Two-Dimensional Magnetic Semiconductor in Feroxyhyte - ACS

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Two-dimensional magnetic semiconductor in feroxyhyte (#-FeOOH) Imran Khan, Arqum Hashmi, M. Umar Farooq, and Jisang Hong ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.7b08499 • Publication Date (Web): 20 Sep 2017 Downloaded from http://pubs.acs.org on September 20, 2017

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ACS Applied Materials & Interfaces

Two-dimensional magnetic semiconductor in feroxyhyte (δFeOOH) Imran Khan1, Arqum Hashmi2, M. Umar Farooq1 and Jisang Hong1,* 1

2

Department of Physics, Pukyong National University, Busan 608-737, Korea

Center for Computational Sciences, University of Tsukuba, Tsukuba 305-8577, Japan

KEYWORDS 2D material, feroxyhyte, magnetic semiconductor, ferrimagnetism, optical properties

ACS Paragon Plus Environment

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ABSTRACT A few years ago, it was claimed that the two-dimensional (2D) feroxyhyte (δ-FeOOH) layer could possess a net magnetic moment and it could be applied for potential spintronics application because it showed a band gap. However, the exact crystal structure is still unknown. Hereby, we investigate the crystal structure, electronic band structure, magnetic and optical properties of 2D δ-FeOOH using density functional calculations. Based on the experimental observation and dynamical stability calculations, we propose that the 2D δ-FeOOH originates from a bulk Fe(OH)2 via oxidation. A perfect antiferromagnetic ground state was observed in 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 bilayer was 1.49 µB per cell. The interlayer distance and film thickness in bilayer δ-FeOOH were 1.68 and 7.37 Å. This interlayer distance was suppressed to 1.47 Å in trilayer system and the band gap of 1.6 eV was found. The trilayer feroxyhyte 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 UV visible optical spectrum measurement, we also calculated the absorption spectra and the onset of the absorption peak in mono, bi- and trilayer were found at 3.2, 2.8 and 2.2 eV. Overall, considering the magnetic state, optical absorption, and film thickness, we propose that the trilayer structure agrees with the experimentally synthesized structure.


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INTRODUCTION Physical properties of a material are basically determined by its electronic structure and the electronic structure significantly depends on the dimensionality of a material. Recently, the study of two-dimensional (2D) materials is receiving extensive research interests due to their peculiar electronic structures and potential device applications. Various types of 2D materials have been introduced and investigated. For instance, a graphene has excellent optical, thermal, electrical, and mechanical properties 1–4. Due to these outstanding physical properties, it can be utilized for various device applications; sensors, actuators, field-effect transistors

5–7

. Apart from the graphene, other 2D

materials such as hexagonal BN 8, transition metal oxides (ZnO and TiO2) 9,10, transition metal dichalcogenides 11–13, and phosphorene

14,15

are also extensively studied for different potential applications. However, most of them are

non-magnetic materials and this characteristic limits their use for next-generation spin related device applications. In these non-magnetic materials, the magnetic state is usually induced by a transition metal impurity doping, an adsorption, a creation of 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 find an intrinsic magnetic 2D material, particularly with a band gap. Then, this can be utilized for a potential spintronic applications. Very recently, Huang et al. reported a layer dependent ferromagnetism in 2D semiconducting chromium triiodide (CrI3) 20,21. In addition, an intrinsic long-range ferromagnetic ordering was also reported in 2D van der Waals semiconducting Cr2Ge2Te6 crystal

22,23

. Besides, it

was shown that the monolayer 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 topochemical transformation process at room temperature

25

. It was claimed that the ultrathin δ-FeOOH

nanosheets could exhibit a room temperature ferromagnetism along with semiconducting behavior in a thickness range of 1.1 ~ 1.3 nm. Using a SQUID magnetometer, the value of saturation magnetization 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 UV-visible light spectrum measurement. The x-ray diffraction analysis proposed that the δ-FeOOH would have a hexagonal structure with a space group P-3m1 and the estimated lattice constants were a = b = 2.95Å. Due to the finite band gap with a


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robust ferromagnetic state, the 2D δ-FeOOH can be a potential spintronics materials. 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.

