Letter pubs.acs.org/JPCL
Long-Range Magnetic Ordering and Switching of Magnetic State by Electric Field in Porous Phosphorene Arqum Hashmi, M. Umar Farooq, and Jisang Hong* Department of Physics, Pukyong National University, Busan 608-737, South Korea S Supporting Information *
ABSTRACT: We explored the possibility of long-range magnetic ordering in two-dimensional porous phosphorene (PP) layer by means of ab-initio calculations. The self-passivated pore geometry showed a nonmagnetic state while the pore geometry with dangling bond at two zigzag edges with a distance of 7.7 Å preferred an antiferromagnetic ordering (AFM). Pore to pore magnetic interaction with a distance of 13.5 Å between two pores was found to be remarkably long ranged, and this emerges from the interactions between the magnetic tails of the edge states in the armchair direction. The AFM state was persisted by the oxidation of the edge. Interestingly, the long-range AFM ordering changed to long-range ferromagnetic (FM) ordering by external electric field. The results are noteworthy in the interplay between electric field and electronic spin degree of freedom in phosphorene studies and may also open a promising way to explore phosphorene-based spintronics devices.
M
ordering in phosphorene layer will bring an intriguing issue for spintronics application. To this end, here, we will explore the physical properties of porous phosphorene (PP) structures. Experimentally, the pores can be created from the perfect 2D layer by using beam treatment, heavy ion bombardment, and by oxidative etching24,25 Hence, in this report, we aim to explore the following issues: (1) effect of pore sizes and edge passivation on the magnetic properties, (2) the possibility of a long-range magnetic ordering, (3) change in magnetic ordering by electric field, and (4) pore size dependent effective mass. In addition, we will investigate the thermodynamic stability of edge passivation with hydrogen (H) and oxygen (O) atom. The pores in phosphorene were obtained by removing 4.3%, 8.6% and 14.3% of phosphorus atoms from a (7 × 5) supercell of phosphorene sheet. The pore size of each structure was characterized by the average of the length (L) and width (W) in the elliptical or rectangular region within the pores. The pore area was estimated according to the area of the ellipse for the small and medium pores, while for largest pore the area of a rectangular was calculated. Figure 1a−c shows a schematic illustration of the top views of three types of pristine PP structures: so-called PP-1, PP-2, and PP-3. Figure 1d−f shows the PPs after structure relaxation. In Table 1, we present the geometric characteristics of each PP system. The change in lattice constant of “b” (along the armchair direction) was more noticeable, while the lattice change of “a” (along the zigzag direction) was rather small. In addition, the geometry of the
echanical exfoliation of a single layer of phosphorene by scotch tape from layered bulk black phosphorus1−3 has opened up exciting opportunities for the design of interesting optoelectronic and optical devices due to its anisotropic electric4,5 and optical properties.6,7 Comparing with graphene, the most striking difference is that phosphorene has a direct band gap.1,2 Due to this semiconducting feature, phosphorene may be superior to graphene for device applications in many ways. Along with the band gap, interestingly, few-layer black phosphorene-based field effect transistors have high mobility and high on/off ratios.1,8 Additionally, it exhibits anisotropic onset energy in the optical absorption peak.6,7 Moreover, the phosphorene layer displays anisotropic electrical transport properties6,9,10 because the effective mass along the zigzag direction is much heavier than that along the armchair direction.1,2,11 Motivated by many studies on the edge magnetism of zigzag graphene nanoribbons, recently edge magnetism has also been explored in zigzag black phosphorene nanoribbons (ZPNR).12−14 It has been shown that pristine ZPNRs show an edge magnetism. However, the structural modification due to the Peierls distortion or edge reconstruction drastically modifies the edge magnetic property of ZPNRs because the edge magnetism of ZPNRs disappears due to this effect.12,13 Regarding the magnetic property in the phosphorene layer, most theoretical works have been done on the existence of the edge magnetism12−15 and magnetic state induced by various factors such as vacancy defect,16,17 adatom defect,18−20 and substitutional doping.21−23 However, it was just a localized magnetism, not ferromagnetism or aniferromagnetism arising from a long-range ordering. Therefore, it will be an intriguing issue if we can find a way to create a magnetic state by manipulating the edge structure. Particularly, a long-range FM © XXXX American Chemical Society
Received: November 21, 2015 Accepted: January 27, 2016
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DOI: 10.1021/acs.jpclett.5b02600 J. Phys. Chem. Lett. 2016, 7, 647−652
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The Journal of Physical Chemistry Letters
Figure 1. Top view of geometric structures of 2D porous phosphorene before structure relaxation: (a) PP-1, (b) PP-2, (c) PP-3, and optimized geometry after structure relaxation: (d) PP-1, (e) PP-2, (f) PP-3.
