Tuning the magnetic and electronic properties of strontium titanate by carbon doping

Abstract

The magnetic and electronic properties of strontium titanate with different carbon dopant configurations are explored using first-principles calculations with a generalized gradient approximation (GGA) and the GGA+U approach. Our results show that the structural stability, electronic properties and magnetic properties of C-doped SrTiO₃ strongly depend on the distance between carbon dopants. In both GGA and GGA+U calculations, the doping structure is mostly stable with a nonmagnetic feature when the carbon dopants are nearest neighbors, which can be ascribed to the formation of a C–C dimer pair accompanied by stronger C–C and weaker C–Ti hybridizations as the C–C distance becomes smaller. As the C–C distance increases, C-doped SrTiO₃ changes from an n-type nonmagnetic metal to ferromagnetic/antiferromagnetic half-metal and to an antiferromagnetic/ferromagnetic semiconductor in GGA calculations, while it changes from a nonmagnetic semiconductor to ferromagnetic half-metal and to an antiferromagnetic semiconductor using the GGA+U method. Our work demonstrates the possibility of tailoring the magnetic and electronic properties of C-doped SrTiO₃, which might provide some guidance to extend the applications of strontium titanate as a magnetic or optoelectronic material.

Graphical abstract

Keywords

strontium titanate / carbon doping / magnetic and electronic states / carbon coupling / C–C dimer pair / GGA+U

1 Introduction

As one of the most fascinating electronic ceramic materials, strontium titanate (SrTiO₃) has attracted much attention because of its high static dielectric constant [1, 2], large electron effective mass and large Seebeck coefficient [3], which has led to promising technological applications [4–7]. Due to its high efficiency, stability and strong reducing ability in the photocatalytic field, SrTiO₃ can also be employed as a feasible photocatalyst [8–13].

It has been found that the performance of SrTiO₃ can be dramatically modified through doping [14–18]; for example, doping is chosen as a typical approach to reduce the bandgap of SrTiO₃ to enhance its response towards the solar spectrum. The absorption of visible light in N-doped SrTiO₃ can be attributed to the induced isolated states above the valence band maximum (VBM) [19, 20]. Doping with only Rh to substitute for Sr can significantly reduce the photoabsorption energy by introducing localized acceptor states. Codoping with La and Rh leads to the formation of clean band structures rather than mid-gap states [8]. Doping approaches mainly include (i) anion doping [5, 21], (ii) cation doping [14, 22, 23], (iii) cation-anion codoping [13, 24–26], (iv) anion-anion codoping [27], and (v) cation-cation codoping [5, 28]. In particular, the anion dopant of carbon (C) to replace oxygen has attracted much attention and is considered one of the appropriate anion alloy elements to introduce acceptor levels above the VBM of SrTiO₃ because its size is closer to the size of the substituted host oxygen atoms, which is favorable for effective incorporation. Theoretical results indicate that C-doping induces a small change in the band gap, and the new absorption edge in the visible light region is attributed to the isolated impurity band [19, 29]. For codoping research, the C element is also considered one of the best candidates for generating the original impurity level between the valence band and conductor band [20]. Investigation of SrTiO_2.875C_0.125 has revealed that it is a magnetic semiconductor, with a magnetic moment of approximately 2.00 µ_B [30]. However, the effect of coupling between C atoms on structural stability, magnetic moment and electronic structure remains unclear; for instance, whether the induced carbons tend to align in a chain sandwiched with Ti atoms or prefer to locate far away from each other remains unclear. For the purpose of exploring the magnetic moment distributions and their related electronic structures in detail, we employ density functional theory (DFT) to simulate seven different configurations separated by different C–C distances in SrTiO_2.75C_0.25. The results of generalized gradient approximation (GGA) and GGA+U are calculated for comparison. We hope the study of carbon coupling in SrTiO_2.75C_0.25 systems can provide theoretical guidance for engineering doping approaches and designing new materials.