NUMERICAL METHOD We employed the Vienna ab initio Simulation Package (VASP) 26,27 to study various physical properties. The HeydScuseria-Ernzerhof screened hybrid functional (HSE06)

28,29

was used to obtain a stable ground structure. This is a

range-separated 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 Perdew-Burke-Ernzerhof (PBE) density functional counterpart while 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 of a = b = 2.95 Å. Thus, we adopted these lattice constant and considered a 2 x 2 supercell to calculate magnetic ground state. A vacuum distance of more than 15 Å in the z direction was imposed to avoid an artificial interaction from 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 energy convergence was reached up to 10-4 eV/atom by using conjugate gradient method. The selfconsistent calculations were performed with a (5 x 5 x 1) k-mesh. For bilayer and 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 structure, the dynamical stability was calculated by the phonon dispersion curve using PHONOPY code 31. Force criterion for 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 dielectric function is determined by the following relation


4

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() =

lim→ ∑,, 2 ( − − ) ×

! "# $

%

! & $

∗

% (1)

where c and v represent the conduction and valence band states while k is the wavevector and uck represent the wavefunction with a periodicity of lattice constant. The imaginary and real part of dielectric function are related with well-known Kramers-Kronig relation

"&

5 - (./ )./

() = 1 + + ,

./ 0. !12

34

(2)

where P denotes the principle value32.

NUMERICAL RESULTS Since 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 while the second possible structure (St-2) is originated from 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 HSE06 hybrid functional until the forces on each atom became less than 0.01 eV/Å. Fig. 1 (a) – (b) shows the proposed crystal structures of 2D δ-FeOOH (namely St-1, and St-2) and Fig. 1 (c) displays the top view of both structures. The purple, red, and green spheres represent the Fe, O and H atoms. 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, H atom is located in the same layer with Fe atom while one O is above and the other O atom is located below this layer. The equilibrium bond lengths between O1-H, O1-Fe and O2-Fe are 1.01, 1.96 and 1.90 Å. In St-2, 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. From these two candidates, we investigated the dynamical stability by calculating phonon dispersion curves using density functional perturbation theory approach. Fig. 1 (d) – (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. In contrast, for the second structure, we find no trace of imaginary frequencies in the Brillouin zone. Consequently, we propose that the sample synthesized by Chen et al. seems to be matching the St-2. Thus, hereafter, we focus on this St-2 and


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explore the magnetic ground state, band structure, and optical properties. To find the magnetic ground state, we considered both ferromagnetic (FM) and antiferromagnetic (AFM) spin configurations using a 2x2 supercell and Fig. 2 (a) – (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 (1x1) unit cell was 1 µB in both FM and AFM states. This spin polarized state was originated from the Fe d-orbitals while both O and H remained nonmagnetic.

Indeed, Chen et al. reported that the 2D δ-FeOOH displayed a room temperature FM state while our 1 ML 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. Since the energy difference was rather small, there may be a chance to show FM state due to thermal excitation at room temperature. Thus, we present the band structures of the monolayer (ML) feroxyhyte both for FM and AFM states in Fig. 2 (c) – (d). The red and blue lines represent the spin up and spin down bands while the horizontal zero line represents the Fermi level. We found indirect gaps of 2.28 eV and 2.4 eV in both FM and AFM spin configurations while the experimental measurement indicated a direct band gap of 2.2 eV. Indeed, the magnitude of 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 while 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 feroxyhyte structure. Here, we considered three different possible stackings namely, H @ hollow site, H @ Fe top, and H @ O top. Fig. 3 (a) – (c) represents these three possible stackings. In 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 the 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