structure, vibration spectrum is calculated. Figure S1 displays the result of phonon dispersion along the high symmetric points in the Brillouin zone. We found no significant imaginary frequency in the phonon dispersion curve. This result shows that the PP-3 structure with zigzag edges is a stable pore geometry. PP-3 structures have magnetic state because of dangling bonds at the two zigzag edges. We found that each P atom at the edge had a magnetic moment of 0.5 μB, and the π-orbital produced the magnetic moment. On the other hand, the P atom on the opposite side had an antiferromagnetic (AFM) coupling. The total energy of an AFM state was more stable than the ferromagnetic (FM) state by 37 meV/cell. For the nonmagnetic (NM) case, it became the most unstable structure. This result is quite consistent with a previous ZPNR report.12 Figure S2a,b shows the band structures of PP-1 and PP-2 in theSupporting Information (SI). From the optimized structure shown in Figure 1d,e, we can find that both PP-1 and PP-2 structures have no edge state and complete their original sp3 bonding. Thus, the band structures of these two systems were
Table 1. Optimized Lattice Constants (a,b in Å), length of pore L (Å), width of pore W (Å), pore size (Å), and pore area (Å2) system pristine layer PP-1 PP-2 PP-3
lattice constant a a a a
= = = =
23.45, 23.21, 23.24, 23.18,
b b b b
= = = =
23.10 22.27 21.68 21.43
L
W
size
area
-5.485 5.588 8.816
-7.218 10.795 7.797
-6.313 8.165 8.296
-31.09 47.38 68.74
porous structure was dependent on the porous size. For instance, both PP-1 and PP-2 showed oval-like porous structures while the PP-3 displayed a rectangular-like porous structure. Moreover, as shown in Figure 1d−f, the structure was greatly modified at the edges of pores after structure relaxation. In PP1 and PP-2 porous structures, the edge atoms were displaced from their original positions, and the edges atoms were selfpassivated. Consequently, they formed three sp3 covalent bonds with three other neighboring P atoms like in a pristine phosphorene layer, and no dangling bond remained. In PP-3 structure, a similar edge reconstruction was found because we observed the sp3 type bond in most of the edge atoms. However, two P atoms indicated by red color in Figure 1f maintain their zigzag shape at edges. One zigzag edge P atom in the upper layer (left atom) of the phosphorene moved in the downward direction, while the other P edge atom on the opposite side in the down layer (right atom) moved a little bit upward in the z-direction to reduce the total energy. To examine the mechanical stability of zigzag edges in PP-3
Table 2. Total Energy Difference (in meV) and Magnetic Moment (μB) in PP-3 Structures
648
system
NM
FM
AFM
μB
bare PP-3 H-passivated PP-3 O-passivated PP-3
102 NM only --
37 6
0 0
0.5 0.32 (P), 0.20 (O)
DOI: 10.1021/acs.jpclett.5b02600 J. Phys. Chem. Lett. 2016, 7, 647−652
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Figure 2. Band structure of PP-3 and the plots of the wave function square modulus for PP-3 magnetic edge states; iso-surface value is 0.04 eÅ−3. In band structures, black lines are spin-up channels, and red ones are spin-down channels. The blue line at zero indicates the Fermi level.
