explored the role of Cr doping in various materials. Nasir et al. [15] investigated the physical properties of XRh₃ inverse perovskites from first principles, showing how transition metal doping can modify electronic and magnetic behaviors. Kishore et al. [16] conducted high-pressure studies on the electronic and mechanical properties of FeBO₃ ceramics doped with Ti, Mn, and Cr, revealing changes in band structure and magnetic properties under different pressure conditions. In 2018, Mahmood et al. [17] used first principles to study ferromagnetism in transition-metal-doped perovskites, emphasizing the role of dopants in enhancing magnetic properties. In 2022, Saad [9] investigated the impact of 3d transition metals on praseodymium perovskites, highlighting the changes in electronic and magnetic properties with different dopants. Moreover, in 2021, Saxena [18] studied the structural and electrical properties of YMnO₃, focusing on the effects of Mn doping. In 2016, Ghebouli et al. [19] performed an ab initio study on the structural, elastic, electronic, and optical properties of double perovskite oxides Sr₂AlXO₆ (X = Ta, Nb, V). Their research predicted a direct bandgap for Sr₂AlXO₆ (X = Ta, Nb) and an indirect bandgap for Sr₂AlVO₆, showcasing how the electronic properties of double perovskites can be tuned through compositional changes. Recently, in 2024, Ait M’hid et al. [3] conducted first-principles investigations and Monte Carlo simulations of Ti- and Cr-doped perovskites, providing detailed insights into the effects of doping on electronic and magnetic properties. This study underscores the importance of combining theoretical methods to achieve a comprehensive understanding of material behavior under various conditions. Several other studies [20,21,22,23] have explored the structural, thermal, elastic, electronic, thermodynamic, and magnetic properties of doped perovskites. These studies demonstrate how doping can significantly alter multiple material properties simultaneously, providing a theoretical framework for understanding the stability and characteristics of these materials. This comprehensive approach is crucial for developing materials that meet specific application requirements. Moreover, these studies highlight the predictive power of first-principles methods in guiding experimental research, offering a thorough overview of how doping affects various material properties and providing valuable data for future research and applications.

The doping of perovskite materials, such as CaTiO₃, with various elements has been extensively studied to modify their properties for different applications. The structure of doped perovskites can vary based on the dopant used. For instance, Cr-doped perovskite materials exhibit an orthorhombic symmetry similar to SmFeO₃ [24]. Doping with divalent and/or trivalent ions can introduce lattice distortions and oxygen vacancies in perovskites like BaTiO₃ or CaTiO₃ [25]. Cation–anion co-doping has been shown to enhance the photocatalytic performance of CaTiO₃ perovskites [26]. Doping with different elements can lead to significant changes in the properties of perovskite materials. For example, Pr- and Eu-doped CaTiO₃ exhibit pronounced photoluminescence emissions, with optimal lanthanide concentrations affecting the intensity of the emissions [27]. Additionally, doping with elements like Rh and Ln in layered perovskite Ca₃Ti₂O₇ can enhance their photocatalytic activity under visible light irradiation [28]. The doping of calcium titanate with various impurities allows for the manipulation of the ionic and electronic structure, thereby affecting the electrical properties of the compounds [29]. Moreover, the doping of nanostructured CaTiO₃ has been found to increase strain and defects in the structure compared to the pure material, impacting its piezoelectric properties [30]. Doping with Fe in CaTiO₃ decreases the bandgap energy of the material [31]. Furthermore, doping can improve the conductivity of perovskites like YMn_1-xCr_xO₃, enhancing their performance in applications such as oxygen evolution [32].