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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 Fig. 3(c) became the most stable structure with energy differences of 123 and 111 meV from H @ hollow and H @ Fe top site. With the most stable bilayer structure, we explored initially three different magnetic configurations, namely FM, AFM1, AFM2 with (2 x 2) supercell and Fig. 4 (a) – (c) displays the initial spin structures. In AFM1, we have an intra-layer FM state while the AFM interlayer coupling takes place between two layers. In AFM2, both inter-layer and intra-layer have an AFM coupling. The total energy calculations revealed that the 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 the hydrogen in the upper layer to O in the lower layer was 1.71 Å without including van der Waals and this reduced to 1.68 Å with an inclusion of van der Waals interaction. Consequently, the thickness of the bilayer FeOOH in 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 due to the interlayer interaction. Consequently, the overall crystal symmetry is further reduced. These different bonding features are displayed in Fig. 4 (d). 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 figure. In monolayer δ-FeOOH, we had a perfect AFM spin configuration with zero magnetization. However, due to 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 had a -1.1 µB inside a Wigner-Seitz cell. Similarly, in the upper layer, one Fe atom showed a magnetic moment of 1.03 µB while 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 a ferromagnetic material because a non-zero magnetic moment appeared.

Similar to bilayer structure, the most stable stacking in trilayer was found in H@ O top configuration. The energy difference of H @ O top from H @ hollow and H @ Fe top sites was 172 and 234 meV. In trilayer, we again considered three different possible magnetic spin configurations, i.e FM, AFM1 and AFM2 in a 2 x 2 supercell and Fig. 5 (a) – (c) shows the optimized structures. In AFM1 spin configuration, an intra-layer FM coupling exists while we find an interlayer AFM coupling between every two facing layers. However, in AFM2 spin configurations, an intra-layer AFM state takes place along with AFM coupling in every two facing layers. We obtained the most stable


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state in 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 Fig. 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 Waal interaction. In Fig. 5 (d), 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. Due to the interlayer interaction with 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 a net magnetic moments of 1.36 and 1.06 µB. Therefore, the trilayer system behaves like a ferromagnetic 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.

Fig. 6 (a) shows the electronic band structure of ferrimagnetic bilayer system. First of all, unlike the monolayer structure, we found a direct band gap at Γ point with a band gap of 0.87 eV. Fig. 6 (b) shows the band structure of ferrimagnetic trilayer system. In trilayer structure, we obtained an indirect band gap like in the monolayer case and the band gap of 1.6 eV was found. As presented in Fig. 2 (d) for monolayer system, the conduction band edge at Γ point originated from the oxygen p orbital while the valence band edge originated from Fe d orbital. As described, the monolayer had a perfect AFM state and we observed completely overlapped two spin bands while the ferrimagnetic state was found in bilayer due to the interlayer interaction. Thus, the splitting of two bands took place. For instance, the occupied majority spin band moved to the Fermi level while the minority spin band shifted to further lower energy region. On the other hand, both spin bands in the unoccupied state felt attractive potential force so that they moved to the Fermi level. This gives rise to a transition from an indirect in monolayer to a direct band gap in bilayer at the Γ point. In trilayer structure, the attractive potential for majority spin electrons is suppressed and the valence band edge for minority spin electrons is pushed away from the Fermi level. Consequently, we obtained an indirect band gap. In addition, the interlayer distance in bilayer was 1.68 Å and this decreased to 1.47 Å. This reduction of interlayer distance could also contribute to enhancing the band gap as compared with that in bilayer system. Fig. 7 (a) – (f) shows the projected density of states (DOS) of Fe and O atoms for monolayer, bilayer


