Two-Dimensional Magnetic Semiconductor in Feroxyhyte - ACS

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Two-Dimensional Magnetic Semiconductor in Feroxyhyte Imran Khan,† Arqum Hashmi,‡ M. Umar Farooq,† and Jisang Hong*,† †

Department of Physics, Pukyong National University, Busan 608-737, Korea Center for Computational Sciences, University of Tsukuba, Tsukuba 305-8577, Japan

‡

ABSTRACT: A few years ago, it was claimed that the twodimensional (2D) feroxyhyte (δ-FeOOH) layer could possess a net magnetic moment and it could be applied for potential spintronics applications because it showed a band gap. However, the exact crystal structure is still unknown. Hereby, we investigate the crystal structure, electronic band structure, and magnetic and optical properties of 2D δ-FeOOH using density functional calculations. On the basis of the experimental observation and dynamical stability calculations, we propose that the 2D δ-FeOOH originates from bulk Fe(OH)2 via oxidation. A perfect antiferromagnetic ground state was observed in the monolayer structure with an indirect band gap of 2.4 eV. On the other hand, the bilayer structure displayed a direct band gap of 0.87 eV, and we obtained a ferrimagnetic state. The net magnetic moment in the bilayer was 1.49 μB per cell. The interlayer distance and film thickness in bilayer δ-FeOOH were 1.68 and 7.37 Å, respectively. This interlayer distance was suppressed to 1.47 Å in a trilayer system, and the band gap of 1.6 eV was found. The trilayer δ-FeOOH had a film thickness of 11.57 Å, and this is comparable to the experimental thickness of 12 Å. To compare with the experimental band gap of 2.2 eV obtained from a UV−visible optical spectrum measurement, we also calculated the absorption spectra, and the onset of the absorption peak in the monolayer, bilayer, and trilayer appeared at 3.2, 2.8, and 2.2 eV, respectively. Overall, considering the magnetic state, optical absorption, and film thickness, we propose that the trilayer structure agrees with the experimentally synthesized structure. KEYWORDS: 2D material, feroxyhyte, magnetic semiconductor, ferrimagnetism, optical properties

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find an intrinsic magnetic 2D material, particularly with a band gap. Then, this can be utilized for potential spintronic applications. Very recently, Huang et al. reported layerdependent ferromagnetism in 2D semiconducting chromium triiodide.20,21 In addition, an intrinsic long-range FM ordering was also reported in a 2D van der Waals semiconducting Cr2Ge2Te6 crystal.22,23 Besides, it was shown that the monolayers Ti2C and Ti2N could exhibit half-metallic ferromagnetism.24 A few years ago, a transition-metal 2D ultrathin film called feroxyhyte (δ-FeOOH) was experimentally synthesized by a topochemical transformation process at room temperature.25 It was claimed that the ultrathin δ-FeOOH nanosheets could exhibit room-temperature ferromagnetism along with a semiconducting behavior in a thickness range of 1.1−1.3 nm. Using a SQUID magnetometer, a saturation magnetization value of 7.5 emu/g at 300 K was reported. Moreover, Chen et al. proposed that their sample had a direct band gap of 2.2 eV via the UV−visible light spectrum measurement. The X-ray diffraction analysis proposed that δ-FeOOH would have a hexagonal structure with a space group P3̅m1, and the estimated lattice constants were a = b = 2.95 Å. Because of

