Tunable Conductivity and Half Metallic Ferromagnetism in Monolayer

Oct 11, 2016 - Defect-induced large spin-orbit splitting in monolayer PtSe 2. Moh. Adhib Ulil Absor , Iman Santoso , Harsojo , Kamsul Abraha , Fumiyuk...
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Tunable Conductivity and Half Metallic Ferromagnetism in Monolayer Platinum Diselenide: A First-Principles Study Muhammad Zulfiqar,†,‡ Yinchang Zhao,†,‡ Geng Li,†,‡ Safdar Nazir,¶ and Jun Ni*,†,‡ †

State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, People’s Republic of China ‡ Collaborative Innovation Center of Quantum Matter, Beijing 100084, People’s Republic of China ¶ Department of Physics, University of Sargodha, 40100 Sargodha, Pakistan S Supporting Information *

ABSTRACT: On basis of the first-principles calculations, we have studied the effects of hole doping and biaxial tensile strain on the electronic and magnetic properties of monolayer of platinum diselenide (PtSe2). Due to the large density of states near the valence band edge, this nonmagnetic monolayer semiconductor switches to a ferromagnetic half metal within a small range of hole doping. With an increase of hole density, average magnetic moment per carrier also increases and reaches at its maximum value over a specific range of carrier density, while the system remains in a half metal state before the magnetic moment abruptly begins to fall. We also predict a critical value of biaxial tensile strain (5%) for doped monolayer PtSe2, after which the optimal carrier density becomes constant, while the magnetic moment/carrier gradually increases and the ferromagnetic state of the system becomes more stable with increasing values of strain. This work paves a possible way to engineer the magnetic properties of the two-dimensional nanomaterials.

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INTRODUCTION Dimensionality plays a vital role in determining the characteristics of materials, which paves the path toward the intensive research on fabricating 2D materials over the past few years. After the most studied graphene,1 recently the researchers have been putting remarkable efforts toward discovery of other 2D materials2−5 with interesting properties. For instance, transition metal dichalcogenide (TMD) monolayers have attracted great interest because of their exceptional properties, which are quite beneficial for some potential applications, e.g., integrated circuits, transparent conducting electrodes, photoluminescence, and valleytronics.6−10 Various experimental techniques have been suggested for the successful synthesis of different kinds of transition metal dichalcogenide (TMD) monolayers, including mechanical exfoliation, liquid exfoliation, and chemical vapor deposition.11−13 Since most of the existing pristine 2D materials such as graphene and boron nitride sheets exhibit nonmagnetic properties, one of the scientific concerns in this regard is whether TMDs can possess desirable magnetic behavior.14 Ma et al. reported that VX2 (X = S, Se) possesses ferromagnetic behavior in its equilibrium states and that the net magnetic moments of these structures can be increased from 0.43 μB for VS2 and 0.58 μB for VSe2 to about 1 μB by doping and biaxial strain.15 Zhou et al. showed that under a biaxial tensile strain nonmagnetic NbX2 (X = S, Se) switch to ferromagnetic state.14 In addition to pristine TMDs, Mn-doped monolayer MoS2 has © 2016 American Chemical Society

been reported to be an atomically thin dilute magnetic semiconductor.15 Furthermore, magnetism and magnetocrystalline anisotropy have been suggested in defective monolayer PtSe2 under the application of biaxial strain.16 In addition, it is also reported that the bandgap of monolayer and bilayer PtSe2 can be tuned via strain engineering.17 Recent researches have revealed that 2D TMDs undergo unusual changes in their physical properties when subjected to strain,14,15,18−25 chemical functionalization,26−30 doping with transition metals,31 and external electric fields.32 Further, it has been shown experimentally that the bandgap of monolayers and bilayers in MoS2 can be modified by application of strain.19 Because of the potential applications in spintronics, ferromagnetism leading to half metallicity is widely studied, previously. Some of the examples include tunable magnetism and half metallicity in monolayer GaSe via hole doping,33 half metallicity in chemically exfoliated MnPSe3 with carrier doping,34 ferromagnetism and half metallicity in chemically exfoliated atomically thin transition metal dinitrides,35 ferromagnetism via hole doping in SnO2,36 effects of charge doping on the magnetic moment formation of hypothetical compounds (SrC, BaC) with zinc-blend crystal structure,37 etc. Received: July 13, 2016 Revised: October 1, 2016 Published: October 11, 2016 25030