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and trilayer systems in ground states. We found very weak DOS for O atom near the band gap energy regime. By comparing these band structures and DOS, we realized that the Fe d orbitals contributed to the valence band maximum while 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 trilayer agrees well with the measurement although the calculated electrical band gaps are rather weak compared with that observed in the experimental measurement using optical absorption method. Once again, it should be remarked that we cannot directly compare the band gap extracted from band structure with the value estimated from 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. Since the real and imaginary parts of the dielectric function are related by well-known KramersKronig relation, we only present the imaginary part of the dielectric function 32. Fig. 8 (a) 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 Fig. 8 (b) – (d). All the three systems are optically transparent in a wide range of photon energy because the reflectivity coefficients are quite small as shown in Fig. 8 (b). Besides, we found that the refractive index has a weak frequency dependency. Fig. 8 (d) shows the frequency dependent absorption spectra. We observed that the onset of absorption appeared around 3.2, 2. 8 and 2.2 eV in mono, bi and trilayer structures. 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 DOS. Since the DOS of O atom is quite weak, the transition from Fe d state to oxygen p state is negligible. In addition, the crystal structure of 2D δ-FeOOH is non-centrosymmetric, the Fe d-d transition is allowed. As indicated in Fig. 2(d) for monolayer structure, the major transition in monolayer AFM took place from dxz, dyz to dz2 and dx2-y2 orbitals. Similarly, in bilayer ferrimagnetic system in Fig. 6(a), the major transition took place from dyz to dxy and at the same time from dx2-y2 to dxz orbitals. As a result, both mono and bilayer systems displayed a similar onset photon energy. In trilayer system, the main transition took place from dyz to dx2-y2 or dx2-y2 to dyz orbitals as shown in Fig. 6 (b). Indeed, the experimentally measured onset energy was also 2.2 eV and our value agrees with this measurement.


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Overall, combining the magnetic ground state, film thickness and optical absorption spectra, we suggest that the trilayer ferroxyhyte proposed in this study agrees with the experimentally fabricated material.

CONCLUSION We investigated the geometric structure, electronic, magnetic, and optical properties of two-dimensional feroxyhyte δ-FeOOH using density functional calculations within HSE06 hybrid functional. We proposed two potential candidate structures and checked their dynamic stability using phonon dispersion curve. Based on phonon dispersion, we suggest that the 2D δ-FeOOH is derived from a 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 antiferromagnetic ground state. Thus, no net magnetization was observed. In bilayer and trilayer systems, the most stable state was found in H @ O top stacking order. Unlike the monolayer system, we obtained a ferrimagnetic ground state with a 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 bilayer system while we obtained an indirect band gap of 1.6 eV in trilayer system and we attribute this to the suppression of interlayer distance. The calculated film thickness in bilayer and trilayer systems were 7.37 and 11.57 Å and the trilayer structure was closed to the experimentally reported sample thickness (~ 12 Å). Since the experimental measurement was performed with UV visible absorption spectrum, we also calculated the optical absorption spectra. From optical absorption spectra, the onset of first absorption peak in monolayer structure was found at 3.2 eV while it was observed at 2.8 eV and 2.2 eV for the bilayer and trilayer ferrimagnetic state. Overall, we find that the physical properties of trilayer structure are in agreement with the experimental measurement. Since 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.


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AUTHOR INFORMATION

Corresponding Author *E-mail: [email protected] Notes The authors declare no competing financial interest. ACKNOWLEDGMENT 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) and by the Supercomputing Center/Korea Institute of Science and Technology Information with supercomputing resources including technical support (KSC-2016-C3-0001).


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Figure Captions 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.

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

Figure 3. Three different stackings in bilayer for (a) H @ hollow (b) H @ Fe top, and (c) H @ O top site. Figure 4. Spin configurations for (a) FM (b) AFM1, and (c) AFM2 in 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 trilayer structure and (d) Bond lengths of Fe with neighboring atoms (in Å) in AFM2.

Figure 6. Calculated band structure of (a) bilayer and (b) trilayer feroxyhyte in ground state. Figure 7. Calculated projected density of states of (a) Fe, (b) O in monolayer, (c) Fe and (d) O in bilayer and (e) Fe and (f) O in trilayer.

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


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Two-Dimensional Magnetic Semiconductor in Feroxyhyte - ACS

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