INTRODUCTION Physical properties of a material are basically determined by its electronic structure, and the electronic structure significantly depends on the dimensionality of the material. Recently, the study of two-dimensional (2D) materials is receiving extensive research interests because of their peculiar electronic structures and potential device applications. Various types of 2D materials have been introduced and investigated. For instance, graphene has excellent optical, thermal, electrical, and mechanical properties.1−4 Because of these outstanding physical properties, it can be utilized for various device applications: sensors, actuators, and field-effect transistors.5−7 Apart from graphene, other 2D materials such as hexagonal boron nitride,8 transitionmetal oxides (ZnO and TiO2),9,10 transition-metal dichalcogenides,11−13 and phosphorene14,15 are also extensively studied for different potential applications. However, most of them are nonmagnetic materials, and this characteristic limits their use for next-generation spin-related device applications. In these nonmagnetic materials, the magnetic state is usually induced by a transition-metal impurity doping, an adsorption, a creation of a vacancy defect, and this usually results in the localized magnetic state, not the long-range ordering magnetism.16−19 Consequently, the localized magnetic state may not participate in the spin-dependent transport phenomenon. For spintronics purposes, it is necessary to maintain a ferromagnetic (FM) state at room temperature. Moreover, it will be highly desirable to © 2017 American Chemical Society

Received: June 13, 2017 Accepted: September 20, 2017 Published: September 20, 2017 35368

DOI: 10.1021/acsami.7b08499 ACS Appl. Mater. Interfaces 2017, 9, 35368−35375

Research Article

ACS Applied Materials & Interfaces

Figure 1. Schematic illustration of (a) side view of St-1, (b) side view of St-2, (c) top view of both structures, and phonon dispersion curves for (d) St-1 and (e) St-2.

the finite band gap with a robust FM state, the 2D δ-FeOOH can be a potential spintronics material. Nonetheless, the explicit crystal structure, thickness-dependent magnetic ground state, electronic band structure, and optical properties are not available yet. Consequently, it will be a very interesting issue to reveal the crystal structure, magnetic ground state, and optical properties of 2D δ-FeOOH. To this end, in this report, we will systematically explore the crystal structure via phonon spectra calculation, magnetic ground state, and optical properties. Here, we will consider monolayer, bilayer, and trilayer structures.

structure, the dynamical stability was calculated by the phonon dispersion curve using the PHONOPY code.31 The force criterion for the ionic step was set to 10−8 eV/Å for the phonon calculations. Force constant matrices used in the phonon calculations were calculated by density functional perturbation theory using the VASP code, through the supercell approach with a 6 × 6 × 1 supercell and 3 × 3 × 1 k-points. The optical properties were calculated from the frequency-dependent dielectric function ε(ω) = ε1(ω) + iε2(ω). The imaginary part of the dielectric function is determined by the following relation

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ε2αβ (ω) =

NUMERICAL METHOD We employed the Vienna ab initio Simulation Package (VASP)26,27 to study various physical properties. The Heyd− Scuseria−Ernzerhof (HSE06) screened hybrid functional28,29 was used to obtain a stable ground structure. This is a rangeseparated hybrid functional which separates the electron− electron interaction into two parts: a short- and a long-ranged part. The slowly decaying long-range part of the Fock exchange interaction is replaced by the corresponding part of the Perdew−Burke−Ernzerhof (PBE) density functional counterpart, whereas the short-range part contains both Hartree−Fock and PBE terms. According to the experimental observation, the 2D δ-FeOOH has a hexagonal structure with lattice constants a = b = 2.95 Å. Thus, we adopted these lattice constants and considered a 2 × 2 supercell to calculate the magnetic ground state. A vacuum distance of more than 15 Å in the z direction was imposed to avoid an artificial interaction from the neighboring unit cell. A plane wave basis set with an energy cutoff of 600 eV was used in our calculations, and all the structures were relaxed until the force on each atom was less than 0.01 eV/Å and the energy convergence reached up to 10−4 eV/atom by using the conjugate gradient method. The selfconsistent calculations were performed with a (5 × 5 × 1) kmesh. For the bilayer and the trilayer, we included the van der Waals interactions. Here, we applied the empirical correction scheme of Grimme (DFT-D2).30 To reveal the stable crystal

4π 2e 2 1 lim ∑ 2ωkδ(εck − εvk − ω) Ω q → 0 q2 c,v, k × uck + eαq|u vkuck + eβq|u v*k

