Letter pubs.acs.org/JPCL
The Intrinsic Ferromagnetism in a MnO2 Monolayer M. Kan,† J. Zhou,† Q. Sun,*,†,‡,§ Y. Kawazoe,⊥ and P. Jena§ †
Department of Materials Science and Engineering, Peking University, Beijing 100871, China Center for Applied Physics and Technology, Peking University, Beijing 100871, China § Department of Physics, Virginia Commonwealth University, Richmond, Virginia 23284, United States ⊥ Institute for Material Research, Tohoku University, Sendai, 980-8577, Japan ‡
ABSTRACT: The Mn atom, because of its special electronic configuration of 3d54s2, has been widely used as a dopant in various two-dimensional (2D) monolayers such as graphene, BN, silicene and transition metal dichalcogenides (TMDs). The distributions of doped Mn atoms in these systems are highly sensitive to the synthesis process and conditions, thus suffering from problems of low solubility and surface clustering. Here we show for the first time that the MnO2 monolayer, synthetized 10 years ago, where Mn ions are individually held at specific sites, exhibits intrinsic ferromagnetism with a Curie temperature of 140 K, comparable to the highest TC value achieved experimentally for Mn-doped GaAs. The well-defined atomic configuration and the intrinsic ferromagnetism of the MnO2 monolayer suggest that it is superior to other magnetic monolayer materials. SECTION: Surfaces, Interfaces, Porous Materials, and Catalysis
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ince the successful synthesis of graphene,1 tremendous efforts have been devoted to two-dimensional (2D) monolayers such as boron nitride (BN), silicene, and MoS2.2−4 These 2D materials exhibit a large variety of physical and chemical properties and have potential applications in integrated circuits, transparent conducting electrodes, photoluminescence and valleytronics.5−9 However, graphene, silicene, BN sheets, and MoS2 are intrinsically nonmagnetic in their pristine forms. In order to explore their applications in spinrelated devices, considerable efforts have been made to introduce magnetic dopants into these materials. For example, Krasheninnikov et al. showed that a graphene sheet can be made magnetic when embedding TM atoms (Sc−Zn, Pt, and Au) in vacancies.10 However, it is difficult to control the defects precisely, and the induced magnetic properties depend strongly on the type and distribution of defects.11 Furthermore, due to the strong d−d interactions, it remains a challenge to prevent the TM atoms from clustering. Although surface decorations can induce magnetism in graphene and BN sheets,12,13 the induced magnetism by the attached radicals is not only weak but also difficult to control experimentally. Following the idea of dilute magnetic semiconductor, Ramasubramaniam and Naveh recently studied Mn-doped MoS2 monolayers14 and found that the substitutional Mn dopants at Mo sites are coupled ferromagnetically via the double-exchange mechanism. When the doping concentration is in the range of 10−15%, the Curie temperature can reach room temperature. Since the distribution of doped Mn atoms in GaAs, GaN, ZnO, AlN, and SiC is known to be highly sensitive to the synthesis process and conditions, the Curie temperatures reported by different groups are quite different.15 To make matter worse, conventional © XXXX American Chemical Society
doping of transition metals (TMs) on substrates also suffers from the problem of low solubility. The question then arises: Can one find a pristine 2D monolayer that contains TM ions in its intrinsic backbone and will show intrinsic and strong ferromagnetism? Here we show that the manganese dioxide (MnO2) monolayer is such a system. This was synthesized successfully16 by Omomo et al. in 2003. Since then, extensive studies have been carried out both experimentally and theoretically. For example, Sakai et al. reported that a unilamellar MnO2 layer with Mn vacancies can generate the anodic photocurrent under visible light irradiation, and the band gap energy was estimated to be 2.23 eV on the basis of the photocurrent action spectrum.17 Although many efforts have been made to explore its potential applications18−22 to the best of our knowledge, no study as yet has been reported on the magnetic properties of the 2D MnO2 monolayer. In the present study, we carry out first-principles calculations combined with Monte Carlo simulations to systematically study the geometric structures, electronic, and magnetic properties of the 2D MnO 2 monolayer. Our results show that the 2D MnO2 is an indirect semiconductor with a band gap of 3.41 eV. Each unit cell of this 2D material possesses a magnetic moment of 3 μB, which is mainly contributed by the Mn atoms. We also find that the Mn atoms prefer ferromagnetic (FM) coupling. Furthermore, the Curie temperature is about 140 K, which can be increased by a Received: August 20, 2013 Accepted: September 22, 2013
