Electronic and optical properties of new multifunctional materials via half-substituted hematite: first principles calculations

Abstract

Electronic structure and optical properties of α-FeMO₃ systems (M = Sc, Ti, V, Cr, Cu, Cd or In) have been investigated using first principles calculations. All of the FeMO₃ systems have a large net magnetic moment. The ground state of pure α-Fe₂O₃ is an antiferromagnetic insulator. For M = Cu or Cd, the systems are half-metallic. Strong absorption in the visible region can be observed in the Cu and Cd-doped systems. Systems with M = Sc, Ti, V, Cr or In are not half-metallic and are insulators. The strongest peaks shift toward shorter wavelengths in the absorption spectra. It is concluded that transition metal doping can modify the electronic structure and optical properties of α-FeMO₃ systems.

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1. Introduction

Since the development of spintronics,^1,2 much attention has been focused on controlling the motion of electrons by efficiently manipulating the spin. In spintronics, high-spin injection from ferromagnets with high spin polarization into a semiconductor is crucial for application at high temperatures, but half-metallic materials such as Fe₃O₄ and CrO₂ (for example) and diluted magnetic semiconductors cannot yet be used in spintronic devices. Therefore, it is important to find new materials with high spin polarization. In general, magnetic elements have been doped into semiconductors to produce spin-polarized carriers. However, the following question remains: if nonmagnetic elements are doped into antiferromagnetic oxide insulators, can high-spin polarized carriers appear?

Recent research on antiferromagnetic hematite (α-Fe₂O₃) has been stimulated by interest in photoelectrochemical (PEC) performance.^3–7 The interest here is in materials that can be manufactured into spintronic devices and that can capture and store solar energy. This will require the development and engineering of multifunctional materials with excellent characteristics of magnetism, electronics and optics. To realize this goal, α-Fe₂O₃ is of interest because of its unique combination of good chemical stability under harsh conditions, low cost, photocatalytic stability, nontoxicity, environmental inertness and a band gap of 1.9–2.2 eV, which allows it to absorb a significant amount of the solar spectrum.^8–11 In addition, α-Fe₂O₃ is also a very promising material in the fields of catalysts, pigments, magnetic materials, gas sensors, and lithium-ion batteries.^12–14 Although α-Fe₂O₃ exhibits potentially good PEC performance, it does have the following drawbacks: a low absorption coefficient, poor conductivity, and high electron–hole recombination rate due to short hole diffusion length.^15–17 A great number of experimental results have been reported on the PEC performance of α-Fe₂O₃ with dopants, such as Zn,^18,19 Al,²⁰ Ti and Si^8,21–23etc. Transition metal doped α-Fe₂O₃ may be potentially applicable to spintronic and PEC applications and this warrants investigation of the spin-polarized characteristics and PEC performance of these materials.

In this paper, the electronic structure and optical properties of α-FeMO₃ systems (M = Sc, Ti, V, Cr Cu, Cd and In) have been systematically investigated by using a local spin density approximation with Hubbard-U corrections (LSDA + U) based on density functional theory (DFT). The following two conclusions are gained: (1) When the impurities are introduced into α-Fe₂O₃, its band structure is modified. In particular, the conductivity of α-FeMO₃ (M = Cu, Cd) is improved since we predict these materials to have half-metallic characteristics; this can lead to significantly enhanced photocurrents and light response. (2) The absorption coefficient is improved. For M = Cu and Cd, the absorption coefficient is noticeably enhanced in the visible range. In addition, the incorporation of Sc, Ti, V and Cr shifts the associated absorption spectra to the low-energy range and enhances the absorption coefficient.