(1)

where c and v represent the conduction and valence band states, k is the wave vector, and uck represents the wavefunction with a periodicity of a lattice constant. The imaginary and the real part of the dielectric function are related with the wellknown Kramers−Kronig relation ε1αβ (ω) = 1 +

2 P π

∫0

∞

ε2αβ (ω′)ω′ ω′2 − ω 2 + iη

dω′

(2)

where P denotes the principle value.32

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NUMERICAL RESULTS Because the exact crystal structure of 2D δ-FeOOH is not known, we investigate the geometry of 2D δ-FeOOH. From the experimental observations, we propose two possible candidates. The first structure (St-1) is made from its bulk parent FeHO2, whereas the second possible structure (St-2) originates from the Fe(OH)2 bulk structure.33,34 Considering the experimental lattice constant of 2.95 Å, the internal coordinates were fully relaxed using VASP with the HSE06 hybrid functional until the forces on each atom became less than 0.01 eV/Å. Figure 1a,b shows the proposed crystal structures of 2D δ-FeOOH 35369


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Figure 2. Spin configuration for (a) FM and (b) AFM and calculated band structures for (c) FM and (d) AFM spin configuration in monolayer feroxyhyte.

Figure 3. Three different stackings in the bilayer for (a) H@hollow, (b) H@Fe top, and (c) H@O top sites.

synthesized by Chen et al. seems to match St-2. Thus, hereafter, we focus on this St-2 and explore its magnetic ground state, band structure, and optical properties. To find the magnetic ground state, we considered both FM and antiferromagnetic (AFM) spin configurations using a 2 × 2 supercell, and Figure 2a,b shows the schematic illustration for the magnetic configuration. We obtained an AFM ground state, and the energy difference between FM and AFM was 36.6 meV. The magnetic moment was insensitive to the magnetic configuration because the magnitude of magnetic moment per (1 × 1) unit cell was 1 μB in both FM and AFM states. This spin-polarized state originated from the Fe d-orbitals while both O and H atoms remained nonmagnetic. Indeed, Chen et al. reported that the 2D δ-FeOOH displayed a room-temperature FM state whereas in our experiment, the monolayer structure had an AFM ground state. It seems that the experimental and theoretical results disagree with each other. However, the exact crystal structure and film thickness were not available in their experimental report. Thus, it is necessary to consider the thickness-dependent magnetic state. Because the energy difference was rather small, there may be a

(namely, St-1 and St-2), and Figure 1c displays the top view of both structures. The purple, red, and green spheres represent the Fe, O, and H atoms, respectively. Note that the top view is the same for both structures. Both candidates have hexagonal crystal structures with a space group of P3m1 with no inversion symmetry. In St-1, the H atom is located in the same layer with the Fe atom, whereas one O atom is located above and the other O atom below this layer. The equilibrium bond lengths between O1−H, O1−Fe, and O2−Fe are 1.01, 1.96, and 1.90 Å, respectively. In St-2, the H atom is located vertically just below one of the O atoms. In this case, the equilibrium bond lengths between O1−Fe, O2−Fe, and O2−H are 1.88, 2.03, and 0.97 Å, respectively. From these two candidates, we investigated the dynamical stability by calculating phonon dispersion curves using the density functional perturbation theory approach. Figure 1d,e shows the calculated results. In St-1, we found imaginary frequencies almost over the whole Brillouin zone. These imaginary phonon modes suggest the dynamical instability of this structure. By contrast, for the second structure, we find no trace of imaginary frequencies in the Brillouin zone. Consequently, we propose that the sample 35370


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Figure 4. Spin configurations for (a) FM, (b) AFM1, and (c) AFM2 in the bilayer structure and (d) bond lengths of Fe with neighboring atoms (in Å) in AFM2.

