rus
Issue #3/2016
V. Ilyasov, I. Popova, I.Ershov
Modeling Of The Electronic Properties Of Graphene Magnetic Heterostructures: Ab Initio Study
Modeling Of The Electronic Properties Of Graphene Magnetic Heterostructures: Ab Initio Study
Magnetism of defect-free graphene is a surprising phenomenon that deserves the attention of theorists and experimentalists, as it gives us a hope for the new discoveries of quantum effects in future. Within the framework of the density functional theory (DFT) we have simulated graphene electronic structure adsorbed on a magnetic insulator MnO (111), limited by oxygen. Interface of graphene heterostructure SLG/H:MnO (111) has been modulated by the degree of its hydrogenation. DFT-based calculation has been used to systematically investigate the local atomic reconstruction of the interface depending on the degree of hydrogenation. It has been shown that the electron spectrum and magnetism in the system SLG/H:MnO (111) can be modulated by the degree of hydrogenation of the oxygen interface layer, suggesting high potential for the use of this system in spintronics.
Теги: charge transfer between graphene and metals electronic properties of graphene magnetism in graphene metatronics spintronics магнетизм в графене метатроника перенос заряда между графеном и металлами спинтроника электронные свойства графена
INTRODUCTION
Graphene, being a material with a reduced dimension, due to the unique properties when combined, with dielectrics for instance, may be a promising object to create devices such as field effect transistors, switching devices, sensors, etc. In this case, classical magnets can be used as a substrate for formation graphene layers, in particular, ultra-thin film of manganese monoxide. Earlier, in the framework of DFT, we have studied the properties of the atomic and band structure of the interface between the graphene and the surface (001) of manganese oxide MnO for ferromagnetic and antiferromagnetic ordering, as a possible base of new materials for spintronics [1]. The electronic properties of graphene are very sensitive to changes in the ambient conditions [2], which also include the state of the substrate surface. It is known [3] that graphene is adsorbed on the polar surface of the silica, and the charge is transferred to the interface. However, the processes of chemisorption in the systems graphene / MnO (111) have not previously been considered. We believe that the change in the structural and electronic properties of graphene as a result of interaction with the dielectric substrate deserves closer attention.
Model and method
The theoretical model of the system under study SLG/H:MnO (111) has been built according to the scheme of triperiodic plate. We have used a supercell of 58 atoms bounded by a monolayer of oxygen atoms containing unit cells (2 × 2) MnO in the plane (111). Figure 1 shows a fragment of the plate simulating the interface SLG/H:MnO (111). Graphene is centered on the oxygen atom of the substrate which corresponds to the position of the linking oxygen atom. This configuration corresponds to the minimum energy as compared with other binding positions. We have examined four different configurations of hydrogen atom arrangement in the interface between graphene and plate MnO (111): b – four (or three) hydrogen atoms are linked to the top layer of oxygen atoms (in case of complete coverage, the 4th hydrogen atom are closed with carbon atom number 10); c – two hydrogen atoms are linked to the closest oxygen atoms; d – one hydrogen atom is linked to an oxygen atom of the upper layer.
The plate of substrate is composed of 11 non-equivalent planes in direction [111]: 4 planes of manganese, 5 planes of oxygen and 2 planes of hydrogen. The vacuum slot is 12 Å wide, which allowed us to exclude any interaction between the translations of the plate in the direction [111]. In this research, we have made self-consistent calculations of the total energy on the basis of the electron density functional theory (DFT) using pseudopotential approximation (Quantum-Espresso code) [4]. PBE functional with dispersion correction (PBE-D2) has been used for the exchange-correlation energy [5]. The energy absorption of the oxygen atom in the system SLG/H:MnO (111) has been determined based on the ratio [6]. The effective charges on the atoms of the interface have been determined based on the Levdin population analysis [7].
ATOMIC STRUCTURE OF MAGNETIC INTERFACE
Atomic structure of a four-layer plate with graphene for four configurations of SLG/H:MnO (111) system after the relaxation is shown in Fig. 1. The equilibrium of grating parameters, atomic positions of carbon atoms in graphene, and the atoms of the upper two double layers of manganese monoxide have been established. The bond length between the carbon atoms in graphene, the distance between the pairs of atoms of interface and the length of Mn-O-bond in the upper layers of manganese oxide plates have been determined for five different configurations of SLG/H:MnO (111) system after relaxation, as listed in Table 1.