2. Calculation details and model

All spin-polarized calculations in this work were performed with ultrasoft pseudopotentials (USPP) as implemented in the Cambridge Serial Total Energy Package (CASTEP) code,²⁴ a plane wave DFT code. Exchange–correlation was treated using the local density approximation (LDA), as parameterized by the Ceperley and Alder-Pedew and Zunger (CA-PZ) functional and strong correlation effects were introduced by means of the LSDA + U scheme. Although the LDA method has some drawbacks, as mentioned in other DFT studies,^25,26 for α-Fe₂O₃, LDA + U gives reasonable results, as shown in another study.⁵ The LDA + U method requires fewer computing resources compared to other approaches to strong correlation. The interactions between valence electrons and ion cores were represented by Vanderbilt-type USPP.²⁷ The valence-electron configuration of O and Fe was chosen as 2s²2p⁴, 3d⁶4s², respectively. A cutoff energy of 380 eV was used along with a 3 × 3 × 1 k-mesh according to the Monkhorst–Pack grid²⁸ for Brillouin zone sampling. The density of states (DOS) were calculated with a 6 × 6 × 2 k-point mesh. The lattice parameters and the atomic coordinates were fully relaxed without any restrictions using the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method.²⁹ In the optimization process, the energy changes as well as maximum tolerances of the force, stress, and displacement were set as 5 × 10⁻⁶ eV atom⁻¹, 0.01 eV Å⁻¹, 0.02 GPa and 5 × 10⁻⁴ Å, respectively.

Hematite has a band gap of 1.9–2.2 eV,³⁰ which allows visible light absorption up to ∼600 nm. It is well known that pure α-Fe₂O₃ has a hexagonal corundum-type structure with a space group of R3̄c (167) at ambient conditions. The hexagonal unit cell has the lattice constants of a = b = 5.0356 Å, c = 13.7489 Å at room temperature,³¹ which contains six Fe₂O₃ formula units including 12 Fe atoms and 18 O atoms. Below the Néel temperature of 953 K, α-Fe₂O₃ is an antiferromagnetic (AFM) insulator.^32,33 Each layer of Fe atoms is separated by a plane of O atoms. The intralayer coupling between the Fe atoms within the same layer is ferromagnetic, but the interlayer coupling between the adjacent Fe layers is AFM.³⁴ The Fe centers are 3d⁵ with a distorted octahedral local environment that produces a high-spin crystal field splitting.^35,36 The experimentally-measured magnetic moment of individual Fe atoms in α-Fe₂O₃ is 4.6–4.9 μ_B.³⁷ However, the magnetic moment of each Fe atom is predicted to be 3.96 μ_B in this study. Compared with other theoretical calculations,^36,38,39 our calculated magnetic moment of the individual Fe atoms is in close agreement. This give us confidence that the chosen k-points mesh is sufficient, and in order to compare the change of the properties after introducing M-atoms into the alpha-Fe₂O₃ lattice, the same k-mesh is applied. Convergence of the magnetic moments for the magnetic systems in this study with respect to k-mesh was not pursued; further details may be found in DFT studies of other magnetic compounds.^40,41

In this study, we account for the strong correlation of Fe d bands, and the inadequate DFT description of the strong coulomb interaction between the 3d electrons localized on metal ions, using the LSDA + U approach (Dudarev DFT + U method)^42,43 with U = 8 eV for the d bands of Fe and doped metal. For the Fe 3d states, U = 5–6 eV is appropriate for the Vienna ab initio simulation package (VASP). However, due to the difference between USPP (employed in the present study) and projector augmented wave (PAW) potentials in VASP: the larger value of U is required by CASTEP. As discussed in Shang et.al.,⁴⁴ it is common practice to compute the U based upon some previously known property of the material. Following this, we find that the calculated bandgap and magnetic moment are in reasonable agreement with existing theoretical results when U = 8 eV is adopted.^5,34,39 The calculated band gap of α-Fe₂O₃ is 2.19 eV, which is in close accord with the experiment value of 2.2 eV. The AFM ordering in α-Fe₂O₃ is important to obtain the ground state electronic structure, and it is recognized that the energy of the AFM ground state is lowest for α-Fe₂O₃.³⁹ Therefore, we choose this ground state as our starting point. To simulate the layer-by-layer AFM order along the z-axis observed in α-Fe₂O₃, a hexagonal representation of the unit cell containing 12 Fe atoms and 18 O atoms is constructed to simulate the magnetic structure. For α-FeMO₃ systems, all of the spin-up Fe atoms are substituted by transitional metal atoms, including Sc, Ti, V, Cr, Cu, Cd and In, which correspond to 50% substitution at the Fe sites, as shown in Fig. 1. The calculations on the partial substitutions of M for spin up and/or spin down Fe ions will be considered in future work, following the procedure detailed for XLi₃N₂ compounds.⁴⁵ Following the structural optimization and total energy calculations, the formation energy (E_f) of the α-FeMO₃ systems is defined as follows: E_f = E_tot(α-FeMO₃) − E_tot(α-Fe₂O₃) + μ(Fe) − μ(M) where E_tot(α-FeMO₃) is total energy of an α-FeMO₃ system, and E_tot(α-Fe₂O₃) is total energy of pure α-Fe₂O₃. The chemical potentials of Fe and M atoms (M = Sc, Ti, V, Cr Cu, Cd and In) are μ(Fe) and μ(M), respectively. The chemical potentials of Fe and M are taken as the energy per atom in bulk metallic Fe and M, respectively. Thus, for all of the cases, the calculated negative formation energies E_f , listed in Table 1, indicate that all of the α-FeMO₃ systems are thermodynamically stable based upon electronic energies.