Figure 5. Spin configurations for (a) FM, (b) AFM1, and (c) AFM2 in the trilayer structure and (d) bond lengths of Fe with neighboring atoms (in Å) in AFM2.

chance to show the FM state due to thermal excitation at room temperature. Thus, we present the band structures of the monolayer δ-FeOOH for both FM and AFM states in Figure 2c,d. The red and blue lines represent the spin-up and spindown bands, whereas the horizontal zero line represents the Fermi level. We found indirect gaps of 2.28 and 2.4 eV in both FM and AFM spin configurations, whereas the experimental measurement indicated a direct band gap of 2.2 eV. Indeed, the magnitude of the band gap from the electronic band structure calculation can be different from that found via an optical method. Even if we ignore this difference in the band gap, we found a perfect AFM spin configuration with no net magnetization, whereas a net magnetic moment was proposed in the experimental measurement. Consequently, we conclude that the monolayer δ-FeOOH does not agree with the measurement. According to the experimental measurement, the thickness of 2D δ-FeOOH was assumed to be less than three unit cells. Thus, we also checked the thickness-dependent magnetic ground state. First, we considered a bilayer δ-FeOOH structure. Here, we considered three different possible stackings, namely, H@hollow site, H@Fe top, and H@O top. Figure 3a−c represents these three possible stackings. In the H@hollow site, the hydrogen atom in the upper layer is exactly located on top of the O−H bond of the lower layer, and both layers follow the

same order. In H@Fe top, the hydrogen atom in the upper layer is on top of the Fe atom of the lower layer. In H@O top, the hydrogen atom in the upper layer is located on top of the O atom in the lower layer. Among these three different stackings, the H@O top in Figure 3c became the most stable structure, with energy differences of 123 and 111 meV from the H@ hollow and H@Fe top site. With the most stable bilayer structure, we initially explored three different magnetic configurations, namely, FM, AFM1, AFM2 with a (2 × 2) supercell; Figure 4a−c displays the initial spin structures. In AFM1, we have an intralayer FM state while the AFM interlayer coupling takes place between two layers. In AFM2, both interlayer and intralayer have an AFM coupling. The total energy calculations revealed that AFM2 became the most stable configuration with energy differences of 271 and 274 meV from FM and AFM1 configurations. In the most stable structure, the interlayer distance from hydrogen in the upper layer to O in the lower layer was 1.71 Å without including van der Waals interaction, and this reduced to 1.68 Å with an inclusion of van der Waals interaction. Consequently, the thickness of the bilayer FeOOH in an AFM2 spin configuration became 7.37 Å. Here, we should remark that the bond length between Fe and its neighboring atoms are different in both upper and lower layers because of the interlayer interaction. Consequently, the overall crystal symmetry is further reduced. These different 35371


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Figure 6. Calculated band structure of (a) bilayer and (b) trilayer feroxyhyte in the ground state.

Figure 7. Calculated projected DOS of (a) Fe, (b) O in the monolayer, (c) Fe and (d) O in the bilayer, and (e) Fe and (f) O in the trilayer.

−1.1 μB inside a Wigner−Seitz cell. Similarly, in the upper layer, one Fe atom showed a magnetic moment of 1.03 μB, whereas we obtained a −1.32 μB in another Fe atom. Therefore, we found a net magnetic moment of 1.49 μB/supercell. This implies that the bilayer 2D δ-FeOOH behaves like an FM material because a nonzero magnetic moment appeared. Similar to the bilayer structure, the most stable stacking in the trilayer was found in the H@O top configuration. The energy differences of H@O top from H@hollow and H@Fe

bonding features are displayed in Figure 4d. Here, we selected two Fe atoms from each layer, one with up spin (purple) and one with down spin (blue), and the bond lengths of Fe−O, Fe−H, and O−H are shown in the figure. In monolayer δFeOOH, we had a perfect AFM spin configuration with zero magnetization. However, because of the interlayer interaction and different bonding features in the bilayer structure, we obtained a ferrimagnetic state. In the lower layer, one Fe atom had a magnetic moment of 0.65 μB and the other Fe atom had a 35372


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Figure 8. (a) Imaginary part of the dielectric function, (b) reflectivity, (c) refractive index, and (d) optical absorption spectra for monolayer, bilayer, and trilayer structures in the ground state.