DOI: 10.1021/acs.jpcc.6b06999 J. Phys. Chem. C 2016, 120, 25030−25036

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other PtSe2 configurations such as H-type or distorted structure induced by doping and strain. The magnetic properties of the doped and stretched monolayer 1T-PtSe2 are expected to be significantly different from its pristine form. In this work, from first-principles investigations, we report the existence of the tunable magnetism in monolayer PtSe2 as EF is tuned, via hole doping, through the van Hove singularities present in the DOS. We find that with a small range of hole doping PtSe2 monolayer can easily be made to switch from nonmagnetic state to ferromagnetic state. Biaxial tensile strain remarkably influences the average magnetic moments as well as the polarization energies of the system over a particular range of carrier density (carrier concentration/cm2). Our results indicate that stable half metallic ferromagnetism via hole doping can be achieved in monolayer PtSe2 and can be further tuned by changing the doping level as well as biaxial tensile strain.

PtSe2 have hexagonal crystal structure composed of a layer of metal atoms (M = Pt) sandwiched between layers of chalcogen atoms (X = Se) with stoichiometry MX2. As shown in Figure 1,

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COMPUTATIONAL METHODS AND STRUCTURAL MODELING Our density functional theory (DFT) calculations employ the projector augmented wave (PAW) method encoded in Vienna ab initio simulation package (VASP).46,47 The electronic exchange-correlation potential is treated by the generalized gradient approximation (GGA) with the Perdew−Burke− Ernzerhof (PBE) functional. Although PBE functional is supposed to slightly overestimate the hybridization, the exchange interaction and thus the magnetism,48 in view of considerably large calculated magnetic moment in this work, it can provide reasonable results qualitatively for the itinerant magnetism Throughout this work, spin-polarized calculations are performed, and energy cutoff of 300 eV is taken for expanding the wave functions into plane-wave basis. The optimized lattice parameter is 3.75 Å, which agrees well with the experimentally reported value of 3.7 Å.45 For various doping and strain conditions, it is found that a minimum number of (90 × 90 × 1) k points is required in sampling the Brillouin zone to converge the magnetic moment since the magnetic instability is quite sensitive to the sampling of the DOS near EF.33 Note that dense k points are adopted for all doping and strain levels to ensure the robustness and

Figure 1. Crystal structure of monolayer PtSe2: (a) side view of a unit cell and (b) top view with the shaded area showing a unit cell.

each Pt atom has octahedral coordination in monolayer PtSe2 (1T structures).38 In general, large DOS at or near the Fermi energy of a system would lead to instabilities and transitions to different phases such as magnetism, superconductivity, and other phenomena.39−41 Moreover, this sharp feature in the DOS near EF typically suggests a material with a large thermoelectric Seebeck coefficient.42,43 Previously this technique has been used to induce superconductivity in MoS2.44 Very recently, ultrathin PtSe2 stable semiconducting nanosheets have been synthesized and experimentally as well as theoretically studied by Yu-Qi Wang et al.45 However, regarding the ferromagnetic half metallicity, effect of tensile biaxial strain on the modulation of carrier density, polarization energy, and net magnetic moment have not been discussed before. 1T-PtSe2 is the most stable configuration according to our calculations. Moreover, we have not found the similar magnetic properties in

Figure 2. Calculated spin polarized (a) electronic band structure, (b) the total DOS, (c) orbital resolved density of states of Pt, and (d) orbital resolved density of states of Se of monolayer PtSe2, respectively. In panels a and b, the blue and red colors correspond to majority and minority spin states, respectively. The horizontal dashed line represents the Fermi energy. 25031