Despite the extensive research on doped perovskite materials, there remains a gap in our understanding of the specific effects of varying Cr contents in CaTi_1-xCr_xO₃ on its magnetic moment and semiconducting properties. Addressing this gap is crucial for advancing the development of materials for spintronic applications, for which the control of both spin and charge is essential. This study aims to provide a detailed theoretical analysis using density functional theory (DFT) to evaluate how the substitution of Ti⁴⁺ with Cr⁴⁺ influences the effective magnetic moment and semiconducting gap of CaTi_1−xCr_xO₃. By employing DFT, this research focuses on analyzing the electronic properties of the perovskite-like material CaTiO₃, particularly examining the effects of substituting Ti⁴⁺ with the magnetic transition metal Cr⁴⁺ across various ratios (x = 0.0, 0.25, 0.5, 0.75, 1.0). The interactions between electronic orbitals associated with Ti-O-Cr inter-octahedral bonds are investigated to understand the resulting changes in magnetic response and semiconductor character. Our calculations encompass the electronic density of states, a band structure analysis, and magnetic moment assessments, thereby providing a comprehensive understanding of how Cr doping affects the material. This integrated approach aims to elucidate the fundamental mechanisms driving the observed modifications in magnetic and electronic properties, contributing valuable insights for the design of materials suitable for spintronic applications. Moreover, as electronic devices continue to miniaturize, materials that offer tunable electronic and magnetic properties become increasingly valuable. This tunability can lead to more efficient and versatile components in spintronic devices, potentially revolutionizing data storage, processing speeds, and energy efficiency. Moreover, the unique properties of perovskites, such as their high-temperature stability and diverse electrical behaviors, make them suitable candidates for applications that demand a robust performance under extreme conditions.

2. Theoretical Calculation Method

For the total energy calculations, we employed the DFT using the projector augmented wavelet (PAW) method [33,34], implemented in VASP software [35], version 6.2.1. The evaluation of the exchange and correlation energy was performed using the generalized gradient approximation (GGA) with Perdew–Burke–Ernzerhof (PBE) functions [36]. A value of U_Cr = 3.7 eV was selected in the calculation because this value provides the highest energy stability for the material in its magnetic state. Additionally, with this value, the material maintains its semiconducting behavior. This correction in the Hubbard potential ensures that the bandgap value is closely aligned with those reported for similar materials, such as CaTiO₃ [7,23]. A cutoff energy of 520 eV was determined for the PAW-PBE potentials, which allowed high convergence in the total energies to be achieved, with discrepancies of less than 0.001 eV per atom. Brillouin zone sampling was performed using the Monkhorst–Pack method, with a k-point grid of 7 × 7 × 5 [37], which was sufficient to obtain highly convergent energies, with variations of less than 1 meV per atom. For the calculation of the partial occupancies of the electronic states near the Fermi level, we applied the blurring technique proposed by Methfessel and Paxton [38], with a blurring parameter of 0.05 eV. Together, these parameters ensured that our calculations achieved convergence in the total energy within 1 meV. In addition, we optimized the lattice parameters and ionic positions until the forces acting on the ions were minimized to less than 30 meV/Å.

3. Results and Discussion

Table 1. Optimized structural parameters of the system perovskite CaTi_1−xCr_xO₃.

Structural Parameters	0%	25%	50%	75%	100%
a (Å)	5.4067 5.3928 [39]	5.3878	5.3929 5.3511 [40]	5.3476	5.3221 5.2886 [41]
b (Å)	5.5056 5.4494 [39]	5.4935	5.4596 5.3936 [40]	5.4748	5.4668 5.3172 [41]
c (Å)	7.6949 7.6582 [39]	7.6552	7.5989 7.5874 [40]	7.5720	7.5341 7.4844 [41]

summarizes the results of the optimized structural parameters for the perovskite-type material CaTi_1−xCr_xO₃. The theoretical data show good agreement with the experimental results, with the overestimation of the lattice parameters not exceeding 2.9% and the deviation in the ratio between them less than 2.2%.

The energetic stability of the structures corresponding to the perovskite-type material CaTi_1−xCr_xO₃, with x = 0.0, 0.25, 0.5, 0.75, and 1.0, representing the Cr substitution in the crystallographic sites of Ti, was analyzed by considering different structural configurations. These configurations are presented in Figure 1, which shows the highest energetic stabilities. Figure 1a shows the orthorhombic structure belonging to the Pbnm space group (#62) [42]. This space group was discovered by Gustav Rose in 1839 [43], from which the perovskites were named. It is characterized by a distribution in which the Ti cation is octahedrally coordinated with six oxygen anions, while the Ca cation adopts a cuboctahedral coordination with 12 oxygen anions.