Fig. 1 A hexagonal hematite unit cell with AFM ordering labeled by different colors at Fe sites. The grey-blue and orange spheres represent the spin-down and spin-up Fe atoms, respectively. The red spheres are oxygen atoms. All of the spin-up Fe atoms are substituted by metal impurities (M = Sc, Ti, V, Cr Cu, Cd and In).

Table 1 The calculated average magnetic moment (μ_B) of the hexagonal unit cell and per atom of Fe, O and doptants. E_f is the formation energy of the calculated cases and its unit is eV (formula unit)⁻¹. The negative sign represents the orientation of the magnetic moment opposite to that of the magnetic moment on the replaced spin-up Fe (5 μ_B) ions

System	pure	Sc	Ti	V	Cr	Cu	Cd	In
Total	0	−30	−24	−18	−12	−18	−24	−30
Fe	±3.96	−4.2	−3.79	−4.04	−4.1	−3.72	−3.68	−4.16
O	0	−0.24	−0.002	−0.34	−0.4	0.12	−0.08	−0.26
Dopant	—	−0.04	−0.07	2.06	3.3	0.36	−0.06	−0.04
E f	0	−4	−3.33	−0.18	−1.03	−1.37	−3.5	−6.47

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Regarding the optical properties of interest in this study, the imaginary part ε₂(w) and the real part ε₁(w) of the complex dielectric function ε(w) = ε₁(w) + iε₂(w) were calculated based on DFT. The real part ε₁ and imaginary part ε₂ of the dielectric function follow from the Kramers–Kronig relationship.^46,47 The spectra resulting from excitations can be thought of as a joint density of states (DOS) between the conduction and valence bands. The imaginary part (ε₂(ω)) of the dielectric function can be written as

where u is the vector defining the polarization of the incident electric field; k is the reciprocal lattice vector; the superscripts c and v represent the conduction band and valence band, respectively; and ω is the frequency of the incident photon. The other optical spectra, such as absorption coefficient α(w), reflectivity R(w), refractivity index n(w), and energy-loss L(w) can be computed from ε₁(w) and ε₂(w)⁴⁸ using the following relations:

L(w) = ε₂(w)/[ε²₁(w) + ε²₂(w)] (5)

3. Results and discussions

3.1. Electronic structure

The calculated band structure, total density of states (TDOS) and partial density of states (PDOS) of pure α-Fe₂O₃ are shown in Fig. 2. From the band structure, the insulating nature of pure α-Fe₂O₃ is reproduced. The calculated band gap is about 2.19 eV, which is consistent with the experimental value of 2.2 eV obtained at room temperature^8,15 as well as the value computed in another theoretical study.⁵ In addition, one can deduce from the symmetric TDOS and asymmetric PDOS of the spin-up Fe atoms that pure α-Fe₂O₃ is an antiferromagnetic insulator, which is consistent with other calculations, such as GGA + U⁵, and GGA-PW91.⁴⁹ Also, from the asymmetry between the spin-up and the spin-down PDOS of the spin-up Fe atoms (shown in the bottom panel of Fig. 2), the calculated magnetic moment per Fe atom is 3.96 μ_B, which is smaller than the experimental value (4.6–4.9 μ_B) obtained at 77 K by neutron diffraction.³⁷ The calculated magnetic moment per Fe atom calculated by using GGA is 3.4 μ_B.³⁹ Simultaneously, the hybridization between the O-2p and Fe-3d states takes place over the whole band. It is also found from the DOS that the valence band mainly consists of the O-2p and Fe-3d states with a bandwidth of 11 eV. The lowest energy region of the valence band from −20.7 to −17.7 eV is from the occupied O-s states, and the upper valence band to the Fermi energy from −7 to 0 eV contains the occupied O-2p states and a minor presence of the occupied Fe-3d states. The region above the band gap mainly contains the unoccupied Fe-3d states and a contribution from the O-2p states. Thus, the valence band maximum (VBM) is mainly from the O-2p bands and the conduction band minimum (CBM) is mainly from the Fe-3d bands, which is consistent with experiments^50,51 and theoretical results based upon the hybrid functional B3LYP,²³ which show that pure α-Fe₂O₃ is a charge-transfer insulator.