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the ground state of the doped monolayer PtSe2 is the ferromagnetic state over a wide range of carrier density ranging from 1.8 × 1014/cm2 to 3.1 × 1014/cm2 and the magnetic moment saturates to a plateau nearly 0.75 μB/carrier. If the carrier density does not fall in this range, D(Ef) is not large enough and the Stoner Criterion is violated. So at carrier density of 3.3 × 1014/cm2 the system switches to nonmagnetic state once again. The polarization energies first decrease then increase to zero with the increase of carrier density. The magnetic moment/carrier shows a nearly linear relationship with carrier density when the system is in ferromagnetic state. For hole doped monolayer PtSe2 under no strain, at optimal carrier density, the polarization energy/carrier and the corresponding magnetic moment/carrier are −1.4 meV and 0.75 μB, respectively. Biaxial Tensile Strain Effect. Besides stabilizing the magnetic state of the system, increasing strain abruptly enhance the magnetic moment per carrier. Figure 3 shows how strain

consistency of our calculations. For the vacancy calculations, 4 × 4 supercell is adopted to simulate the system with defects. To avoid the interactions between the vacancies, lateral distance between vacancies is set at 13 Å. The vacancies are obtained by removing the considered atoms from a 4 × 4 supercell that consists of 16 Pt atoms and 32 Se atoms. A set of 5 × 5 × 1 centered k points is used for defect calculations. A 15 Å vacuum layer is used in our calculations to avoid interaction between images. The tolerance for energy convergence is chosen to be 10−5 eV, and we relax the structure until the maximum Hellmann−Feynman force acting on each atom becomes less than 0.02 eV/Å. The formation energy of Pt vacancies is calculated according to the following formula:49 EF(V) = Etot,V − Etot, perfect + μPt(Se). Here, μPt(Se) is the chemical potential of Se or Pt. Etot,perfect and Etot,V denote the total energies of the perfect 4 × 4 supercell and the 4 × 4 supercell containing one or two vacancies, respectively. The μPt(Se) is related to the growth condition. In Se rich condition, μSe is subject to an upper bound given by the energy of Se in the bulk phase, for hexagonal Se μSe = 1/3ESe,hex, which results in the lower limit on μPt: μPt = Etot,f.u − 2μSe, where Etot,f.u is the total energy of formula unit of perfect PtSe2. To examine the stability of all the structures considered, we have performed ab initio molecular dynamics simulations at 300 K for 5000 steps with 10 ps using the VASP code.

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RESULTS AND DISCUSSION Electronic Structures and Hole-Induced Magnetism for Monolayer PtSe2. Results of our calculations indicate that the pristine PtSe2 is nonmagnetic. The spin polarized band structure of monolayer PtSe2 is shown in Figure 2. Monolayer PtSe2 is an indirect bandgap semiconductor with a bandgap of 1.22 eV. The bottom of the conduction band is mainly attributed to Pt dx2−y2 and dz2 orbitals, slightly hybridized with px, py, and pz orbitals of Se. The top of the valence band is primarily attributed to Se px, py, and pz orbitals, hybridized strongly with px, py, pz, dx2−y2, and dz2 of Pt. Due to this orbital character, the band near the Γ point shows rather flat dispersion, which induces a van Hove singularity near the valence band edge (VBE). The DOS near the valence band edge is large enough, which indicates flatness of the valence band. According to band picture model, spontaneous ferromagnetism originates if the relative exchange interaction is larger than the loss in kinetic energy i.e., when it satisfies the Stoner Criterion: ID(Ef) > 1, where D(Ef) represents the DOS at the Fermi energy Ef and I represents the strength of exchange interactions.50 We show that there exists a Stoner-type magnetic instability in monolayer PtSe2 with hole doping, leading to a half-metallic ferromagnetic ground state. Our calculated results can easily be explained by this simple model. In the present case, the DOS near VBE is relatively large enough, so there exists a possibility of hole doping into this system to increase D(Ef). In order to investigate the stability of magnetization, we have calculated the polarization energy Ep of the system, which is equal to difference of energies between the spin-polarized and nonspin polarized states. We find an averaged magnetic moment of 0.4 μB/carrier at the lowest carrier density of 1.2 × 1014/cm2, with a small spin polarization energy ( 1, get easily satisfied. Hence, once the applied strain becomes 5% or beyond, the Stoner Criterion is satisfied and the system attains more stable half metallic ferromagnetic state (as discussed in Figure 4). Almost all the available electrons in the system are fully spin polarized. So, with increasing strain, the magnetic moments/carrier increase, while the optimal carrier density becomes constant once the strain reaches 5%. All magnetic moments correspond to the ferromagnetic state for all strain ranges. In all cases, the atomic magnetic moments increase with increasing strain. For example, in the doped PtSe2, the strains of 4% and 10% yield ferromagnetic moments of 0.89μB/carrier and 0.94μB/carrier, respectively. Coincidentally, at about 10% strain, the maximum stability of the ferromagnetic state with the largest magnetic moment/carrier is reached. Furthermore, it can be noticed from the bond length evolution that the structure of the doped monolayer PtSe2 with the carrier density 1 × 1014/cm2 remains stable even at 10% biaxial tensile strain, which indicates that the doped monolayer PtSe2 can be realized experimentally. The 25033