Our DFT calculations of interplanar spacing in SLG/H:MnO (111) system have shown that the distance in the direction occurs between the layers of manganese and oxygen atoms, the average value of which varies depending on the degree of hydrogen coverage of O-polar interface surface. These calculations are shown in Table 2. To summarize the data given in Tables 1 and 2, we should note a significant restructuring of local atomic structure due to the binding position of the hydrogen atoms on the surface of the polar oxygen in the interface SLG/H:MnO (111).
ADSORPTION OF GRAPHENE
Adsorption of hydrogenated graphene on the surface of the magnetic interface leads to a change of interplanar spacing between the upper layers of manganese and oxygen atoms (see Table 2). The nature of the observed adjustment of atomic structure in the interface SLG/H:MnO (111) associated with the adsorption of graphene on the surface of the interface can be understood by a detailed study of the electronic structure of each of the considered models of graphene adsorption. For the configurations caused by varying degrees of hydrogenation of the interface layer in the oxygen system SLG/H:MnO (111) we have obtained graphen adsorption energies on non-hydrogenated and hydrogenated substrates, as shown in Table 2.
The analysis of the results presented in Table 2 shows that the process of hydrogen passivation of surface oxygen reduces the amount of energy absorption by the amount = 27 meV/atom. The nature of this phenomenon has not been discussed in the literature. By increasing the coverage of oxygen with hydrogen interface layer to a value of θ = 1.0 ML, adsorption energy value is reduced by 1.7 times. In our opinion, the decrease of adsorption energy by 40.7% in the hydrogenation of the interface SLG/H:MnO (111) should be associated with the decrease in the interaction of graphene with the substrate. It should be noted that in this system, oxygen hydrogenation interface layer is a determining mechanism in the implemented chemisorption processes.
For a better understanding of the processes of chemisorptions, one should examine the distribution of the effective charges on the atoms of the interface SLG/H:MnO (111) for the different degrees of hydrogenation. The results of DFT calculations of effective charges on the carbon atoms and the closest surface atoms of hydrogen, oxygen and manganese for the studied configurations of systems SLG/H:MnO (111) are shown in Table 3.
The analysis of the data shown in table 3 allows us to note the existence of a general tendency of the charge transfer from the carbon atoms to atoms of the interface (hydrogen and oxygen), as was the case in the researches [3]. The results of the value of effective charges on the atoms of manganese, oxygen and carbon for non-hydrogenated interface surface are out of the common picture. It should be noted that for the degree of hydrogenation θ = 0.75 ML, the effective charges on the carbon atoms have been less than two times, and the hydrogen atoms have been three times larger than those of completely hydrogenated interface surface (θ = 1.0 ML). The reason for this effect may be found in the atomic configuration features, which is characterized by a decrease of 3% of the distance between the interface layer and the underlying oxygen manganese layer (see Table 2) with respect to a completely hydrogenated interface surface (θ = 1.0 ML). In this regard, there are differences due to the intensity of the effective charge transport mechanisms. For all configurations, there is a charge transfer from the manganese atoms to the oxygen atoms. In general, the charge transfer determines the mechanisms of chemisorption processes of grapheme on the polar surface (111) and causes significant difference in electronegativity (according to Pauling) of the manganese atoms (1.55 X), oxygen (3.44 X), carbon (2.55 X) and hydrogen (2.20 X) [9]. However, it is known [10] that in the context of a weak charge-transfer interaction in the interface, the mechanism of physical adsorption is a controlling one. The process of charge transfer will occur until the equilibrium of chemical potentials of graphene and the substrate H: MnO (111) when combined.