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between two O atoms in a plane ΔO−O, and the angle between Mn−O bonds θMn−O−Mn are calculated to be 2.925 Å, 1.914 Å, and 97.8°, respectively. For the mechanical properties, the calculated uniaxial elastic moduli (Young’s Modulus) of 2D MnO2 along the X and Y directions are found to be 135 GPa· nm and 134 GPa·nm, as shown in Figure 1c,d, suggesting that the MnO2 sheet is a soft and flexible material as compared to graphene. Thus, as shown in this work, it is possible to tune properties through mechanical stress and strain. The spin-polarized calculations are carried out to check the possibility of a magnetic ground state. It is found that the MnO2 monolayer is indeed ferromagnetic with a magnetic moment of 3.319 μB on each Mn site. The O atoms are antiferromagnetically polarized with a magnetic moment of −0.155 μB. Consequently, each unit cell has a net magnetic moment (μuc) of 3 μB. This is quite high compared to other 2D monolayers studied previously.10,11,36 The origin of the integral magnetic moment of 3 μB can be understood by the following arguments: In an octahedral coordination, the d orbitals are split into eg* (dz2 and dx2−y2) and t2g (dxy, dyz, and dxz), the latter having lower energy. Each octahedrally coordinated Mn atom has a 3d3 configuration, and the three t2g orbitals are singly occupied with parallel spin due to the Hund’s rules, thus resulting in 3 μB per unit cell. Next we study the preferred magnetic coupling of the MnO2 monolayer. To this end, a (2 × 2) supercell is constructed with two different magnetic configurations as shown in Figure 1a: the FM and AFM states. The calculated total energies show the ground state of the MnO2 monolayer to be FM with an exchange energy Eex (= EAFM − EFM) = 247 meV. The isosurface of the spin density (ρ↑ − ρ↓) for FM 2D MnO2 is plotted in Figure 2a, showing that the TM atoms are highly spin-polarized, and the O atoms are slightly antiferromagnetically polarized. To confirm the electronic properties of this 2D system, the hybrid functional HSE06, which describes band gap more precisely, is used to calculate the band structure of FM MnO2 monolayer. The corresponding band structure and projected density of states (PDOS) are shown in Figure 3c, indicating that the MnO2 monolayer is an indirect band gap semiconductor with the valence band maximum (VBM) located between K→Γ and the conduction band minimum (CBM) located between Γ→M of the Brillouin zone. The band gap is 3.41 eV, which is in agreement with previous studies22,37 showing that the band gap of a perfect 2D MnO2 monolayer is expected to be larger than 2.23 eV and smaller than 3.50 eV. Furthermore, the band structure and PDOS both show that the VBM and CBM are dominated by the magnetic spin up orbitals. The virtual hopping between them implies that the FM coupling of the system is due to double exchange interaction between two Mn ions. To further study the sensitiveness of the magnetic state to the choice Ueff, calculations with different Ueff values (2.0−4.5 eV) are performed. The results are shown in Figure 2d, which confirms that FM state is more stable than the AFM state for all Ueff values. Next we study the Curie temperature. By using Monte Carlo simulations,37 we calculated the average magnetic moment of one unit cell at different temperatures. Details of the method can be found in our previous study.37 Based on the Ising model, the magnetic coupling Hamiltonian can be written as
biaxial tensile strain, indicating that the MnO2 monolayer is a promising material for spintronics applications. Our first-principles calculations are based on spin-polarized density functional theory (DFT) with Perdew−Burke− Ernzerhof (PBE) form for the generalized gradient approximation (GGA)23 for exchange-correlation potential. Planewave basis sets with the projector augmented plane-wave method (PAW)24 are used as implemented in the Vienna ab initio simulation package (VASP).25 To properly describe the strongly correlated electrons in the partially filled d subshells, we use the GGA+Ueff method introduced by Dudarev et al.26 with Ueff = 3.9 eV27−29 for Mn. This has been tested in previous studies of bulk MnO2.30−32 We use a vacuum space of 25 Å along the z axis in order to avoid interactions between two neighboring images. The reciprocal space is represented by a Monkhorst−Pack special k-point scheme33 with 25 × 25 × 1, 9 × 9 × 1, and 5 × 5 × 1 grid meshes for a unit cell, and (2 × 2) and (4 × 4) supercells, respectively. The energy cutoff and convergence criteria for energy and force are set to be 400 eV, 1 × 10−4 eV, and 0.01 eV/Å, respectively. In addition, the stateof-the-art hybrid functional (HSE06),34,35 which is believed to give a better description of the band structure, is carried out to calculate the electronic properties. The geometric structure of the 2D MnO2 monolayer is shown in Figure 1. Each Mn atom is in an octahedral configuration bonded to six O atoms. We find that the optimized bond distance between Mn and O atoms dMn−O is 1.94 Å, which agrees well with previous experimental18 and theoretical22 results. The lattice parameter a0, the distance
Figure 1. (a) Top view geometry and (b) side view of a MnO2 monolayer where Mn atoms are purple and O atoms are red. The rhombic unit cell is marked by a black dotted line, while FM and antiferromagnetic (AFM) configurations are marked by yellow and blue dotted lines, respectively. The energy changes with uniaxial strains along the (c) X and (d) Y directions.