2 Computational details

Our first-principles calculations are performed using the Vienna ab initio Simulation Package (VASP) [31, 32] based on DFT [33] with projected augmented wave (PAW) potentials. The generalized gradient approximation (GGA) parameterized by Perdew-Burke-Ernzerhof (PBE) is used for the exchange-correlation functional [34]. We employ an on-site U = 5.8 eV on the Ti 3d orbitals to consider the strongly correlated effects and provide a proper description of the Ti 3d localized states [22, 35–37]. For some typical configuration cases, we also investigate the magnetic properties as a function of U to examine the localization influence. The atomic reference electron configurations for the PAW potentials are 4s²4p⁶5s² for Sr, 3s²3p⁶3d²4s² for Ti, 2s²2p⁴ for O and 2s²2p² for C.

For the calculations of bulk SrTiO₃ and different configurations sets for the deficient SrTiO₃ systems, a large 2×2×2 supercell containing 40 atoms is chosen. In the supercell, two O atoms are replaced by two C atoms, namely, SrTiO_2.75C_0.25. The doped model is shown in Fig. 1, in which the position of carbon atom i (location of first dopant in the supercell) remains invariable, while the other carbons (second dopant in the supercell) are labeled A–G away from i with increasing separation. Hereinafter, we name A–G carbon-doped combinations configurations A–G. The effects of the separating distance between dopants on properties were investigated in detail. Electronic structures are calculated on the corresponding optimized crystal geometries. A cutoff energy of 450 eV for the plane-wave basis set and a 5 × 5 × 5 k-point grid centered at the Gamma (or Γ) point are used. The convergence threshold for self-consistent iteration is set at 10⁻⁵ eV, and all the atomic positions are fully optimized until all components of the residual forces are smaller than 0.01 eV/Å.

3 Results and discussion

3.1 Magnetic property

To explore the spin-polarized properties, we discuss the specified magnetic moment distributions in seven different SrTiO_2.75C_0.25 configurations. Detailed calculation results are shown in Table 1. To explain the most stable magnetic states with carbon impurities incorporated within the accepted lattice, we employ the relative energy (∆E) in different SrTiO_2.75C_0.25 configurations based on the following equation: ∆E = E_meta−E_stable, where E_meta is the total energy of the calculated metastable configuration, and E_stable is the total energy of the stable configuration that has the lowest energy among different magnetic states in C-doped SrTiO₃ (eV/dopant), which is referred to as the NM (nonmagnetic) state in configuration A (E_stable is set as 0 eV). The initial magnetic calculations under ferromagnetic (FM) and antiferromagnetic (AFM) alignments for configuration A both converged to NM states, indicating an NM nature for the ground magnetic state (GMS). With respect to all other configurations, configuration B is endowed with the highest total energy and illustrates the most unstable configuration, which is consistent with the following investigation of electronic properties. The relative energy of other configurations in FM/AFM states and NM states is approximately 2.5 eV/2.9 eV higher than that of configuration A, respectively. In addition, compared to pristine SrTiO₃, configurations A–G are characterized by approximately 3.25 eV, 8.43 eV, 8.24 eV, 8.08 eV, 8,24 eV, 8,33 eV, and 8.27 eV higher energies, respectively.

As the dopant-dopant distance increases, the GMS for various configurations switches to FM or AFM states. All the magnetic configurations are endowed with similar FM magnetic moments of approximately 4.0 µ_B, which can be qualitatively ascribed to the magnetic moment of the carbon dopants. Bannikov et al. revealed that the overall magnetic moments in SrTiO_2.875C_0.125 (with one carbon dopant) acquired a net spin moment of 2.02 µ_B [30], and the magnetic moment originated mainly from the spin splitting of states for impurity carbon atoms, which is consistent with our results. In fact, the unpaired or uncompensated electrons induced by carbon dopants lead to the appearance of magnetism, which may provide additional approaches to yield magnetic moments by introducing nonmagnetic ions.