The consideration of different configurations of atomic surfaces of magnetic interface SLG/H:MnO (111) has showed that the hydrogenation of the interface surface results in a significant rearrangement of local atomic structure. It can be summarized that the hydrogenation of the interface layer partially reduces oxygen interaction with the substrate of graphene H: MnO (111), which is observed in the DFT calculations (see Table 2). The above mentioned disorders of local atomic structure should appear in the energy spectrum of surface atoms of carbon, oxygen, hydrogen and manganese in the above configurations of the systems SLG/H:MnO (111).
INTERFACE ELECTRONIC STRUCTURE
We have calculated the band structure for different configurations of the interface SLG/H:MnO (111) after relaxation. The band spectrum of the system with a full hydrogenation interface is shown in Figure 2. The analysis of the band spectra has shown that the hydrogen coating in the range of θ = 0÷1,0 ML (monolayers) of the interface surface leads to a substantial rearrangement of electronic structure near the Fermi level. It should be noted that the substrate without hydrogenation contributes to the opening of the energy gap between bonding and antibonding valence π-bands of graphene about 0.85 eV wide for electronic subsystems of both spins. The linear dispersion law in the tops of the π-bands has been replaced by a parabolic one, indicating the final appearance of the effective masses of the charge carriers. These bands are shifted up in energy relative to the Fermi level, which indicates the charge transfer in the interface. In turn, the charge transfer in the interface shifts the Fermi level relative to the top of the Dirac cone and is controlled by work function channel of substrate [11]:, where is the middle of graphene gap adsorbed on the surface of the magnetic insulator. This consideration suggests that the doped graphene has a band structure of p-type semiconductor. The observed phenomenon may be due to the difference in work function and the surface of graphene monoxide MnO (111). The results of DFT calculations of work function and other parameters of the electronic structure and magnetism are shown in Table. 4.
The analysis of the data shown in table 4 allows us to note that when the shift mechanism of hydrogenation is involved, the value of the Fermi level decreases down almost linearly in the range of coverings θ = (0÷0.75) ML. For the degree of covering θ = 0.75 ML, the value of down shift of the Fermi level is only = 0.02 eV. The value of the difference between the surface of the work functions of MnO (111) and that of graphene without substrate is = –0.21 eV. The band of forbidden gap is = 11 meV and the charge transfer from graphene to hydrogen atoms is reduced to a value of 0,010 e. The band structure of the interface retains the p-type semiconductor. However, with increasing hydrogenation up to θ = 1.0 ML, the Fermi level is shifted upward by an amount of = –0.09 eV. Such a band structure (see Fig. 2a) can be interpreted as n-type semiconductor, provided the availability of the gap. The results of DFT calculations of the forbidden gap width are shown in Table 4. It therefore results, that the band structure of graphene contains the forbidden gap, the value of which may vary in the range from 1 MeV to 85 MeV.
The features of formation of energy bands near the Fermi level is well illustrated with patterns of partial densities of states (DOS) of the atoms: carbon, manganese, oxygen, and the total density of electronic states (TDOS) (Figure 2.). In particular, Fig. 2a shows that in system SLG/MnO (111) hybridization of 2p-orbitals of oxygen and carbon with 3d-orbitals of manganese occurs without hydrogenation, which is responsible in the formation of the peak occupied electron states with energy of –0.1 eV in the TDOS curve. With the degree of hydrogenation of the interface to the value of θ = 1.0 ML, the electronic structure of system SLG/H:MnO (111) has experienced significant changes in the vicinity to the Fermi level. Thus, the partial 2p-states of the carbon atoms lie below the Fermi level and are localized at the energy level of –0.1 eV. For electronic subsystems with spin-down, partial 2p- and 3d-states of electrons in the atoms of oxygen and manganese are highly localized, forming a series of peaks in the TDOS curve in the range of energies of – (0.4—1.7) eV. The band structure of system SLG/H:MnO (111) in this energy range is also greatly disturbed.
It should be emphasized that the hydrogenation of the interface leads to a substantial change in the electronic properties of the interface, in particular to reduction of the quantities of adsorbed graphene work function and manganese monoxide surface (see Table 4). Importantly, the hydrogenation process of the interface to the coverage of θ = 1.0 ML gives a new qualitative effect – n-type semiconductor. The latter opens up the possibility of creating graphene FET of n-type, that is of considerable interest for nanoelectronics. As a possible mechanism for controlling p-n-transition hydrogenation degree of oxygen interface layer in the interface SLG/H:MnO (111) may be used. In particular, the research [8] has considered the possibility to control the electronic properties of graphene by chemical modification of the substrate surface prior to deposition of graphene.