top sites were 172 and 234 meV, respectively. In the trilayer, we again considered three different possible magnetic spin configurations, that is, FM, AFM1, and AFM2 in a 2 × 2 supercell; Figure 5a−c shows the optimized structures. In the AFM1 spin configuration, an intralayer FM coupling exists, whereas we find an interlayer AFM coupling between every two facing layers. However, in AFM2 spin configurations, an intralayer AFM state takes place along with an AFM coupling in every two facing layers. We obtained the most stable state in the AFM2 configuration. The calculated energy differences were 1.01 and 0.61 eV compared with FM and AFM1 states. The interlayer distances in all three spin configurations are displayed in Figure 5. In AFM2, the interlayer distance between every two layers was 1.55 Å, and this further reduced to 1.47 Å after an inclusion of van der Waals interaction. In Figure 5d, we show the different bonding features of Fe atoms in different layers. Here, we selected two Fe atoms with spin up (purple) and spin down (blue) in every layer. These different bonding features are mainly responsible for the reduction of the symmetry. We found that this lowered symmetry results in a ferrimagnetic state. Because of the interlayer interaction with the upper and lower layer, the central layer had no net magnetic moment, and it became a magnetically dead layer. However, the top and bottom layers had net magnetic moments of 1.36 and 1.06 μB. Therefore, the trilayer system behaves like an FM material because the trilayer structure has a net magnetic moment of 2.40 μB per supercell. Interestingly, the thickness of trilayer FeOOH investigated in our calculations is 11.57 Å (∼1.2 nm), and this is quite close to the experimentally measured thickness from high-resolution transmission electron microscopy. Figure 6a shows the electronic band structure of the ferrimagnetic bilayer system. First of all, unlike the monolayer structure, we found a direct band gap at the Γ point with a band gap of 0.87 eV. Figure 6b shows the band structure of the ferrimagnetic trilayer system. In the trilayer structure, we obtained an indirect band gap such as in the monolayer case,

and a band gap of 1.6 eV was found. As presented in Figure 2d for the monolayer system, the conduction band edge at the Γ point originated from the oxygen p orbital, whereas the valence band edge originated from the Fe d orbital. As described, the monolayer had a perfect AFM state, and we observed completely overlapped two spin bands, whereas the ferrimagnetic state was found in the bilayer because of the interlayer interaction. Thus, the splitting of two bands took place. For instance, the occupied majority-spin band moved to the Fermi level, whereas the minority-spin band shifted to a further lower energy region. On the other hand, both spin bands in the unoccupied state felt an attractive potential force so that they moved to the Fermi level. This gives rise to a transition from an indirect band gap in the monolayer to a direct band gap in the bilayer at the Γ point. In the trilayer structure, the attractive potential for majority-spin electrons is suppressed, and the valence band edge for majority-spin electrons is pushed away from the Fermi level. Consequently, we obtained an indirect band gap. In addition, the interlayer distance in the bilayer was 1.68 Å, and this decreased to 1.47 Å. This reduction of the interlayer distance could also contribute to enhancing the band gap as compared with that in the bilayer system. Figure 7a−f shows the projected density of states (DOS) of Fe and O atoms for monolayer, bilayer, and trilayer systems in ground states. We found a very weak DOS for the O atom near the band gap energy regime. By comparing these band structures and the DOS, we realized that the Fe d orbitals contributed to the valence band maximum, whereas the oxygen p orbital was responsible for the conduction band minimum. As mentioned above, the bilayer and trilayer structures had a net magnetic moment, and the thickness of the trilayer agrees well with the measurement, although the calculated electrical band gaps are rather weak compared with that observed in the experimental measurement using the optical absorption method. Once again, it should be remarked that we cannot directly compare the band gap extracted from the band structure with the value 35373