The relative contributions from carbon atoms to the total magnetization in different arrangements are summarized in Table 1, which manifests the following three features: (i) No noticeable magnetic moments are observed for carbon atoms in configuration A; (ii) Compared within magnetic systems, configuration B depicts a rather small total magnetic moment, and the magnetic moments on two isolated carbon atoms are unequal; (iii) There appears to be an equal contribution of approximately 0.7 µ_B for the magnetic moment per carbon atom in configurations C–G. Table T1 in the supplemental materials shows the averaged contribution of the Sr atom, Ti atom, and O atom to magnetism. It shows that no noticeable contribution of magnetic moments is related to Sr and Ti atoms, while relatively small localized magnetic moments appear at O atoms, suggesting that the resolved magnetic moment originates mainly from impurity carbon atoms. We note that due to the default radius set for the integration of the magnetic moment in VASP, the total magnetic moment is less than the sum of the magnetic moment of each atom, which does not affect our conclusion, especially for the trend we will discuss in the following sections. Configuration A shows a more favorable NM GMS even though it is associated with unpaired electrons similar to configurations B–G. Thus, to explore the coupling mechanism of the observed peculiarity, we will present the investigation of NM in configuration A later on.

3.2 Structural stability

To further acknowledge the differences in the doped configurations, we investigate the structural stability and charge transfer information. The relaxed lattice parameters for pristine SrTiO₃ are a = b = c = 3.935 Å, which is in good agreement with the experimentally obtained lattice constants (a = b = c = 3.905 Å). The optimized C–C distance in different combinations ranges from 1.297 Å to 6.868 Å (see supplemental materials Fig. S1), and the interrelated calculated results are summarized in Table 2.

The substantial displacement of the C–C bond length before and after a relaxation of approximately 1.5 Å in configuration A can be attributed to the strong attraction between carbon atoms inducing a dimer pair with a C–C distance of 1.297 Å. The dimer pair between carbon and carbon atoms has also been reported in monolayer ZnO when two neighboring O atoms are substituted by C atoms [38], resulting in an n-type semiconductor with a NM ground state. In addition, the significant displacement of the C–C bond length is responsible for the considerable shift of C–Sr and C–Ti, whereas the attraction or repulsion in all other configurations is less than 0.1 Å. Configurations C and F also show a tiny C–C attraction and only the two configurations on the Sr–O face, while other configurations except for configuration A express repulsion between carbons. The altered distances for C–Sr show similar results accompanied by a repulsion of approximately 0.04 Å in all configurations except for configurations A and F. Ti atoms tend to attract the nearest carbon atom in configuration B, whereas Ti atoms move away from carbon atoms for all other cases.

To further investigate the structural properties in more detail, we examine the interactions between C atoms and the nearest Sr and Ti ions, as well as the effects of such interactions on volume or lattice parameters. Herein, for instance, we select configuration A with the nearest neighbor C–C and configuration B with the second nearest neighbor C–C to perform the comparison. The optimized structures of configuration A and configuration B are presented in Figs. 2(a) and (c). First, as shown in Table 2, compared to pristine SrTiO₃, C-doped SrTiO₃ shows a larger volume (all positive∆a,∆b, and∆c) in all configurations. The relaxed lattice parameters in configuration A are a = c =3.960 Å and b =3.954 Å, which are approximately 0.02 Å larger than those of pristine SrTiO₃. As mentioned above, two carbons lean very closer and tend to form a C–C dimer pair in configuration A. The changes in the bond length before and after relaxation for C–C, C–Sr, and C–Ti are 1.496 Å, 0.141 Å, and 0.216 Å, respectively. For configuration B, as marked in Fig. 2(c), two doped carbons align linearly along the C–Ti–C axis. The C₁–Ti₁ bond length is decreased by 0.042 Å, while the C₂–Ti₁ bond length is increased by 0.081 Å. This triggers a small rotation of the O₁–Ti₁–O₂ angle and significantly increases the c lattice constant by approximately 0.053 Å, while the lattice constants a and b remain unchanged.

To understand the charge transform and redistribution, we employ the following formula to calculate the charge density difference \rho ={\rho }_{\text{total}}-{\rho }_{\text{STO}}-{\rho }_{C_1}-{\rho }_{C_2} , where ρ_total, ρ_STO, {\rho }_{C_1} and {\rho }_{C_2} are the charge of the Sr-TiO_2.75C_0.25 system, pristine SrTiO₃, carbon1 and carbon2 atoms, respectively. The charge density difference plots of configuration A and configuration B are shown in Figs. 2(b) and (d), respectively. Herein, the isosurface level value is set as 0.005 e/ų, and the yellow areas represent charge accumulation, while blue violet areas represent charge depletion. The variation in the electronic distribution due to charge transfer to the carbon is rather obvious. Significant charge accumulation near the carbon and a small amount of charge depletion around the titanium atoms closest to the carbon in configurations A and B gives rise to strong electrostatic interactions between titanium atoms and carbons. Other charge difference plots for configuration C–G are characterized with similar properties and are listed in supporting information S2. In addition, Bader charge analysis indicates that each C dopant acquires on average approximately 0.75e charge in configuration A and 0.91e charge in configuration B.