DOI: 10.1021/acs.jpcc.6b06999 J. Phys. Chem. C 2016, 120, 25030−25036

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The Journal of Physical Chemistry C the tunable magnetism in monolayer PtSe2. It has been observed that the carrier density can be easily achieved in atomically thin materials as compared to their bulk counter parts. The low hole density can be induced in a system by means of the electric carrier doping technique. Previously, in graphene by ion liquid gating technique51,52 carrier densities up to the order of 1014/cm2 and in transition metal dichalcogenide monolayers by back-gate gating technique carrier density up to the order of 1013/cm2 have been achieved.53,54 So, we suggest electric carrier doping or gating techniques to achieve the optimal carrier densities discussed in this article for developing spontaneous magnetism in monolayer PtSe2 because the optimal carrier density in our case is close to 1 × 1014/cm2. The p-type dopants and defects may play key roles in achieving the predicted magnetic state. Therefore, we have utilized the phenomena of defects by creating single Pt vacancy and double Pt vacancies in monolayer PtSe2 to justify our results. Our calculations show similar magnetic properties for defects that are obtained from hole doping as discuss below. Moreover, there are various methods available to detect this induced magnetism upon hole doping in monolayer PtSe2. For examples of transport measurements, direct detections and optical measurements such as themagneto-optic Kerr effect provide evidence for such magnetization. Defective Monolayer PtSe2. The intrinsic vacancies play a crucial role in determining the n-type or p-type conductance of the semiconductors. 55 Here, we exploit this effect by introducing intrinsic vacancies in PtSe2 monolayer. Under the Se rich condition, the formation energies of a single Pt vacancy and double Pt vacancies are 3.7 and 11.1 eV, respectively. Thus, a single Pt vacancy is more likely to be favorable under the Se enriched conditions. This can be a reason for p-type conductance in PtSe2. Interestingly, this formation energy can be decreased significantly by the strain. For instance, at 6% strain the formation energy reduced to 1.42 and 10.7 eV for single and double Pt vacancies, respectively. At 10% strain formation energy for single and double Pt vacancies decreased to 0.38 and 9.7 eV by strain, respectively. These results show that suitable strain may play an important role in creation of the vacancy that is very useful for practical applications. The results obtained from molecular dynamics simulations suggest that the monolayer PtSe2 with single Pt vacancy is stable, indicating that it is possible to realize such systems in experiments, as shown in Figure 1 in the Supporting Information. As we have discussed above in details, to achieve magnetism in monolayer PtSe2, hole doping is proved to be an essential feature. Furthermore, to justify our hole doping procedure to achieve magnetism, we have investigated the effects of single Pt vacancy and double Pt vacancies, which actually correspond to low and high concentrations, respectively. Single Pt Vacancy. After relaxation, Se atoms lying at the top layer around the neutral Pt vacancy move outward, while the Se atoms lying at the bottom layer vacancy move downward. This movement of the Se atoms results into the shrinkage of Pt−Se bond lengths surrounding the vacancy in the top and the bottom layers from 2.68 to 2.47 Å in monolayer PtSe2. Figure 5b shows the spin-resolved total DOS of the 4 × 4 supercell containing one Pt vacancy. The origin of local moment resulted from single Pt vacancy can be understood in the following way. The monolayer PtSe2 with single Pt vacancy exhibits the P3̅m1 space group symmetry. Because of the single Pt vacancy, some of the unpaired electrons become available on the Se atoms