Fig. 2 The calculated band structure, total and partial DOS of α-Fe₂O₃. The Fermi level is set to zero. Up/down arrows stand for the spin-up/spin-down channel. The 3d PDOS of the single spin-up Fe atom is given in the bottom figure.

Substitution of Cu and Cd into α-Fe₂O₃ leads to a half-metallic band structure of these materials. Here, the spin-up channel is semiconducting and spin-down channel is metallic, as shown in Fig. 3(a) and (b) for the Cu- and Cd-containing materials, respectively. In both cases, the TDOS results clearly indicate that there is a value of DOS at the Fermi level in the spin-down channel whereas it is zero in the spin-up channel. Only the DOS of spin-down electrons passes through the Fermi level into the conduction bands, implying that the spin polarization of the conduction carriers is 100%. Due to the introduction of Cu and Cd, the symmetry of the crystal field surrounding each atom is broken, leading to split O-2p and Fe-3d levels into asymmetric states. From the PDOS, when Cu is added, Cu (3d¹⁰4s¹) donates one s and one d electron to the surrounding O atoms, leaving nine d electrons on the Cu site. Acceptor states are induced above the VBM of α-Fe₂O₃. The spin-down O-2p state extends toward higher energies. The O-2p states dominate the DOS near the Fermi level with a small contribution from Cu-3d and Fe-3d states. In the spin-down channel, the Cu-3d states overlap with the O-2p states at the Fermi level, suggesting that there is a hybridization between the Cu-3d and O-2p states. In the spin-up channel, Fe-3d and O-2p are responsible for the unoccupied states above the Fermi level. The bottom of the conduction band is mainly occupied by Fe-3d states and a minor amount of O-2p states. The topmost level of the valence band is mainly from spin-down O-2p states. For α-FeCdO₃, similar results are gained despite the absence of acceptor states induced by Cd. However, for α-FeInO₃, no half-metallic character is predicted, but the spin-down band gap is reduced to about 0.98 eV, which would be beneficial for the enhancement of the conductivity, as shown in Fig. 3(c). By introducing Cu and Cd into α-Fe₂O₃, the electrical conductivity is enhanced due to the half-metallic character, which is beneficial for hindering the recombination of the electron–hole pair and extending the life of carriers. The half-metallic characteristics make this system potentially useful in spintronic devices and suggest that attempts at synthesis are warranted.

Fig. 3 LSDA + U calculated total and partial DOS of α-FeMO₃, M = (a) Cu, (b) Cd and (c) In. The Fermi level is set to zero. Up/down arrows stand for the spin-up/spin-down channel.

The electronic structure of α-FeMO₃ (M = Sc, Ti, V, Cr) is also calculated, as shown in Fig. 4. It is found that the results are different from the Cu and Cd-added cases. For the Sc, Ti, V, Cr-doped cases, the systems are predicted to be insulating in both the spin-up and spin-down channels. However, the TDOS and PDOS of the spin-up and spin-down channels are asymmetric. Therefore, all of the cases are ferromagnetic. The magnetic moments of the unit cell and individual atoms of the α-FeMO₃ systems (M = Sc, Ti, V, Cr) systems have been given in Table 1. It is clear that the maximum moment is from α-FeScO₃, and the minimum moment is from α-FeCrO₃.

Fig. 4 Total and partial DOS of α-FeMO₃, M = (a) Sc, (b) Ti, (c) V and (d) Cr. Herewith, U is 8 eV. The Fermi level is set to zero. Up/downs arrow stand for the spin-up/spin-down channel.