As mentioned above, the relative energy (∆E) is important to evaluate the coupling strength of the substitutional dopant. Figure 3(a) illustrates the calculated relative energy in different configurations, and it can be seen that the formation of a C–C dimer pair in configuration A is the most favorable with the lowest energy, where two impurity carbons tend to strongly attract each other. Moreover, the energy is far lower than that for the other six configurations. Except for configuration A, a comparatively low energy is observed in configuration D. Two doped carbons aligned linearly along the C–Ti–C axis in configuration B are endowed with a relatively high energy, which suggests that it may be difficult to synthesize configuration B through carbon doping. Figure 3(b) illustrates the calculated relative energy versus different separated distances between two carbon atoms (before relaxation) in the Sr-TiO_2.75C_0.25 system. Even with the same C–C distance, the total energy depicts visible diversity for configurations B and C, as well as E and F. It is found that the C–C pair tends to remain at the Sr–O face. For example, compared to configuration B, the C–C pair tends to remain at the Sr–O face in configuration C, in which the pairs align along the x-axis with no other atoms between them. The C–C pair also prefers to remain at the Sr–O face in configuration F with respect to configuration E.

To provide insights into the origin of the nonmagnetic property in configuration A and to explain the induced different magnetic features in other doped configurations, we further analyze the partial density of states (PDOS) of Ti 3d orbitals, C 2p orbitals and O 2p orbitals with different relaxed steps, as shown in Fig. 4(a). Three criteria are applied in our calculations: (i) The C–C bond length before relaxation is 2.792 Å, named step I (initial step, ideal doping site), while, after relaxation, it is 1.296 Å, labeled step V (final step, completely relaxed site); (ii) The coordinates for the two carbon atoms at steps I and V are (0.250, 0.500, 0.250), (0.500, 0.750, 0.250) and (0.346, 0.537, 0.250), (0.463, 0.654, 0.250), respectively. Other intermediate steps indicate that the coordinates for the two carbon atoms sit between I and V. For instance, step III is associated with the carbon coordinates of (0.298, 0.519, 0.250) and (0.482, 0.702, 0.250), which correspond to the middle position of the separated C–C distance between the initial step I and the final step V in configuration A; (iii) Coordinates of the carbon atoms remain unchanged under every condition in our calculations.

As illustrated in Fig. 4(a), at the initial step I, C 2p and Ti 3d orbitals show a strong pd orbital hybridization near the Fermi level, and most of the unequal spin-up and spin-down electrons are ascribed to the foreigner carbons, which introduce a remarkable magnetic moment. As the C–C distance approaches step V, the hybridization between C 2p and Ti 3d gradually weakens. Simultaneously, Ti 3d orbitals are pulled down to lower energies and depict a more dominant contribution with respect to equal spin-up and spin-down channels, which results in a decrease in the magnetic moment, as shown in Fig. 4(b). The magnetic moment varies from 2.3 µ_B to 0 µ_B when the step evolves from I to V. Therefore, the nonmagnetic character mainly originates from the competition between C–C hybridization and C–Ti hybridization, where the stronger C–C hybridization and weak C–Ti hybridization give rise to equal spin-up and spin-down channels. Figure 4(b) also shows the corresponding energies with respect to different relaxed steps. The energy in step I is set as the reference energy (i.e., set as 0). An obvious decrease in energies from step I to step V indicates a more stable state as the two carbon atoms get closer, which is consistent with our research above.