Figure 5. Calculated spin polarized band structure and the total DOS of PtSe2 (4 × 4) supercell: (a) the pristine PtSe2 (b) with one Pt vacancy and (c) with double Pt vacancies. The blue and red colors correspond to majority and minority spin states, respectively. The horizontal dashed line represents the Fermi energy.

surrounding the vacancy. Because of the crystal field effect, the impurity states associated with the single Pt vacancy appear in DOS as shown in Figure 5b. Because of the single Pt vacancy, new states arise near the Fermi energy, which leads to the half metallic character. This half metallic character can be noticed from the band structure of Figure 5b, where the minority states cross the Fermi energy only at the Γ points. The fully occupied states lie below the Fermi energy, while the states above the Fermi energy remain empty. The calculated magnetic moment of 4 μB is developed due to single Pt vacancy. The polarization energy Ep is about 0.12 eV per defect site in PtSe2. The magnetic moments mainly locate at the Se atoms surrounding the Pt vacancy, as shown in Figure 6. Two Pt Vacancies. In the case of the double Pt vacancies, the mirror symmetry of the system is restored. The total magnetic moment is mainly localized at the Se atoms surrounding the vacancy without relaxation. However, the

Figure 6. Spin-resolved charge density isosurface (isosurface value = 0.002 e/Å3) of one Pt vacancy in monolayer PtSe2. 25034

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magnetic moment vanishes after relaxation due to the movement of Se atoms surrounding the Pt vacancy. The length of Pt−Se bonds in both layers shrinks to 2.38 Å. The spin-resolved density of states of the 4 × 4 supercell containing two Pt vacancies is shown in Figure 5c. Before relaxation, defect states split up because of the presence of the unpaired electrons on Se atoms surrounding the two Pt vacancies. The imbalance between the occupied majority spin and minority spin states implies a net magnetic moment, and the different majority spin and minority spin densities of states at the Fermi energy indicate that the conducting charges are spin-polarized. The calculated magnetic moment is close to 6.94 μB, i.e., 0.43 μB/ primitive cell. However, after relaxation, the energy of all the electrons contributing to magnetic states increases. As a result, all the states get fully occupied, which forces the system to switch into the nonmagnetic state after relaxation as shown in Figure 5c.

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CONCLUSION In summary, we have carried out first-principles calculations to investigate the effects of hole doping and biaxial tensile strain on the electronic and magnetic properties of monolayer PtSe2. Our results show that the large density of states near the valence band edge can be shifted to Fermi energy via small range of hole doping. With an increase of hole density, average magnetic moment per carrier also increases and reaches its maximum value over a specific range of carrier density, while the system remains in a half metal state before the magnetic moment falls abruptly. Biaxial tensile strain can effectively modify the magnetic moment per carrier and the optimal carrier density, besides stabilizing the ferromagnetic state of the system. We also predict a critical value of biaxial tensile strain (5%) for the doped monolayer PtSe2. Once this critical strain is reached, the optimal carrier density becomes constant with increasing biaxial tensile strains, while the optimal magnetic moment gradually increases and magnetic state of the system becomes more stable as well. Our results provide useful information for the potential applications of doped PtSe2 in spintronics.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.6b06999. Structure stability of doped and defective monolayer PtSe2, effect of energy cutoff on the structural and magnetic properties, and van Hove singularities (PDF)

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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 research was supported by the National Natural Science Foundation of China under Grant No. 11374175. REFERENCES

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DOI: 10.1021/acs.jpcc.6b06999 J. Phys. Chem. C 2016, 120, 25030−25036