Using first-principles calculations, we investigate the magnetic order in the ground state of several ternary chromium chalcogenide compounds. Electronic band structure calculations indicate that these compounds are either metallic or semiconductors with relatively low bandgap energies. The large optical absorption coefficients, predicted by our calculations, suggest that some of these compounds may be useful as light harvesters in solar cells or as infrared detectors.
National Science FoundationHRD-15477723DMR-152358851. Introduction
Ternary compounds of the form ABX3, where A and B are metal atoms and X is a halogen or a chalcogen, are exciting candidates as semiconductors for photovoltaics and other applications. These materials are highly tunable due to the large variety of possible elements that can be included. In addition to tunability, their low cost, facile synthesis, and long carrier lifetimes have gained the attention of the research community [1–3]. In particular, perovskite solar cells made from lead halide materials (APbX3) have enjoyed rapid development, with measured power conversion efficiencies rivaling state-of-the-art silicon devices [4–7]. As a result, there is interest in commercial application of lead-halide perovskites for photovoltaics; however, concerns regarding the toxicity of lead and high instability in the presence of moisture have hindered these efforts [2]. Thus, it would be of great interest to find materials with better stability and nontoxic composition, while still keeping the attractive properties of these lead-halide compounds.
Recently, ternary metal chalcogenide materials have been proposed as alternatives to these lead-halide perovskites [8, 9]. Materials of the form ABO3 have been extensively studied and have been shown to be resilient in the presence of moisture [8, 10]. Unfortunately, the energy difference between transition metal d orbitals and the 2p orbitals of oxygen results in a large bandgap; in fact, BiFeO_{3}, with a bandgap of 2.7 eV, has the lowest bandgap among this class of materials [10]. Solid solutions have been reported with bandgaps between 1.1 and 3.8 eV [8]; however, these materials have high intrinsic disorder.
To lower the bandgap of these ABO3 materials, substitution of oxygen with chalcogens such as sulfur or selenium has been recently explored. Although reports of synthesis of these ternary transition metal chalcogenides have been around for a long time [11], there are still few studies focusing on their optoelectronic properties. Theoretical studies have been reported on substitution of oxygen with sulfur [12, 13]. Additionally, experimental reactions of perovskite oxides with gaseous H_{2}S or CS_{2} [14], as well as solid-state reactions have been recently reported as methods of substituting oxygen with sulfur [15, 16]. It has been shown that transition metal chalcogenides are widely tunable, ranging from metallic to semiconducting with gaps exceeding 2 eV [9, 16]. Several materials are predicted to have bandgaps corresponding to theoretical photovoltaic power conversion efficiencies above 28 percent [9], and zirconium sulfide perovskites have been experimentally measured to have strong optical absorption and a bandgap suitable for photovoltaic applications [16].
One interesting subset of these ternary transition metal chalcogenides are those of the form ACrX3, where X = S, Se, or Te. Because of the presence of chromium, these materials tend to exhibit magnetic properties and have recently seen a resurgence of interest [17, 18]. Several of these materials, such as SbCrS_{3} [19], SbCrSe_{3} [18–20], and SiCrTe_{3} [21, 22], have been the subjects of recent experimental studies as magnetic materials with metallic or semiconducting behavior. However, many of these materials, including many of the lanthanide chromium sulfides, have not been thoroughly studied even though their syntheses have been reported a long time ago [11].
In this work, we present first-principles calculations on some chromium chalcogenides where experimentally determined crystal data are available, but electronic or magnetic properties have not been thoroughly investigated. Using total energy calculations, we determine the ground-state magnetic ordering at 0 K and then calculate optoelectronic properties to determine their usefulness in various applications.
With the exception of PCrSe_{3} and SiCrTe_{3}, all the structures examined have the space group 62 (Pnma) and they adopt the NH_{4}CdCl_{3} prototype structure. This structure contains dimers of CrX6 (X = S, Se, or Te) octahedra and ninefold coordination between the A site and the chalcogen atoms. Unlike the perovskite structure, which contains corner-sharing octahedra [23, 24], the octahedra in this structure share edges, as shown in Figure 1.
Visualization of the unit cell of the NH_{4}CdCl_{3} prototype structure, which contains edge-sharing octahedra.
The structure of PCrSe_{3} is monoclinic with space group 12 (C2/m). This structure contains layers of a single P atom surrounded by six CrSe_{6} octahedra in the ab plane, as pictured in Figure 2.
Visualization of the unit cell of PCrSe_{3}.
The structure of SiCrTe_{3} is rhombohedral with space group 148 (R3¯) and is shown in Figure 3. In this structure, edge-sharing CrTe_{6} octahedra form layers on the ab plane, while the Si atoms have threefold coordination with the Te atoms.
Visualization of the unit cell of SiCrTe_{3}.