3.3 Electronic structure

The calculated total density of states (DOS) and the PDOS for the O 2p, Ti 3d t_2g and Ti 3d e_g orbitals for pristine SrTiO₃ are shown in Figs. 5(a) and (b), respectively. This illustrates that pristine SrTiO₃ possesses a band gap of 1.69 eV [39–41], which is in good agreement with other calculations. This value is smaller than the experimental value of 3.20 eV due to the well-known underestimation of the band gap by LDA or GGA. As seen from Fig. 5(b), the valence bands of pristine SrTiO₃ are predominantly composed of O 2p orbitals, and the conduction bands mainly correspond to Ti 3d orbitals. Because of the cubic crystal field in the TiO₆ octahedron surrounded by six nearest-neighbor O atoms, the empty Ti 3d orbitals split into three lower energy t_2g orbitals (3d_xy , 3d_yz , 3d_zx) and two higher energy e_g orbitals (3{\text{d}}_{z^2}\mathrm{,}3{\text{d}}_{x^2-y^2}). Pristine SrTiO₃ exhibits a nonmagnetic property due to the symmetric populations of spin-up and spin-down channels.

The calculated spin-polarized DOS for configurations A–G are shown in Figs. 6(a)–(g). Compared to pristine SrTiO₃, the introduced carbon impurities lead to the appearance of a new impurity 2p band localized in the band gap of the matrix and shift the Fermi level in all configurations. In addition, the splitting of the impurity band into spin-resolved bands and the unequal spin-up and spindown electrons in configuration B–G contribute to a remarkable magnetic moment, while equal spin-up and spindown channels result in the nonmagnetic ground state in configuration A. Based on electronic structures and magnetic features, three different SrTiO_2.75C_0.25 are classified. The C-doped SrTiO₃ undergoes a change from n-type NM metal to FM/AFM half-metal and to AFM/FM semiconductor with increasing dopant-dopant distance. Detailed electronic structures for different categories will be presented in the following subsections.

3.3.1 n-type NM metal

From Fig. 6(a), the equal occupancy of spin-up and spindown states indicates no extra local magnetism in configuration A, which is consistent with our magnetic studies above. On the other hand, it is obvious that both spin-up and spin-down channels cross the Fermi level in the conduction bands compared to pristine SrTiO₃, which suggests that configuration A shows n-type nonmagnetic metallic characteristics. Due to the higher energies of the 2p orbitals for foreigner C compared with host O, doped C will introduce an acceptor level and occupy the VBM. The states are somewhat delocalized. The hybridization of C 2p orbitals and Ti 3d orbitals pulls the conduction band minimum (CBM) downwards by approximately 0.22 eV below the Fermi level while compelling the VBM located at 2.08 eV below the Fermi level, which provides a band gap of 1.86 eV. Therefore, the bands originating from C 2p states lead to a widening instead of a narrowing of the band gap.

3.3.2 FM/AFM half-metal

The calculated spin-polarized DOS for configuration B are shown in Fig. 6(b), where the uncompensated majority (spin down) and minority (spin up) channels illustrate the existence of magnetic moments. Meanwhile, the majority channels depict a conducting nature, while the minority channels show semiconducting behavior, which gives rise to an FM/AFM half-metal characteristic in configuration B with a second-nearest C–C. As shown in Fig. 6, the DOS for different configurations demonstrates that the semiconductor or insulator feature for Configuration C–G is characterized by a more stable state than the half-metal electronic property of configuration B. Although configuration A is endowed with a metal nature, the induced dimer pair between the two boron dopants makes it the most stable among all configurations. Therefore, configuration B is the most unstable among all configurations, which is in agreement with the observed peculiarity in energy.

It is clear that the introduced C mixed with O 2p states indeed increases the width of the valence band. Moreover, unoccupied C 2p states lead to a downshift of the CBM. Both of these contributions produce a significant narrowing of the band gap.

3.3.3 AFM/FM semiconductor

The calculated spin-polarized DOS for configurations C–G are shown in Figs. 6(c–g), which all exhibit semiconductor behavior as the C–C distance increases, resulting in AFM or FM semiconductor characteristics in C–G. The introduction of C 2p orbitals hybridized with O 2p states in these configurations leads to a reduction in the band gap. Moreover, additional localized bands are obviously formed near the Fermi level in configurations C–G. Note that even though configurations B and C are endowed with the same C–C distance, they exhibit distinct differences both in terms of the electronic band structures and magnetic peculiarities.