The calculated DOS of α-FeScO₃ is depicted in Fig. 4(a). A Sc³⁺ ion at a Fe³⁺ site loses its three valence electrons, which forms a closed shell electronic d⁰ configuration. Thus, Sc³⁺ ions are theoretically predicted to have no net magnetic moment, while the replaced Fe atom has a formal Fe³⁺ ionization state with a nominal local magnetic moment of 5 μ_B. In fact, a single Sc³⁺ ion has a small magnetic moment of −0.04 μ_B and each Fe³⁺ ion has a magnetic moment of −4.2 μ_B from our calculations. The net magnetic moment of the system is −30 μ_B, opposite to that of the spin-up substituted Fe atom. The band gaps are 2.3 eV and 4.85 eV for the spin-up and spin-down channels, respectively. The CBM of α-FeScO₃ has almost no change and the Fe-3d state still dominates. The Sc-3d states are positioned at higher energies. This suggests that the heavy effective mass for electrons remains unchanged and Sc substituted into α-Fe₂O₃ will not enhance the initial electronic conductivity.

For α-FeTiO₃, the calculated DOS is shown in Fig. 4(b). We find that Ti (3d²4s²) loses its four valence electrons, yielding a Ti⁴⁺ state and a surplus electron. Due to the relatively weak electronegativity, the surplus electron isn't trapped on the Ti center but it is localized at Fe sites. Therefore, the surplus electron has almost no effect on the conductivity, which is consistent with previous results.^23,34 Although the Ti⁴⁺ ion has no magnetic moment due to its closed shell electronic configuration, its calculated magnetic moment of Ti⁴⁺ is −0.07 μ_B (replacing a spin-up Fe³⁺ ion of 5 μ_B). Each Fe atom has a magnetic moment of −3.79 μ_B. Thus, the total magnetic moment of the α-FeTiO₃ unit cell is −24 μ_B, opposite to that of the replaced Fe. Electrically, α-FeTiO₃ is an insulator. The band gaps are 2.8 and 2.4 eV for the spin-up and spin-down channels, respectively. Compared with α-Fe₂O₃, Ti introduction makes the Ti-3d state into the CBM and decreases the electron effective mass due to the relatively weak localization of the Ti-3d state, which results in a higher mobility of electrons. This result is consistent with the previously reported experimental results^6,21 that the Ti-doping in α-Fe₂O₃ plays a positive role in improving the PEC performance.

When the spin-up Fe atoms are replaced by V, α-FeVO₃ is also predicted to be an insulator in both the spin-up and spin-down channels, as shown in Fig. 4(c). Vanadium (3d³4s²) donates two s electrons and one d electron to the O atoms, leaving two occupied V d levels. In the calculated the DOS, two occupied states are in the spin-up channel below the Fermi level, hybridizing with the O-2p state near the VBM. The unoccupied states fall on the site of the unoccupied Fe-3d state and upper energy states. The spin-up band gap is 1.12 eV, which is much narrower than that of α-Fe₂O₃. Also, a more dispersive CBM is beneficial for improving the carrier mobility to enhance PEC performance. The calculated magnetic moment per V³⁺ ion is 2.06 μ_B and each Fe³⁺ ion has a magnetic moment of −4.04 μ_B. Due to the hybridization of O-2p with the Fe-3d and V-3d states, each O²⁻ ion has a magnetic moment of −0.34 μ_B polarized oppositely to the moment of the replaced spin-up Fe ions. Therefore, α-FeVO₃ has a net moment of −18 μ_B.

In α-FeCrO₃, the behavior depicted in Fig. 4(d) is predicted. It is well known that each Cr atom has six valence electrons that form the electronic configuration of 3d⁵4s¹. By substitution of Cr for the spin-up Fe, Cr (3d⁵4s¹) loses one s electron and two d electrons, and forms a Cr³⁺ charge state. The remaining three filled states fall just below the Fermi energy, hybridizing with the O-2p state in the spin-up channel of the VBM; the unoccupied states fall on the site of unfilled Fe-3d state and upper energy states, as shown in Fig. 4(d). Although the system remains an insulator, its CBM is more dispersive than that of α-Fe₂O₃ and the spin-up band gap is 1.45 eV, which is much smaller than that of α-Fe₂O₃. This reduction may enhance the conductivity due to improved carrier mobility.³⁴ The Cr³⁺ ion has a magnetic moment of 3.3 μ_B and each Fe³⁺ ion has a magnetic moment of −4.1 μ_B. As mentioned above, owing to the exchange interaction among the O-2p with the Fe-3d and Cr-3d states, each O²⁻ ion has a magnetic moment of −0.4 μ_B. Thus, α-FeCrO₃ has a net moment of −12 μ_B, which is opposite to the moment of the replaced Fe.