2. Methods
To determine the ground-state magnetic ordering of the chromium chalcogenides, we used density functional theory (DFT) as implemented in the Vienna Ab Initio Simulation Package (VASP) [25–28] code, which uses the projector-augmented wave (PAW) pseudopotentials and a plane-wave basis set to expand the electronic wave function. The Perdew–Burke–Ernzerhof implementation of the generalized gradient approximation (PBE–GGA) was used to model the exchange-correlation effects [29, 30]. We performed spin-polarized calculations, where varying spin orderings were imposed on the chromium ions. A Hubbard on-site Coulomb term (U = 4 eV) and Hund’s exchange term (J = 0.7 eV) for the chromium ions are included in the calculation. Experimentally determined crystal structures from the Inorganic Crystal Structure Database were used in our calculations, with the exception of SiCrTe_{3}, where the X-ray diffraction measurements at 292 K of Casto et al. were used [21]. The total energies of different magnetic orders were compared to determine the ground state.
The electronic band structures, density of states, and optical properties were calculated using the full-potential, linearized, augmented plane wave (FP–LAPW) method, as implemented in the WIEN2k code [31]. Here, space is divided into an interior region of nonoverlapping muffin tin spheres centered on each atom and an exterior region comprising the interstitial space between these spheres. Within the spheres, the electronic wave function is treated as atomic like, with an expansion in spherical harmonics up to ℓmax=10. Within the interstitial space, the wave function is expanded in plane waves, with a maximum wave vector of kmax. The maximum wave vector is determined by setting Rmtkmax=8, where Rmt is the radius of the smallest sphere. The charge density is Fourier expanded up to a maximum wave vector of 14/a0, where a0 is the Bohr radius. On-site Coulomb interaction was taken into account, using the same U and J values from the VASP total energy calculation. We performed self-consistent field calculation until energy convergence within 10−4 Ry and charge convergence within 10−3e were achieved. The calculations were spin polarized, and we used the magnetic order in the ground state which was determined in the VASP calculation.
The optical properties of the chromium chalcogenides were calculated using the wave functions obtained from the electronic calculation. Specifically, the imaginary part of the dielectric function ε2ω was obtained using the following momentum matrix elements [32]:(1)ε2ω=Vcelle22πℏm2ω2∫d3k∑nn′knpkn′2×fkn1−fkn′δEkn−Ekn′−ℏω,where p is the momentum operator, kn is a crystal wave function with energy eigenvalue Ekn, ℏω is the photon energy, and f is the Fermi-Dirac distribution function. A Kramers–Kronig transformation was used to obtain the real part of the dielectric function ε1ω, and the absorption coefficient αω was calculated as(2)αω=2ωε1ω2+ε2w2−ε1ω1/2.
3. Results and Discussion
The energies of different magnetic structures for the chromium chalcogenides studied are listed in Table 1. Here, A-type antiferromagnetism (A-AFM) denotes ferromagnetism within the ac plane and antiferromagnetism between planes, C-type antiferromagnetism (C-AFM) denotes ferromagnetism between planes and antiferromagnetism within the plane, and G-type antiferromagnetism (G-AFM) denotes antiferromagnetism both within and between planes. Experimental results have shown that most of these materials, such as SbCrS_{3} [19], SbCrSe_{3} [18], and SiCrTe_{3} [21], have magnetic order at low temperatures but are paramagnetic at room temperature. The predicted magnetic structure of SbCrS_{3} [19], SbCrSe_{3} [19], LaCrS_{3} [33], SbCrS_{3} [33], and SiCrTe_{3} [21] agree with experimental measurements. For LaCrSe_{3} and CeCrSe_{3}, there seems to be ambiguity as to whether the structure is antiferromagnetic or weakly ferromagnetic [34], and this is reflected in our calculations by the fact that the energy differences between ferromagnetic and antiferromagnetic states are very small.
Calculated energies (in meV per formula unit) of different magnetic states of the chromium chalcogenides. The energy of the lowest state for each material is set to zero for ease of comparison. For PCrSe_{3}, α=γ=90∘ and β=107.71∘. For SiCrTe_{3}, α=β=γ=50.56∘. For SiCrTe_{3}, each unit cell contains two Cr atoms; hence, there is only one possible antiferromagnetic state.