When 25% of the Ti is substituted by Cr, in the same oxidation state, the space group is maintained, so that there is one out of four octahedra containing a Cr instead of a Ti, as exemplified in Figure 1b. It is necessary to note that Cr is substituted for Ti with the same 4+ oxidation state. With octahedral coordination, it does not present crystal field splitting, so Jahn–Teller type distortions are not expected [44], although a small decrease in the unit cell is expected due to its slightly smaller ionic radius—that of Ti⁴⁺ is 0.60 Å and Cr⁴⁺ is 0.55 Å. For 50% substitution, the energetically most favorable state is that of a superstructure in which Ti and Cr cations alternate successively along the three crystallographic axes as shown in Figure 1c. In the case represented in Figure 1d, the partial substitution of Cr in the Ti sites reaches 75%, corresponding to the inverse case to that of Figure 1b, since now Cr is the majority in the cell, such that three out of four cations in this crystallographic site are occupied by Cr and only one by Ti. Finally, Figure 1e corresponds to the orthorhombic cell for CaCrO₃, that is, for 100% Cr substitution in the octahedral Ti sites.

Figure 2 illustrates the variation in the total energy of the perovskite-type material as a function of the different Cr concentrations studied in this work. It is observed that, as the Cr percentage increases, the total energy of the composite decreases linearly. This trend suggests that the material becomes more stable with higher Cr concentrations, which is consistent with the observed stability of the crystal structures obtained in this study.

Although Cr³⁺ is the most stable and commonly observed oxidation state for chromium, the stability of the ABO₃ perovskite structure strongly depends on the oxidation states of both the A and B cations. In particular, perovskites with A²⁺B⁴⁺O²⁻₃ valence distribution are known to exhibit a higher stability compared to those with A³⁺B³⁺O²⁻₃ oxidation states [45]. Given that the starting point of this study is the Ca²⁺Ti⁴⁺O²⁻₃ perovskite, the substitution of Ti by Cr necessitates the adoption of a +4 oxidation state by Cr to preserve the stability and charge balance of the crystalline structure. This approach aligns with established methods for predicting perovskite-type crystal structures, for which the oxidation state is fundamental for the calculation of the bond valence sum [46]. The bond valence sum, in combination with the tolerance factor, allows for the calculation of the global instability index, which is crucial in determining the likelihood of crystallization for the material [47].

Figure 3 shows the density of electronic states (DOS) for all cases considered for the CaTi_1−xCr_xO₃ system. The upper part of each of the pictures is the representation of spin-up polarization contributions and the lower ones correspond to spin-down orientations. Conventionally, the value E = 0 eV is established as the Fermi level. In Figure 3a–c, the total density of states, the contributions of the 3d-Ti and 2p-O orbitals, respectively, is exemplified for the CaTiO₃ material, i.e., CaTi_1−xCr_xO₃ (x = 0). It is observed from the total and partial DOS that the states obtained from the calculation are symmetric for the two spin orientations, both in the valence and conduction bands, so that the bandgap is the same for the two cases, reaching a value of E_g = 2.34 eV. This value, which is typical of semiconductor materials, has been observed in CdS films produced using the techniques of chemical bath deposition and pulsed direct current magnetron sputtering [48], and is among the bandgap values expected for CaTiO₃ [49]. It is observed in Figure 3a–c that, in the vicinity of the Fermi level, the predominantly contributing states in the valence band correspond to the 2p-O orbitals, while in the conduction band, the available states are due to the 3d-Ti orbitals.

When Cr⁴⁺ is partially and fully incorporated into the structure (Figure 3d–o), the valence band is not substantially affected, so that the 2p-O orbitals continue to provide the charge carriers in the material for both spin-up and spin-down polarizations. Thus, in this band, neither the total DOS nor the partial DOS show changes, as shown in Figure 3c,f,i,l,o. Meanwhile, a systematic decrease in the small contributions of 3d-Ti orbitals, as opposed to a low but recurring increase in the contributions of 4d-Cr orbitals, is observed in this band as the proportion of Cr⁴⁺ in the structure increases, as shown in the Figure 3b,e,h,k,n. Due to the magnetic character of Cr⁴⁺, the symmetry between the up and down states is slightly modified, not only in the valence band but also in the conduction band, when this cation is included in the structure of the material.