in the realistic condition. Interestingly, by comparison of H and O passivated structures, we found that the oxygen passivated system had a lower Gibbs free energy. This implies that the oxygen passivated structure will be observed, even if the sample is grown in both H- and O-rich conditions. With the passivation of H at the edge, the dangling bond disappeared, and the sp3 bonding of a hydrogen atom with the P atom was completed. Consequently, the magnetic moment at the edge disappeared, and the calculated band structure was almost the same as that in the pristine layer. However, we still found the spin polarized state at the edge in the O passivation, and this result is quite consistent with previous theories.12 The oxygen atom attached to the upper P layer edge atom has 114° tilted angle in the upward direction with the edge atom, while the oxygen with lower P edge atom has the same tilted angle in the downward direction. Figure S4a in the Supporting Information shows the band structure for O-passivated structure. As shown, the impurity state still existed in the Opassivation, and we found a similar band structure observed in the bare PP-3. In this case, both O and P atoms have magnetic moments of 0.32 and 0.20 μB, respectively. Unlike the hydrogen atom, the oxygen atom has two unpaired electrons. One electron contributed to completing the bonding, and the other electron contributed to the magnetic state. Here, the AFM coupling between two edges was observed. However, the energy difference between the FM and AFM states was from 37 to 6 meV. This may suggest that the FM state can also be observed in a real sample growing condition because it has such a small energy difference. To explore the possibility of longrange magnetic ordering in an oxygen passivated system, we show the π−π*orbital wave functions of hybridized P−O edge states in Figure S4b in the Supporting Information. The spin polarization originates from the pz orbitals of P and O atoms. Here, we find that the spatial distribution of wave functions have rather localized features in the zigzag direction as compared to bare PP-3, and wave functions show that the
not strongly deviated as compared with that of the pristine layer, and we observed a nonmagnetic state in these two systems. By contrast, the edge atoms in PP-3 have magnetic state because of dangling bonds, as displayed in Figure 1f. In many systems, it is not surprising to find local spin magnetic moment owing to impurity doping, vacancy defect, or adatom doping. However, it will be more interesting to find a longrange ordering magnetic state for spintronic device applications. To explore pore-to-pore long-range magnetic ordering, we calculated the spin polarized wave functions. Figure 2 shows the band structure of PP-3 and spatial distribution of wave functions of both dangling bond states of π-orbitals. The spin polarized wave functions of edge states in the valence band are delocalized, and the decaying tails of the wave function are extended in the armchair direction between the two edges. Since the magnetic tail has a finite decay length, the long-range magnetic ordering can be observed if the distance between the two pores is not too long. The gold color represents the wave functions of the spin-up state, while the cyan color represents wave functions of the spin-down state. The wave functions above the Fermi level have comparatively localized behavior near the edge atoms, but the magnetic tail in the armchair direction is still delocalized and protracted up to the boundary of the cell to form a long-range magnetic ordering. We now discuss the effect of H and O passivation. Since the PP-3 has a dangling bond at the edge and spin polarized state, we focus on the PP-3 structure. In real experimental conditions, the sample growing will be taking place at finite temperatures, and the vacuum chamber may contain some molecular gas such as H2 or O2. Thus, it will be more informative to calculate the thermodynamic Gibbs free energy (G) to explore the stability of the passivation. Figure S3 in the Supporting Information shows the calculated result at 300 K. Since the ultrahigh vacuum corresponds to ∼10−12 bar, we focus on the pressure in the range from 10° to 10−12 bar. We found that the passivated system was more stable than the unpassivated porous structure 649
DOI: 10.1021/acs.jpclett.5b02600 J. Phys. Chem. Lett. 2016, 7, 647−652
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passivation because it has a lower Gibbs potential energy. Here, we assume that the external electric field is applied perpendicular to the layer surface. Figure 3a shows the total energy difference as a function of the electric field strength. As presented in Table 3, the oxygen passivated system had an AFM ground state at zero field. With increasing the electric field, the total energy difference between the FM and the AFM state gradually suppressed, and we observed an FM ground state at an electric field of 1.6 eV/ Å. It must be noted that the AFM state at 1.6 eV/Å was actually ferrimagnetic because one edge has a magnetic moment of 0.53 μB, while the other edge has a magnetic moment of −0.33 μB. In FM state, the total magnetic moment is 3.3 μB. We found that the edge geometry was greatly affected by the external electric field. Figure 3b shows the edge structure with increasing applied electric field. As the electric field increased, the O atom at both edges gradually moved downward. Thus, the structural asymmetry appeared as compared with that at zero field. When we applied the electric field, the relative electrostatic potential difference was generated at the edge oxygen atoms. For instance, the oxygen atom attached to the right P edge has a higher potential than the oxygen atom bonded to the left P edge in PP-3. The pore-to-pore FM interaction can be understood in a semiqualitative manner. If two spins at both edges have an antiparallel configuration, the overall spatial wave function should be symmetric, and this increases the Coulomb repulsive energy. On the other hand, the parallel spin configuration has an antisymmetric spatial wave function, and this causes relatively weaker Coulomb repulsive energy. With increasing the electric field, the distortion of wave function will be enhanced, and this results in increasing the kinetic energy in both FM and ferrimagnetic spin configurations. Consequently, the relative importance of the Coulomb repulsive interaction
magnetic state originating from the hybridization of the P edge state with O atoms by oxidation. The magnetic tails of the πorbital wave functions are extended in the armchair direction. Thus, both AFM edge tails are interacting with each other and a long-range magnetic ordering is preserved by oxidation of the edges. Figure S4c,d in the Supporting Information shows the partial DOS of P and O atoms of both edges. Both P and O atoms were strongly hybridized. The DOS confirms that the spin polarization originates from the pz orbital of both P and O atoms. One of the main issues is to investigate the possibility of long-range magnetic ordering in a porous phosphorene layer. To check pore-to-pore magnetic coupling, the PP-3 cell size is twice that along the armchair direction. It should be noted that pore-to-pore distance is 13.53 Å in the armchair direction, and no pore deformation was found when two pores coexisted. Table 3 shows the total energy in each pore-to-pore magnetic Table 3. Total Energy Difference (in meV) in (Pore-to-Pore) PP-3 Structure system
NM
FM
AFM
Bare PP-3 H-passivated PP-3 O-passivated PP-3
213 NM only --
85 10
0 0
interaction. The total energy in AFM was set to zero. We found an AFM ground state not only within each pore but also between two pores. This result indicates an existence of a longrange AFM ordering in porous phosphorene as we deduced in a single pore geometry. We further investigated the electric field effect on the poreto-pore magnetic interaction in PP-3 structure with O-
Figure 3. (a) Energy difference among different magnetic configurations. (b) Change in edge structure with the applied electric field. 650
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Figure 4. FM ground state band structure and wave functions of the π−π* hybridized P−O magnetic edge states with the same iso-surface value of 0.035 e/Å3 at 1.6 eV/Å electric field. Black lines correspond to the majority spin band while the red dashed lines represent the minority spin band.