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the experimental measurement was performed with the UV− visible absorption spectrum, we also calculated the optical absorption spectra. From the optical absorption spectra, the onset of the first absorption peak in the monolayer structure was found at 3.2 eV, whereas it was observed at 2.8 and 2.2 eV for the bilayer and trilayer ferrimagnetic states. Overall, we find that the physical properties of the trilayer structure are in agreement with the experimental measurement. Because the 2D δ-FeOOH has a net magnetic moment with a finite band gap, we propose that this 2D material can be utilized for potential spintronics applications.

estimated from the optical absorption measurement. Indeed, it is necessary to investigate the optical property. We now present the optical properties. Here, we assume that the electromagnetic wave is propagating perpendicular to the film surface. Because the real and imaginary parts of the dielectric function are related by the well-known Kramers− Kronig relation, we present only the imaginary part of the dielectric function.32 Figure 8a shows the imaginary part of the frequency-dependent dielectric functions for monolayer, bilayer, and trilayer systems in the ground state. From this frequency-dependent dielectric function, we calculated the reflectivity R(ω), refractive index N(ω), and absorption spectra, and the results are presented in Figure 8b−d. All three systems are optically transparent in a wide range of photon energies because the reflectivity coefficients are quite small as shown in Figure 8b. Besides, we found that the refractive index has a weak frequency dependency. Figure 8d shows the frequencydependent absorption spectra. We observed that the onset of absorption appeared around 3.2, 2.8, and 2.2 eV in monolayer, bilayer, and trilayer structures, respectively. Despite the different electronic band gap in monolayer and bilayer structures, the onset of absorption was rather close to each other in these two systems. This can be understood from the band structure and the DOS. Because the DOS of the O atom is quite weak, the transition from the Fe d state to the oxygen p state is negligible. In addition, the crystal structure of 2D δFeOOH is noncentrosymmetric, and the Fe d−d transition is allowed. As indicated in Figure 2d for the monolayer structure, the major transition in monolayer AFM took place from dxz, dyz to dz2 and dx2−y2 orbitals. Similarly, in the bilayer ferrimagnetic system in Figure 6a, the major transition took place from dyz to dxy and at the same time from dx2−y2 to dxz orbitals. As a result, both monolayer and bilayer systems displayed a similar onset photon energy. In the trilayer system, the main transition took place from dyz to dx2−y2 or dx2−y2 to dyz orbitals, as shown in Figure 6b. Indeed, the experimentally measured onset energy was also 2.2 eV, and our value agrees with this measurement. Overall, combining the magnetic ground state, film thickness, and optical absorption spectra, we suggest that trilayer ferroxyhyte proposed in this study agrees with the experimentally fabricated material.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Jisang Hong: 0000-0002-5895-8700 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (2016R1A2B4006406).

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REFERENCES

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CONCLUSION We investigated the geometric structure and electronic, magnetic, and optical properties of 2D δ-FeOOH using density functional calculations within the HSE06 hybrid functional. We proposed two potential candidate structures and checked their dynamic stability using a phonon dispersion curve. On the basis of phonon dispersion, we suggest that the 2D δ-FeOOH is derived from bulk Fe(OH)2 via oxidation. We found that the 2D δ-FeOOH monolayer had an indirect band gap of 2.4 eV with a perfect AFM ground state. Thus, no net magnetization was observed. In bilayer and trilayer systems, the most stable state was found in the H@O top stacking order. Unlike in the monolayer system, we obtained a ferrimagnetic ground state with net magnetic moments of 1.49 and 2.40 μB in bilayer and trilayer systems. A direct band gap of 0.89 eV was found in the bilayer system, whereas we obtained an indirect band gap of 1.6 eV in the trilayer system, and we attribute this to the suppression of the interlayer distance. The calculated film thicknesses in bilayer and trilayer systems were 7.37 and 11.57 Å, and that of the trilayer structure was close to the experimentally reported sample thickness (∼12 Å). Because 35374


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Two-Dimensional Magnetic Semiconductor in Feroxyhyte - ACS

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