Above the Fermi level, the changes introduced by the inclusion of Cr⁴⁺ in the structure are more drastic. This effect is due to the appearance of 3d-Cr states that contribute to the decrease in the bandgap for the spin-up orientation. This decrease is initially large but tends to saturate for high Cr⁴⁺ concentrations. Likewise, the magnitude of the DOS increases for these 3d-Cr orbitals in the conduction band as the proportion of Cr⁴⁺ in the material is increased. On the other hand, for spin-down polarization, there are no marked systematics in the bandgap changes, but there is an increase in the DOS due to the presence of 3d-Cr orbitals.

These changes can be best observed in the band structure for the two spin polarizations that are exemplified in Figure 4.

A decrease in the bandgap value can be expected with the inclusion of Cr⁴⁺ in the crystallographic sites of Ti⁴⁺, since the former has two electrons in the 3d orbitals while Ti⁴⁺ does not. The presence of these two electrons is represented in the band structure of Figure 4 by the appearance of new orbitals in the conduction band, which tend to decrease the total bandgap value according to the proportion of Cr₄₊ in the unit cell.

For the pristine material CaTiO₃, both for spin-up and spin-down polarization, it is evident in Figure 4a,b that the material behaves as a direct bandgap semiconductor. The inclusion of Cr⁴⁺ in all ratios modifies this characteristic of the compound, making it an indirect bandgap for both spin orientations. Meanwhile, for spin-up orientation, a new band appears for spin-up polarization, decreasing the bandgap when 25% Cr is introduced into the crystal cell. More states appear in this band as the Cr⁴⁺ concentration is increased, as shown in Figure 4a. This phenomenon takes place thanks to the magnetic character of Cr⁴⁺, whose [Ar]4s⁰3d² electronic configuration allows for the occurrence of two unpaired spins in the d orbitals.

The behavior of the bandgap variation for the spin-up and spin-down polarizations is exhibited in Figure 5, in which it is clear the rapid decrease in the bandgap for the spin-up orientation is due to the appearance of a transport channel due to the 3d²-Cr orbitals, which are distributed with the same polarization, following Hund’s rules. For higher Cr⁴⁺ concentrations, although more orbitals appear in the band structure, the bandgap decreases slowly with a tendency towards saturation, being the lowest for 100% substitution, reaching a value E^↑_g = 0.65 eV corresponding to 28% of the bandgap value of the pristine compound (E^↑_g = 2.34 eV).

This behavior is characteristic of magnetic semiconductor materials, in which each spin orientation corresponds to a distinct charge transport channel. Such materials are particularly valuable in spintronic devices [50], in which the ability to generate and control spin-polarized currents is crucial. The tunability of the bandgap and magnetic properties observed in Cr-doped CaTiO₃ suggests that these materials could be effectively integrated into spintronic applications, such as non-volatile memory, spin transistors, and magnetic sensors. The potential to engineer specific electronic and magnetic configurations in these perovskites opens up new avenues for developing advanced components that can operate with higher levels of efficiency and reliability in spintronic technologies.

On the other hand, for the spin-down orientation, there is an initial decrease in the bandgap value for x = 0.25, increasing thereafter and remaining constant at E^↓_g = 1.95 eV, which is 83% of the value obtained for CaTiO₃ (E^↓_g = 2.34 eV). The asymmetry of the bands for the two spin polarizations, as well as the type of indirect bandgap and the difference in the bandgap value, are features that can be seen in Figure 5b. As mentioned above, the charge-bearing states in the valence band are mostly contributed by the 2p orbitals of oxygen, while the available states in the conduction band are due to the 3d orbitals of chromium. The difference between the bandgap values for the up- and down-spin polarizations allows us to infer that energetic excitations in the E^↑_g < E < E^↓_g regime could contribute to the generation of currents with a single spin orientation (spin polarized currents), giving rise to the possibility of transporting both electric charge and electronic spin. This behavior is characteristic of so-called magnetic semiconductors, which have a wide range of applications in the spintronics industry [50].