MAGNETISM OF THE INTERFACE
SLG/H:MNO (111)
The analysis of Table 4 allowed us to note that local magnetic moments (MW) are induced on the carbon atoms, whose average value is an order of magnitude less than for the other interface atoms. However, the study of the nature of magnetism in graphene remains a matter of intense interest of the researchers [12]. We have shown that in the case of non-hydrogenated surface of the interface, local moments of different directions are induced on both gratings (A and B) of grapheme, perpendicular to the graphene plane. This pattern is disturbed in the vicinity of the graphene grating defects caused by the establishment of a chemical bond between the individual carbon and oxygen atoms in a state of chemical bond. Induced local magnetic moment on such carbon atoms is maximum (—0.011), and the direction is of the same sign as the magnetic moment of the next layer of manganese atoms (—4.87). The carbon atoms of immediate environment induce local magnetic moments (0.001), the value of which averagely is one order of magnitude less, and the direction is opposite. The observed symmetry breaking in the vicinity of such gratings of carbon atoms and inducing of maximum MM allows us to draw an analogy with the boundary magnetism in graphene nanoribbons of zigzag type ZGNR/h-BN (0001) [12] and claim that MM (—0.011) on carbon atom can be induced by a deformation of gratings due to the correlation of main singlet state of unpaired electron of carbon atoms, as in the research [13]. When including hydrogenation of oxygen interface layer, the configuration of distribution of the effective charges of carbon atoms changes its selective character to the constant sign. In particular, for the degree of coverage θ = 0.25 ML effective charge on the carbon atoms become positive only, and its average value is 0,032 e. The induced local magnetic moments on the carbon atoms are practically the same by their magnitude (—0.0017), that is in 1, 8 times less than for the non-hydrogenated surface. The direction of the local magnetic moments on the carbon atoms has the same sign as the magnetic moment on the atom of manganese, lying under a layer of interface oxygen. By increasing the degree of coverage of up to θ = 1.0 ML, there is a decrease in size of induced local magnetic moment on the carbon atoms. In the hydrogenation of the considered interface, the direction of local MM on the carbon atoms is retained.
The nature of magnetism of defect-free graphene layer being a part of system SLG/H:MnO (111) as a possible basis for applications in molecular magnets and spintronic devices is of particular interest. Our DFT calculation of local magnetic moments on the carbon atoms has shown that for the degree of hydrogenation θ = 0.25 ML, the total magnetic moment of the graphene sheet is –0.02 µB per supercell. It should be noted that in the hydrogenation of the interface surface for graphene gratings (A and B), there is a degeneration in the direction of the induced local moments. All local MM on the carbon atoms are in the same direction. This degeneracy is retained up to the degree of hydrogenation θ = 1.0 ML. By increasing the degree of hydrogenation from θ = 0.25 ML to θ = 1.0 ML, the magnitude of the local magnetic moment at the carbon atom decreases by 1.5 times. The orientation of the local magnetic moments on the carbon atoms, which coincides with the direction of the local MM atoms at the surface layer of manganese may occur similar to the mechanism of superexchange interaction characteristic for the majority of ferromagnetic and ferrimagnetic insulators.
It has been shown that the hydrogenation of the interface leads to a significant change in its electronic properties. As a result of the charge transfer, p-doping of graphene occurs and semimetal-semiconductor transition is observed. In the case of the hydrogenation of the interface to the degree of coverage θ = 1.0 ML, there is p-n-transition in graphene and a new qualitative state, n-type semiconductor, occurs. The latter gives us the possibility of creating graphene n-type FET, that is of considerable interest for nanoelectronics.