was increased to reduce the total energy. Due to this feature, the FM becomes a ground state. Figure 4 shows the band structure for the FM ground state along with the wave functions corresponding to the edge states of the PP-3 system at 1.6 eV/Å. Here, for simplicity, we present the band structure of single pore because the same result of edge states with delocalized wave functions was obtained with the existence of two pores. The α and β represent the spin-up states in the occupied states, while the α′ and β′ represent spin-down components in the unoccupied states. The spin polarized wave functions of edge states in the valence band are highly delocalized as compared with the O-passivated system at zero field. Consequently, we found that the electric field contributed to enhancing the long-range FM interaction. This long-range FM ordering can be utilized for potential spintronics applications. We estimated the effective mass of porous phosphorene along the gamma-Y direction (armchair direction) because charge transport along the gamma-Y direction is more efficient than the gamma-X direction (zigzag direction). In Table SI, we present the calculated effective masses for porous systems. As shown in Figure S5 in the Supporting Information (SI), both hole and electron effective masses were greatly suppressed at small electric fields, and we found an asymmetric behavior. The large modulation of the effective mass of the electrons and hole by the electric field demonstrates the possibility of tuning the mobility and helps to design the microelectronic and optoelectronic nanodevices. In conclusion, we investigated the possibility of long-range magnetic ordering in two-dimensional porous phosphorene (PP-X) material with different porous sizes. The two zigzag edges in PP-3 preferred an antiferromagnetic ordering, and the magnetic tails along the armchair direction were delocalized and extended up to the boundary of the cell to form long-range AFM ordering. The thermodynamic Gibbs free energy calculation indicated that the O edge passivation system was more stable than the pristine and H-passivated PP-3. Long-
range AFM ordering in PP-3 structure is preserved by oxidation of the edges. With the applied electric field, the total energy difference between FM and AFM states were gradually suppressed, and we observed an FM ground state at 1.6 eV/ Å. The magnetic tails of the edge states with electric field was more delocalized, and this resulted in more enhanced longrange pore-to-pore FM interaction. Along with this change in the magnetic ground state, we observed a significant change in the effective mass because of external electric field. Our finding may provide a fundamental basis for the application of the porous phosphorene and open up an effective way to modulate its effective mass through an external perpendicular electric field.
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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.jpclett.5b02600. Computational details, thermodynamic stability of edges, band structures of PP-1 and PP-2, Gibbs free energy calculations of passivated system, O-passivated PP-3 band structure with wave functions and DOS, and effective masses of porous systems (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 Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 2013R1A1A2006071) and by the Supercomputing Center/Korea Institute of Science and Technology 651
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(22) Sui, X.; Si, C.; Shao, B.; Zou, X.; Wu, J.; Gu, B.-L.; Duan, W. Tunable Magnetism in Transition-Metal-Decorated Phosphorene. J. Phys. Chem. C 2015, 119, 10059−10063. (23) Khan, I.; Hong, J. Manipulation of Magnetic State in Phosphorene Layer by Non-Magnetic Impurity Doping. New J. Phys. 2015, 17, 023056. (24) Fischbein, M. D.; Drndić, M. Electron Beam Nanosculpting of Suspended Graphene Sheets. Appl. Phys. Lett. 2008, 93, 113107. (25) Lehtinen, O.; Kotakoski, J.; Krasheninnikov, A. V.; Tolvanen, A.; Nordlund, K.; Keinonen, J. Effects of Ion Bombardment on a TwoDimensional Target: Atomistic Simulations of Graphene Irradiation. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 81, 153401.
Information with supercomputing resources including technical support (KSC-2015-C3-040).
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