3.4 GGA+U

GGA+U calculations are usually applied to deal with strong correlations in localized d- or f-electron systems, and, thus, partially correct the band gap estimation. Therefore, we also employ GGA+U to describe magnetic moments and electronic structures in SrTiO_2.75C_0.25 systems considering the localized d–d interactions. A value of U = 5.8 eV is employed to describe Ti 3d orbitals [19], which increases the band gap of pristine SrTiO₃ up to 2.57 eV, as shown in Fig. 7(f). The results for the magnetic properties with GGA+U are summarized in Table 3 and Table T2 in the supplemental materials. Table T2 in the supplemental materials shows the averaged contribution of each Sr atom, Ti atom, and O atom to magnetism. In general, the main results from GGA+U are similar to those obtained from GGA calculations. For instance, the relative energy for different configurations from GGA+U follows the same trend as for the GGA calculations. Configuration A shows an NM nature for the GMS accompanied by a remarkable lowest energy, while configuration B is the most unstable state with a relatively high energy among all configurations in both GGA and GGA+U calculations. The GMS for most configurations in GGA+U calculations is also similar to the results obtained from GGA calculations, except for configuration D. The GGA+U calculations predict AFM, while GGA calculations suggest FM/AFM as the GMS of configuration D. Additionally, the electronic structures of configuration A are different in GGA and GGA+U calculations.

The GGA+U calculated spin-polarized DOS in different configurations is shown in Figs. 7(a–g). Configuration B exhibits a half-metal peculiarity, while C–G is characterized by semiconductor behavior, which is the same as that observed in GGA calculations. In addition, more obvious isolated bands are formed above the O 2p orbitals in all configurations under the GGA+U calculations, which can be ascribed to the higher 2p orbitals of carbon compared to the O 2p orbitals. Compared with the GGA calculation, the dominant difference is that configuration A shows a semiconductor feature rather than a metal nature, which is attributed to the more localized Ti orbitals and weaker Ti-C hybridization under the GGA+U calculation.

As shown in Table 1 and Table 3, GGA and GGA+U calculation results, respectively, show obvious magnetic distinctions in configuration D, i.e., an FM/AFM state versus AFM state in combination D, indicating that the GMS is U affected. To further examine the effects of strongly correlated effects, we perform additional calculations for the energy difference between AFM and FM states in configuration D as a function of different U values and take configuration B for comparison, as shown in Fig. 8. We employ the formula∆E = E_AFM−E_FM to illustrate the evolution of GMS, where E_AFM and E_FM represent the energy in the AFM state and FM state, respectively. Within numerical uncertainty, the energy difference∆E in configuration B as a function of U is rather small, and it tends to be a constant value above 0, indicating an FM/AFM for the GMS. However, for configuration D, a clear crossover is observed from FM to AFM GMS at approximately U = 1.6 eV, implying a more stable AFM characteristic in configuration D with strongly correlated effects taken into account.

3.5 Conclusions

The magnetic and electronic properties of different Sr-TiO_2.75C_0.25 configurations were explored using first-principles calculations with GGA and GGA+U . Our calculation results show that the GMS undergoes a change in magnetic states as the C–C distance increases, i.e., it starts with no noticeable magnetic moments at the shortest C–distance, followed by a rather small total magnetic moment with unequal carbon contributions on magnetic moments, and, finally, leads to an equal contribution of approximately 0.7 µ_B of magnetic moment per carbon atom. No noticeable contribution of the magnetic moment is related to Sr and Ti atoms, while a relatively small localized magnetic moment is resolved at O atoms. In both GGA and GGA+U calculations, the ground state exhibits NM features when two carbon atoms are nearest neighbors, which mainly originates from the stronger C–C and weaker C–Ti hybridizations with the shortest C–C distance and leads to equal spin-up and spin-down channels. In addition, both calculations demonstrate that two carbon atoms tend to form a dimer pair with a remarkable displacement of approximately 1.5 Å, while two doped carbons aligned linearly along the C–Ti–C axis are endowed with relatively high energies. The calculation results also show the bandgap modifications when the C–C dopant distance is changed. Our work shows the tunable magnetic and electronic properties of C-doped SrTiO₃, which is expected to promote its applications in a variety of fields. In addition, we note the possible doping site of Ti and other sites substituted by C and will investigate these in our future work.

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