Magnetism of defect-free graphene in the system SLG/H:MnO (111) is definitely an amazing phenomenon, and deserves the attention of theoreticians and experimentalists as the new quantum effects and new multi-functional properties can be discovered. The question of the mechanisms of magnetism inducing in a defect-free graphene, in our view, remains open. It is interesting to draw an analogy in the mechanism of magnetization of graphene in the system SLG/H:MnO (111) and system SLG/YIG (yttrium-iron-garnet) [14], since the substrate acts as a magnetic insulator in both cases.
This review has shown that the electron spectrum and magnetism in the system SLG/H:MnO (111) can be modulated by the degree of hydrogenation of the interface layer of oxygen, suggesting high potential for the use of this system in spintronics.
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[1] Ab initio – (с лат. – "от начала")
** SLG – single-layer graphene (однослойный графен)
Graphene, being a material with a reduced dimension, due to the unique properties when combined, with dielectrics for instance, may be a promising object to create devices such as field effect transistors, switching devices, sensors, etc. In this case, classical magnets can be used as a substrate for formation graphene layers, in particular, ultra-thin film of manganese monoxide. Earlier, in the framework of DFT, we have studied the properties of the atomic and band structure of the interface between the graphene and the surface (001) of manganese oxide MnO for ferromagnetic and antiferromagnetic ordering, as a possible base of new materials for spintronics [1]. The electronic properties of graphene are very sensitive to changes in the ambient conditions [2], which also include the state of the substrate surface. It is known [3] that graphene is adsorbed on the polar surface of the silica, and the charge is transferred to the interface. However, the processes of chemisorption in the systems graphene / MnO (111) have not previously been considered. We believe that the change in the structural and electronic properties of graphene as a result of interaction with the dielectric substrate deserves closer attention.
Model and method
The theoretical model of the system under study SLG/H:MnO (111) has been built according to the scheme of triperiodic plate. We have used a supercell of 58 atoms bounded by a monolayer of oxygen atoms containing unit cells (2 × 2) MnO in the plane (111). Figure 1 shows a fragment of the plate simulating the interface SLG/H:MnO (111). Graphene is centered on the oxygen atom of the substrate which corresponds to the position of the linking oxygen atom. This configuration corresponds to the minimum energy as compared with other binding positions. We have examined four different configurations of hydrogen atom arrangement in the interface between graphene and plate MnO (111): b – four (or three) hydrogen atoms are linked to the top layer of oxygen atoms (in case of complete coverage, the 4th hydrogen atom are closed with carbon atom number 10); c – two hydrogen atoms are linked to the closest oxygen atoms; d – one hydrogen atom is linked to an oxygen atom of the upper layer.
The plate of substrate is composed of 11 non-equivalent planes in direction [111]: 4 planes of manganese, 5 planes of oxygen and 2 planes of hydrogen. The vacuum slot is 12 Å wide, which allowed us to exclude any interaction between the translations of the plate in the direction [111]. In this research, we have made self-consistent calculations of the total energy on the basis of the electron density functional theory (DFT) using pseudopotential approximation (Quantum-Espresso code) [4]. PBE functional with dispersion correction (PBE-D2) has been used for the exchange-correlation energy [5]. The energy absorption of the oxygen atom in the system SLG/H:MnO (111) has been determined based on the ratio [6]. The effective charges on the atoms of the interface have been determined based on the Levdin population analysis [7].
ATOMIC STRUCTURE OF MAGNETIC INTERFACE
Atomic structure of a four-layer plate with graphene for four configurations of SLG/H:MnO (111) system after the relaxation is shown in Fig. 1. The equilibrium of grating parameters, atomic positions of carbon atoms in graphene, and the atoms of the upper two double layers of manganese monoxide have been established. The bond length between the carbon atoms in graphene, the distance between the pairs of atoms of interface and the length of Mn-O-bond in the upper layers of manganese oxide plates have been determined for five different configurations of SLG/H:MnO (111) system after relaxation, as listed in Table 1.
Our DFT calculations of interplanar spacing in SLG/H:MnO (111) system have shown that the distance in the direction occurs between the layers of manganese and oxygen atoms, the average value of which varies depending on the degree of hydrogen coverage of O-polar interface surface. These calculations are shown in Table 2. To summarize the data given in Tables 1 and 2, we should note a significant restructuring of local atomic structure due to the binding position of the hydrogen atoms on the surface of the polar oxygen in the interface SLG/H:MnO (111).