H = −∑ Jij μi μj i,j
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temperature is plotted in Figure 3. We see that the magnetic moment per unit cell starts to drop gradually from 3 μB and the Curie temperature (TC) is about 140 K. This is comparable to the highest TC value achieved experimentally in Mn-doped GaAs.38 Since the Curie temperature of MnO2 monolayer is below room temperature, it is important to examine whether some strategy can be employed to increase the Curie temperature. Motivated by previous studies, which shows that applied inplane tensile strain can effectively enhance ferromagnetism,11,36 we employ biaxial strain to tune the magnetic states. We define the biaxial tensile strain as ε = (a − a0)/a0 × 100%, where a0 and a are the lattice constants of the 2D MnO2 in its equilibrium and strained states, respectively. The changes in exchange energy, magnetic moments and Curie temperature with the tensile strain are given in Figure 4. We clearly see that under strain, due to the increased Mn−O bond length, the orbital hybridization is reduced, and the magnetic moments at Mn and O sites are increased. This would enhance the magnetic coupling between Mn atoms mediated by the polarized O sites, thus resulting in larger exchange energy and higher Curie temperature. For example, under 1%, 3%, and
Figure 2. (a) Spin density isosurface with a value of 0.1 e/Å3 in the FM state and (b) spin density isosurface with a value of 0.1 e/Å3 in the AFM state. (c) Band structure and corresponding PDOS of the FM MnO2 monolayer. (d) Changes of energy with Ueff.
Figure 3. Variation of the total magnetic moment per unit cell of 2D MnO2 with respect to the temperature.
where i/j, Jij, and μi/μj represent the nearest-neighbor unit cell sites, the exchange parameter, and the magnetic moment of nearest-neighbor unit cells, respectively. As indicated in Figure 2a,b, the exchange parameter J = (EAFM − EFM)/4 μuc2 = 1.72 meV, where EFM = −3Jμuc2 and EAFM = +Jμuc2. In the MC simulations, we used a (100 × 100) supercell to reduce the periodic constraints. Also, at each temperature, 5 × 109 loops are taken to achieve an average magnetic moment value. The variation of the magnetic moment per unit cell with respect to
Figure 4. Changes of (a) the magnetic moments at Mn site and O site, (b) the exchange energy per unit cell, and (c) the Curie temperature with respect to the tensile strain. 3384
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5% strain, the calculated Eex are about 67.71, 79.59, and 92.79 meV per unit cell, which is almost 1.1, 1.3, and 1.5 times that of Eex in the strain free state. From MC simulation we see that the Curie temperature can be increased to 210 K under 5% strain. In summary, we have systematically studied the electronic and magnetic properties of the MnO2 monolayer. The following conclusions can be drawn: (1) The MnO2 monolayer is an indirect band gap semiconductor with a band gap of 3.41 eV. (2) The Mn atoms in the monolayer are ferromagnetically coupled with each other with the coupling mediated by the polarized O atoms. Each unit cell possesses the magnetic moments of 3 μB, which is much larger than that in other 2D materials. (3) The Curie temperature of MnO2 monolayer in the equilibrium state is 140 K, which is comparable to the highest TC value achieved experimentally in Mn-doped GaAs; Tc can be further increased to 210 K under 5% strain. (4) Compared to the existing doping strategy applied to other monolayer materials, MnO2 monolayer has the following advantages: it contains Mn ions in the intrinsic structural frame and hence does not suffer from the problems of low solubility of dopant or their clustering on substrates. We hope the present study will stimulate further experimental effort in this subject.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work is partially supported by grants from the National Natural Science Foundation of China (NSFC-21173007, 11274023), from the National Grand Fundamental Research 973 Program of China (2012CB921404), and from the United States Department of Energy. The authors thank the crew of the Center for Computational Materials Science, the Institute for Materials Research, Tohoku University (Japan), for their continuous support of the HITACHSR16000 supercomputing facility.
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