The variation in the effective magnetic moment in the unit cell as Cr⁴⁺ is substituted at the Ti⁴⁺ sites is shown in Figure 6, in which a linear increase in the magnetic moment in the unit cell is observed with increasing Cr⁴⁺ ratio. In the calculation, the average over the whole material is considered, normalized with respect to the unit cell, since it is not possible to have only 1/4, 1/2, or 3/4 Cr or Ti cations in the unit cell. Only in the case of a 100% inclusion of Cr⁴⁺ is there an integer number of these cations in the cell, for which it is expected that the two electron spins in the d orbitals contribute a magnetic moment $\mu =\sqrt{n\left(n+1\right)}$ μ_B, where n represents the number of unpaired spins. Thus, with n = 2, considering zero contributions from Ti and O ions, the expected magnetic moment is μ = 2.45 μ_B. However, this value is only an estimate. The value found by the DFT calculation of this work is close to 2.0 μ_B because spin–orbit interactions were not taken into account, which, in some materials, tend to decrease the value of the total effective magnetic moment [51]. The value of the effective magnetic moment in the cell then corresponds to the ratio of Cr.

CaTiO₃’s magnetic moment is zero, so the partial substitution of Ti⁴⁺ by Cr⁴⁺ is expected to be related to the proportion of this cation in the unit cell; thus, for x = 1/4, 1/2, 3/4, and 1 in the generic formula CaTi_1−xCr_xO₃, effective magnetic moments of 0.5, 1.0, 1.5, and 2.0 μ_B/f.u would be expected, as shown in Figure 6.

4. Conclusions

An energy stability analysis was conducted for the perovskite-type system CaTi_1−xCr_xO₃ (x = 0.0, 0.25, 0.5, 0.75, 1.0), establishing the most favorable crystallographic configurations in the Pbnm space group (#62) for various substitution ratios of Cr⁴⁺ at the Ti⁴⁺ sites. The density of electronic states and band structure results revealed that the unsubstituted CaTiO₃ material exhibits direct bandgap semiconductor-like behavior, with orbitals defining symmetric bands for the two spin polarizations both below and above the Fermi level.

The introduction of Cr in the unit cell led to the emergence of states that decrease the bandgap value, with a more pronounced reduction for the spin-up orientation, resulting in a bandgap that is 28% of the value for the pure system. For the other spin polarization, the bandgap value is 83%. Furthermore, the presence of Cr introduced asymmetry between the states for the spin orientations, transforming the material into an indirect bandgap semiconductor type. This behavior is indicative of magnetic semiconductor characteristics, suggesting significant potential for technological applications in generating spin-polarized currents.

However, this study is not without its limitations. The primary limitation is the absence of an experimental validation of the theoretical findings, which would be crucial for confirming the practical applicability of the results. Additionally, the study focuses on specific Cr doping levels, leaving other potentially relevant concentrations unexplored. Future research could address these limitations by conducting experimental validations and investigating a broader range of doping levels. Such studies would further elucidate the tunability of perovskite materials and their potential for advanced spintronic applications.

To transition from theory to real-world applications, several practical steps need to be considered. First, the experimental validation of the theoretical findings is essential to confirm the predicted properties. This includes synthesizing the Cr-doped CaTiO₃ materials and characterizing their electronic and magnetic properties using techniques such as X-ray diffraction, scanning electron microscopy, and magnetometry. Second, the scalability of the material synthesis process must be evaluated to ensure that these materials can be produced on an industrial scale. Challenges such as maintaining material uniformity and controlling defect concentrations will need to be addressed. Finally, integrating these materials into actual spintronic devices will require collaboration with industry partners to test their performance in real-world conditions. These steps are critical for realizing the full potential of the theoretical insights gained from this study.

The originality and relevance of this study lie in its detailed theoretical analysis using density functional theory to elucidate the specific effects of Cr doping on the electronic and magnetic properties of CaTiO₃. The findings provide novel insights into the tunability of perovskite materials for advanced spintronic applications, highlighting the ability to engineer materials with tailored electronic and magnetic properties for next-generation electronic devices.