After introducing M (M = Cu, Cd, In, Sc, Ti, V, and Cr) into α-Fe₂O₃, the electronic structure of α-FeMO₃ shows some surprising changes, such as the emergence of half-metallic character and a large net magnetic moment. In particular, the systems with M = Cu and Cd show half-metallic character and p-type conductivity, improving the conductivity to suppress the recombination of electron–hole pairs and promoting the chance for the carriers to participate in a photo-oxidation reaction. Although no half-metallic behavior appears for M = Sc, Ti, V and Cr, these systems display a ferromagnetic insulating ground state, which is consistent with other theoretical results.⁵² Furthermore, for α-FeMO₃, the calculated negative formation energies E_f detailed in Table 1 indicate that α-FeMO₃ systems are thermodynamically stable. While the DFT prediction that α-FeMO₃ systems are thermodynamically stable is intriguing, they will ultimately require experimental corroboration. The importance of experimental validation of hypothetical structures predicted with DFT is discussed in detail by Hector and Herbst.⁵³

3.2. Optical properties

Due to the potential application in PEC and other optical devices, it is important to investigate the optical properties of α-FeMO₃ (M = Sc, Ti, V, Cr, Cu, Cd and In). For this purpose, it is necessary to calculate the complex dielectric function, ε = ε₁(w) + iε₂(w). According to the Kramers–Kronig relationship between the real part ε₁(w) and imaginary part ε₂(w), the real part is evaluated from the imaginary part.⁵⁴

The calculated ε₂(w) values of α-FeMO₃ are shown in Fig. 5. For α-Fe₂O₃, two peaks can be observed. The P₁ peak at 3.22 eV results from the electron transition from the O-2p state into the VBM and Fe-3d states in the CBM; the broader P₂ peak at 11.45 eV likely arises from the transition between the deeper valence band and conduction band. After introducing Cu and Cd into α-Fe₂O₃, a new peak appears at a lower energy of 0.255 eV. This new peak can be attributed to the electron transition from the occupied O-2p states near the Fermi level into unoccupied states, which is consistent with its half-metallic character. Additionally, the P₁ peak of α-FeCuO₃ and α-FeCdO₃ shifts to 3.05 and 4.03 eV, respectively, which is consistent with the change of band gap in the spin-up channel. However, the new peak at a lower energy is not observed in α-FeInO₃, but it is observed that the P₁ peak shifts to a higher energy due to a larger band gap in the spin-up channel. Furthermore, the calculated ε₂(w) of α-FeMO₃ (M = Sc, Ti, V, Cr) around the P₁ and P₂ peaks are almost similar, which is a result of their similar band structures and density of states. Moreover, the single P₁ peak of α-FeMO₃ (M = Sc, V, Cr) emerges into double peaks, which correspond to the difference of the band gap between the spin-up and spin-down channels. Meanwhile, for M = Sc, Ti, V, Cr, the P₂ peak gradually moves to a higher energy and the intensity of the P₂ peak is gradually weakened. However, compared with α-Fe₂O₃, the intensity of the P₂ peak is enhanced.

Fig. 5 The imaginary part ε₂(w) of the dielectric function of α-FeMO₃ with M = Cu, Cd, In, Sc, Ti, V and Cr.