Crystal
Space group
Lattice constants (Å)
A-AFM
C-AFM
G-AFM
FM
PCrSe_{3}
12 (C2/m)
a=6.15,b=10.59,c=6.69
0
88.50
46.00
27.25
SbCrS_{3}
62 (Pnma)
a=8.67,b=3.62,c=12.87
24.07
3.50
15.20
0
SbCrSe_{3}
62 (Pnma)
a=9.14,b=3.78,c=13.32
41.83
2.42
27.95
0
LaCrS_{3}
62 (Pnma)
a=7.87,b=3.85,c=13.84
12.62
0
6.81
0.43
LaCrSe_{3}
62 (Pnma)
a=8.11,b=3.96,c=13.79
13.52
5.57
0
9.29
CeCrS_{3}
62 (Pnma)
a=7.76,b=3.79,c=13.16
0
14.93
34.51
13.27
CeCrSe_{3}
62 (Pnma)
a=8.08,b=3.95,c=13.74
12.97
2.20
2.87
0
GaCrSe_{3}
62 (Pnma)
a=10.12,b=3.73,c=12.39
14.66
1.05
13.64
0
SiCrTe_{3}
148 (R3¯)
a=b=c=8.00
39.87
—
—
0
The bandgaps calculated using DFT + U for the chalcogenides are given in Table 2 and compared with experimental results. These compounds range in character from metallic to semiconducting with small gaps, the largest of which is 1.29 eV. Due to the scarcity of experimental studies on these materials, information regarding the bandgaps of most materials is not available; however, we remark that the calculated bandgap values for SbCrSe_{3} and SiCrTe_{3} with our chosen values of U and J are in good agreement with experiment.
Comparison of DFT + U bandgaps with experimental results.
Crystal
Calculated gap (eV)
Experimental gap (eV)
PCrSe_{3}
0
—
SbCrS_{3}
0.98
—
SbCrSe_{3}
0.63
0.6–0.7 [18]
LaCrS_{3}
0.20
—
LaCrSe_{3}
0.07
—
CeCrS_{3}
0
—
CeCrSe_{3}
0
—
GaCrSe_{3}
1.29
—
SiCrTe_{3}
0.40
0.4 [21]
The calculated electronic band structure and density of states of the majority-spin carriers in GaCrSe_{3} and SbCrS_{3} are shown in Figures 4 and 5, respectively. These structures were chosen because their bandgaps are suitable for photovoltaic applications. For GaCrSe_{3}, we find a direct bandgap of 1.29 eV at Γ, while for SbCrSe_{3}, we find a direct bandgap of 1.47 eV at Γ and an indirect bandgap of 0.98 eV corresponding to the Γ⟶T transition. In both of these structures, the density of states near both conduction band and valence band edges are primarily contributed by chromium d orbitals and chalcogenide p orbitals. In GaCrS_{3}, the narrowness of the bands gives rise to high density of states, reaching a maximum of around 20 states/eV above the conduction band. SbCrSe_{3} has a slightly smaller density of states, with a maximum of around 15 states/eV above the conduction band.
Calculated electronic band structure and density of states for GaCrSe_{3}.
Calculated electronic band structure and density of states for SbCrS_{3}.
In addition to the density of states, we also calculated the optical properties for GaCrSe_{3} and SbCrS_{3}, as well as CrSiTe_{3} and SbCrSe_{3}, which were found to be narrow-gap semiconductors. The absorption curves, shown in Figure 6, agree with the bandgap values calculated for these chalcogenides. From this figure, we see that they exhibit strong absorption (>105 cm^{−1}) in the infrared and visible regions, suggesting that these materials may be of interest for photovoltaic applications. These large values for the absorption coefficients are comparable to those measured in Zr-based chalcogenides [16]. Additionally, absorption coefficients larger than 105 cm^{−1} are observed at significantly lower energies than that of pure silicon, which is the industry standard for photovoltaics. Silicon does not achieve such a value for the absorption coefficient until a photon energy of approximately 3 eV is reached [35]; on the contrary, we observe that SbCrS_{3} and GaCrSe_{3}, with comparable bandgaps to silicon, achieve this value at 1.5 eV and 2 eV, respectively. This would allow for better capture of light in the near-infrared and visible ranges. The narrow bandgap SbCrSe_{3} and SiCrTe_{3} may be useful for infrared detection applications, while SbCrS_{3} and GaCrSe_{3} may be possible candidates for use as light absorbers in photovoltaics.
Calculated optical absorption spectra for semiconductor chromium chalcogenides.
4. Conclusion
In conclusion, we have carried out density functional theory calculations on various chromium chalcogenide materials. We have demonstrated that calculations within the DFT + U scheme accurately predict the magnetic structure and energy gaps of this class of materials. We have identified two materials, namely, GaCrSe_{3} and SbCrS_{3}, whose bandgaps and strong optical absorption make them candidates for use in photovoltaics, as well as the narrow-gap semiconductors SbCrSe_{3} and SiCrTe_{3}, which may be of interest for infrared detection applications.
Data Availability
No supporting information is available.
Conflicts of Interest
The authors declare no conflicts of interest.
Acknowledgments
This work was supported by the National Science Foundation under grant HRD-15477723 and grant DMR-15235885.
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