ADSORPTION OF GRAPHENE
Adsorption of hydrogenated graphene on the surface of the magnetic interface leads to a change of interplanar spacing between the upper layers of manganese and oxygen atoms (see Table 2). The nature of the observed adjustment of atomic structure in the interface SLG/H:MnO (111) associated with the adsorption of graphene on the surface of the interface can be understood by a detailed study of the electronic structure of each of the considered models of graphene adsorption. For the configurations caused by varying degrees of hydrogenation of the interface layer in the oxygen system SLG/H:MnO (111) we have obtained graphen adsorption energies on non-hydrogenated and hydrogenated substrates, as shown in Table 2.
The analysis of the results presented in Table 2 shows that the process of hydrogen passivation of surface oxygen reduces the amount of energy absorption by the amount = 27 meV/atom. The nature of this phenomenon has not been discussed in the literature. By increasing the coverage of oxygen with hydrogen interface layer to a value of θ = 1.0 ML, adsorption energy value is reduced by 1.7 times. In our opinion, the decrease of adsorption energy by 40.7% in the hydrogenation of the interface SLG/H:MnO (111) should be associated with the decrease in the interaction of graphene with the substrate. It should be noted that in this system, oxygen hydrogenation interface layer is a determining mechanism in the implemented chemisorption processes.
For a better understanding of the processes of chemisorptions, one should examine the distribution of the effective charges on the atoms of the interface SLG/H:MnO (111) for the different degrees of hydrogenation. The results of DFT calculations of effective charges on the carbon atoms and the closest surface atoms of hydrogen, oxygen and manganese for the studied configurations of systems SLG/H:MnO (111) are shown in Table 3.
The analysis of the data shown in table 3 allows us to note the existence of a general tendency of the charge transfer from the carbon atoms to atoms of the interface (hydrogen and oxygen), as was the case in the researches [3]. The results of the value of effective charges on the atoms of manganese, oxygen and carbon for non-hydrogenated interface surface are out of the common picture. It should be noted that for the degree of hydrogenation θ = 0.75 ML, the effective charges on the carbon atoms have been less than two times, and the hydrogen atoms have been three times larger than those of completely hydrogenated interface surface (θ = 1.0 ML). The reason for this effect may be found in the atomic configuration features, which is characterized by a decrease of 3% of the distance between the interface layer and the underlying oxygen manganese layer (see Table 2) with respect to a completely hydrogenated interface surface (θ = 1.0 ML). In this regard, there are differences due to the intensity of the effective charge transport mechanisms. For all configurations, there is a charge transfer from the manganese atoms to the oxygen atoms. In general, the charge transfer determines the mechanisms of chemisorption processes of grapheme on the polar surface (111) and causes significant difference in electronegativity (according to Pauling) of the manganese atoms (1.55 X), oxygen (3.44 X), carbon (2.55 X) and hydrogen (2.20 X) [9]. However, it is known [10] that in the context of a weak charge-transfer interaction in the interface, the mechanism of physical adsorption is a controlling one. The process of charge transfer will occur until the equilibrium of chemical potentials of graphene and the substrate H: MnO (111) when combined.
The consideration of different configurations of atomic surfaces of magnetic interface SLG/H:MnO (111) has showed that the hydrogenation of the interface surface results in a significant rearrangement of local atomic structure. It can be summarized that the hydrogenation of the interface layer partially reduces oxygen interaction with the substrate of graphene H: MnO (111), which is observed in the DFT calculations (see Table 2). The above mentioned disorders of local atomic structure should appear in the energy spectrum of surface atoms of carbon, oxygen, hydrogen and manganese in the above configurations of the systems SLG/H:MnO (111).