Fig. 6 shows the optical absorption spectra of all α-FeMO₃ systems considered in this study. It is clear that the absorption region of the systems with M = Cu and Cd is very wide, and the main absorption part still locates in the ultraviolet (UV) (i.e. short wavelength) region of the visible region. Compared with the absorption spectra of α-Fe₂O₃, the absorption edges of the systems with M = Cu and Cd shift toward the longer wavelength region, which can be attributed to the appearance of half-metallic character. Moreover, multiple peaks appear in the absorption spectra of the systems with M = Cu and Cd. The absorption intensity of the systems with M = Sc, Ti, V and Cr is significantly enhanced, which indicates that substitution of these constituents may improve the PEC performance and enhance the utilization of solar energy in the resulting α-FeMO₃ materials. Furthermore, the absorption edges of α-FeMO₃ systems without M = Cu and Cd shift toward shorter wavelengths, which is consistent with the band gap becoming wider than that of pure α-Fe₂O₃. Especially in the absorption spectra of α-FeMO₃ with M = Sc, Ti, V and Cr, some sharpened absorption peaks appear in the 29–40 nm range. The appearance of these peaks in the short wavelength region suggests that the utilization of UV light is significantly improved.

Fig. 6 Optical absorption spectra of calculated for various types of α-FeMO₃ with M = Cu, Cd, In, Sc, Ti, V and Cr.

Fig. 7–9 show, respectively, the reflectivity R(w), refractive index n(w), and energy-loss function L(w) spectra of the α-FeMO₃ systems. For α-FeMO₃ (M = Sc, Ti, V and Cr) in a photon energy range of 0–13 eV, the reflectivity and refractivity display an opposite trend. The low energy range of 0–3 eV is characterized by small reflectivity and the strongest refractivity, while in the 3–13 eV range, the refractivity goes through a change from the strongest to the weakest, and the reflectivity reaches the strongest value at ∼12.5 eV. In a photon energy range of 34–47 eV, the reflectivity and refractivity of α-FeMO₃ (M = Sc, Ti, V and Cr) have the second strongest peak and a change from the second strongest one to the second weakest one, respectively. The energy loss function describes the energy loss of the electrons traversing the materials. The sharp peaks located at 12–13 and 34, 39, 42, 46 eV also correspond to the trend of the reflectivity spectrum. With M = Cu and Cd, the reflectivity and refractivity show a decreasing trend with increasing energy in the whole region. However, the reflectivity and refractivity spectra of α-Fe₂O₃ and α-FeInO₃ show an increase then a gradual decrease with an obvious peak.

Fig. 7 Reflectivity R(w) of α-FeMO₃ with M = Cu, Cd, In, Sc, Ti, V and Cr.

Fig. 8 Refractivity index n(w) of α-FeMO₃ with M = Cu, Cd, In, Sc, Ti, V and Cr to the photon energy.

Fig. 9 Energy-loss functions L(w) of α-FeMO₃ with M = Cu, Cd, In, Sc, Ti, V and Cr.

Although much experimental work has been carried out on improving the PEC performance by doping, few reports show the results from a systematic theoretical study of relevant optical properties. In this study, the optical properties of α-FeMO₃ have been systematically investigated, including absorption coefficient α(w), reflectivity R(w), refractivity index n(w), and energy-loss L(w). For systems with M = Cu and Cd, the enhancement of conductivity and strong absorption in the visible region suggests potential improvements in PEC performance, such as increasing the carrier concentration, suppressing electron–hole recombination and improving the utilization of solar energy. For α-FeTiO₃, the enhanced absorption coefficient may be beneficial for improving the PEC performance, which is consistent with the experimental results.^6,21 In addition, for M = Sc, V, and Cr, the strongest peaks are observed in the short wavelength region of the absorption spectra.

4. Conclusion

First-principle calculations were performed to study the electronic structure and optical properties of α-FeMO₃ systems. Most of the substituted elements can be viewed as cations with a three valence electron configuration substituting for Fe³⁺ in the α-Fe₂O₃ lattice except Cu²⁺, Cd²⁺ and Ti⁴⁺. The systems with M = Cu and Cd are p-type, display a half-metallic character, and hold promise for enhancing the electrical conductivity of these materials and extending the life of carriers. The absorption peaks in the visible light region are enhanced in α-FeMO₃ systems with M = Cu and Cd. In the systems with M = Sc, Ti, V and Cr, the absorption spectra indicate that the strong absorption peaks shift toward the short wavelength region. A large magnetic moment appears in each α-FeMO₃ material. We conclude that transition metal doping is an effective way of improving the electronic structure and optical properties of α-FeMO₃ systems.

Acknowledgements

This work was supported by National Natural Science Foundation of China (51171126) and the Key Project of the Natural Science Foundation of Tianjin City (12JCZDJC27100).

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