INTERFACE ELECTRONIC STRUCTURE
We have calculated the band structure for different configurations of the interface SLG/H:MnO (111) after relaxation. The band spectrum of the system with a full hydrogenation interface is shown in Figure 2. The analysis of the band spectra has shown that the hydrogen coating in the range of θ = 0÷1,0 ML (monolayers) of the interface surface leads to a substantial rearrangement of electronic structure near the Fermi level. It should be noted that the substrate without hydrogenation contributes to the opening of the energy gap between bonding and antibonding valence π-bands of graphene about 0.85 eV wide for electronic subsystems of both spins. The linear dispersion law in the tops of the π-bands has been replaced by a parabolic one, indicating the final appearance of the effective masses of the charge carriers. These bands are shifted up in energy relative to the Fermi level, which indicates the charge transfer in the interface. In turn, the charge transfer in the interface shifts the Fermi level relative to the top of the Dirac cone and is controlled by work function channel of substrate [11]:, where is the middle of graphene gap adsorbed on the surface of the magnetic insulator. This consideration suggests that the doped graphene has a band structure of p-type semiconductor. The observed phenomenon may be due to the difference in work function and the surface of graphene monoxide MnO (111). The results of DFT calculations of work function and other parameters of the electronic structure and magnetism are shown in Table. 4.
The analysis of the data shown in table 4 allows us to note that when the shift mechanism of hydrogenation is involved, the value of the Fermi level decreases down almost linearly in the range of coverings θ = (0÷0.75) ML. For the degree of covering θ = 0.75 ML, the value of down shift of the Fermi level is only = 0.02 eV. The value of the difference between the surface of the work functions of MnO (111) and that of graphene without substrate is = –0.21 eV. The band of forbidden gap is = 11 meV and the charge transfer from graphene to hydrogen atoms is reduced to a value of 0,010 e. The band structure of the interface retains the p-type semiconductor. However, with increasing hydrogenation up to θ = 1.0 ML, the Fermi level is shifted upward by an amount of = –0.09 eV. Such a band structure (see Fig. 2a) can be interpreted as n-type semiconductor, provided the availability of the gap. The results of DFT calculations of the forbidden gap width are shown in Table 4. It therefore results, that the band structure of graphene contains the forbidden gap, the value of which may vary in the range from 1 MeV to 85 MeV.
The features of formation of energy bands near the Fermi level is well illustrated with patterns of partial densities of states (DOS) of the atoms: carbon, manganese, oxygen, and the total density of electronic states (TDOS) (Figure 2.). In particular, Fig. 2a shows that in system SLG/MnO (111) hybridization of 2p-orbitals of oxygen and carbon with 3d-orbitals of manganese occurs without hydrogenation, which is responsible in the formation of the peak occupied electron states with energy of –0.1 eV in the TDOS curve. With the degree of hydrogenation of the interface to the value of θ = 1.0 ML, the electronic structure of system SLG/H:MnO (111) has experienced significant changes in the vicinity to the Fermi level. Thus, the partial 2p-states of the carbon atoms lie below the Fermi level and are localized at the energy level of –0.1 eV. For electronic subsystems with spin-down, partial 2p- and 3d-states of electrons in the atoms of oxygen and manganese are highly localized, forming a series of peaks in the TDOS curve in the range of energies of – (0.4—1.7) eV. The band structure of system SLG/H:MnO (111) in this energy range is also greatly disturbed.
It should be emphasized that the hydrogenation of the interface leads to a substantial change in the electronic properties of the interface, in particular to reduction of the quantities of adsorbed graphene work function and manganese monoxide surface (see Table 4). Importantly, the hydrogenation process of the interface to the coverage of θ = 1.0 ML gives a new qualitative effect – n-type semiconductor. The latter opens up the possibility of creating graphene FET of n-type, that is of considerable interest for nanoelectronics. As a possible mechanism for controlling p-n-transition hydrogenation degree of oxygen interface layer in the interface SLG/H:MnO (111) may be used. In particular, the research [8] has considered the possibility to control the electronic properties of graphene by chemical modification of the substrate surface prior to deposition of graphene.
MAGNETISM OF THE INTERFACE
SLG/H:MNO (111)
The analysis of Table 4 allowed us to note that local magnetic moments (MW) are induced on the carbon atoms, whose average value is an order of magnitude less than for the other interface atoms. However, the study of the nature of magnetism in graphene remains a matter of intense interest of the researchers [12]. We have shown that in the case of non-hydrogenated surface of the interface, local moments of different directions are induced on both gratings (A and B) of grapheme, perpendicular to the graphene plane. This pattern is disturbed in the vicinity of the graphene grating defects caused by the establishment of a chemical bond between the individual carbon and oxygen atoms in a state of chemical bond. Induced local magnetic moment on such carbon atoms is maximum (—0.011), and the direction is of the same sign as the magnetic moment of the next layer of manganese atoms (—4.87). The carbon atoms of immediate environment induce local magnetic moments (0.001), the value of which averagely is one order of magnitude less, and the direction is opposite. The observed symmetry breaking in the vicinity of such gratings of carbon atoms and inducing of maximum MM allows us to draw an analogy with the boundary magnetism in graphene nanoribbons of zigzag type ZGNR/h-BN (0001) [12] and claim that MM (—0.011) on carbon atom can be induced by a deformation of gratings due to the correlation of main singlet state of unpaired electron of carbon atoms, as in the research [13]. When including hydrogenation of oxygen interface layer, the configuration of distribution of the effective charges of carbon atoms changes its selective character to the constant sign. In particular, for the degree of coverage θ = 0.25 ML effective charge on the carbon atoms become positive only, and its average value is 0,032 e. The induced local magnetic moments on the carbon atoms are practically the same by their magnitude (—0.0017), that is in 1, 8 times less than for the non-hydrogenated surface. The direction of the local magnetic moments on the carbon atoms has the same sign as the magnetic moment on the atom of manganese, lying under a layer of interface oxygen. By increasing the degree of coverage of up to θ = 1.0 ML, there is a decrease in size of induced local magnetic moment on the carbon atoms. In the hydrogenation of the considered interface, the direction of local MM on the carbon atoms is retained.
The nature of magnetism of defect-free graphene layer being a part of system SLG/H:MnO (111) as a possible basis for applications in molecular magnets and spintronic devices is of particular interest. Our DFT calculation of local magnetic moments on the carbon atoms has shown that for the degree of hydrogenation θ = 0.25 ML, the total magnetic moment of the graphene sheet is –0.02 µB per supercell. It should be noted that in the hydrogenation of the interface surface for graphene gratings (A and B), there is a degeneration in the direction of the induced local moments. All local MM on the carbon atoms are in the same direction. This degeneracy is retained up to the degree of hydrogenation θ = 1.0 ML. By increasing the degree of hydrogenation from θ = 0.25 ML to θ = 1.0 ML, the magnitude of the local magnetic moment at the carbon atom decreases by 1.5 times. The orientation of the local magnetic moments on the carbon atoms, which coincides with the direction of the local MM atoms at the surface layer of manganese may occur similar to the mechanism of superexchange interaction characteristic for the majority of ferromagnetic and ferrimagnetic insulators.
It has been shown that the hydrogenation of the interface leads to a significant change in its electronic properties. As a result of the charge transfer, p-doping of graphene occurs and semimetal-semiconductor transition is observed. In the case of the hydrogenation of the interface to the degree of coverage θ = 1.0 ML, there is p-n-transition in graphene and a new qualitative state, n-type semiconductor, occurs. The latter gives us the possibility of creating graphene n-type FET, that is of considerable interest for nanoelectronics.
Magnetism of defect-free graphene in the system SLG/H:MnO (111) is definitely an amazing phenomenon, and deserves the attention of theoreticians and experimentalists as the new quantum effects and new multi-functional properties can be discovered. The question of the mechanisms of magnetism inducing in a defect-free graphene, in our view, remains open. It is interesting to draw an analogy in the mechanism of magnetization of graphene in the system SLG/H:MnO (111) and system SLG/YIG (yttrium-iron-garnet) [14], since the substrate acts as a magnetic insulator in both cases.
This review has shown that the electron spectrum and magnetism in the system SLG/H:MnO (111) can be modulated by the degree of hydrogenation of the interface layer of oxygen, suggesting high potential for the use of this system in spintronics.
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[1] Ab initio – (с лат. – "от начала")
** SLG – single-layer graphene (однослойный графен)
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