First-Principles Electronic-Structure Study of Graphene Decorated with 4d-Transition Atoms

Abstract

Adsorption configurations, electronic structures and net spins of graphene adsorbing 4d transition atoms are calculated by first-principles calculations to explore the magnetic modification of decorating metal atoms on graphene. Y, Zr and Nb atoms can be adsorbed on graphene sheet via ionic bonds with an evident charge transfer, while Mo, Tc, Ru and Rh atoms form covalent-like bonding with graphene carbon atoms due to orbital hybridization, as indicated by Mulliken atomic charges and electron density differences. The 4d-transition atoms can be adsorbed on a carbon-ring center and atomic-bridge with a high binding energy as the typical chemisorption, which leads to specific modifications in electronic-band character and magnetic properties by introducing electron-states near Fermi-level. By adsorbing 4d-transition atoms, the electronic structure of graphene will alter from a semi-metal to a metal character, and engender net spin magnetism from the spin-polarization in 5s and 4d orbitals of adsorption atoms. This paper provides a significant theoretical basis for further experimental explorations of the atom-decorated graphene in nanoelectronics.

1. Introduction

In recent years, graphene has regained major attention for prospective applications of nanoscience and condense physics due to its distinctive electronic structure and excellent mechanical and thermal properties [1,2,3,4]. The sp² hybrid bonding in the carbon atom plane and the large conjugated π bond formed by vertical p_z orbitals make graphene exhibit non-magnetic semi-metal electrical properties [3]. In particular, graphene represents a linear energy dispersion of electronic-states near the Fermi-level to engender a Dirac cone electronic structure. A diversity of exquisite graphene nanostructures obtained through elaborate nanotechnology processes has been successfully applied for chemical catalysts, energy storage mediums, nanoelectronic and spintronic devices, and gas detectors [5,6,7,8,9,10,11]. Through specific processing schemes, graphene can achieve comprehensive functions to further extend its practical applications. Electrical conductivity could be effectively modified by adjusting the width of graphene nanoribbons [12,13]. Recent literature reports have noted that several frontier works are focusing on exploring nanomeshed and doping-decorated graphene for modifying electronic structures [14,15,16].

At present, considerable progress has been made in theoretical research on graphene adsorption of metal atoms. Valencia performed first-principles calculations on the atomic structure, adsorption binding energy and molecular-orbital caused magnetism of the graphene and single-wall carbon nanotubes (SCNT) adsorbed by 3d-transition atoms, which proved the stable and dispersive adsorptions of Sc, Ti, Fe and Co atoms on graphene sheet without surface migration [17]. Yagi used theoretical methods to investigate the stable configurations and magnetic properties of the graphene and SCNT adsorbing Fe, Co and Ni atoms, indicating that an electronic transition from 4s-orbital to 3d-orbital of the adsorbed atoms results in an evident decrease of the magnetic moment [18]. It has been theoretically demonstrated that the main group I−III metal atoms can be adsorbed on the graphene surface by ionic bonds as manifested by the large charge transfer, which leads to a slight change in electronic states, while the transition metal, noble metal and main group IV atoms are capable of forming covalent bonds with the graphene carbon atomic-layer through strong orbital hybridization [19]. By adsorbing main group IV atoms, graphene wills from semi-metallic to metallic characters and acquires a magnetic moment from the localized p-orbital of IV atoms [20]. With the projected augmented wave method of first-principles calculations, Sun elucidated the metallic band-structure and the s-orbital derived magnetism of the graphene being adsorbed with alkali metal atoms [21]. It has been also reported that Mg and Ca atoms can be adsorbed on graphene sheet by using van der Waals interaction and ionic bonding, respectively [22]. Ataca investigated hydrogen storage performances of graphene adsorbed with Ca atoms by the pseudopotential plane-wave first-principles method, suggesting that chemical adsorption of Ca atoms on graphene surface leads to the metallic character of electrical conductance [23]. Furthermore, it was proposed that applying planar strains on graphene could efficiently increase the adsorption binding energy of Ca atoms on graphene [24].

There are a variety of adsorbable elements for graphene decorations which can be fulfilled by the advanced nanotechnologies recently used for graphene adsorption experiments. Therefore, new functions can be realized by graphene adsorption of atoms or molecules to provide a promising route for nano-applications. Although the low spin-orbit coupling of carbon and the long-term spin-coherence residing in graphene promise favorable applications in spintronics, the non-magnetic behaviors of pristine graphene are the first obstacle to overcome. Controllable spin magnetism can be introduced by bombarding graphene with electron and ion beams to produce regulated defects [25,26,27]. Recent theoretical works focus on introducing controllable magnetic orders by creating defects into graphene, such as doping substitutional 4d and 5d-transition atoms in graphene, which however are poorly feasible in fabrication processes [28,29]. In contrast, atomic-decoration of chemically adsorbing magnetic d-transition atoms start-up a practical route to realize controllable magnetism in graphene. Up to now, adsorbing 4d-transition metals on a graphene surface has not been comprehensively reported in literature. After being intrigued by the significant research with a prospective deliberation, in the present study, we pursue theoretical calculations of the adsorption configuration, binding energy electronic structure and magnetic characteristics with the pseudopotential plane-wave first-principles method to reveal the adsorption behavior and magnetic generation mechanism.

2. Calculation Methodology

Conforming to the pseudopotential plane-wave first-principles method based on spin density functional theory, the atomic structure, electronic structure and magnetic moment of single-layered graphene adsorbed with 4d-transtion atoms are calculated as implemented in CASTEP code of the Materials Studio v2017R2 (Accelrys Inc., San Diego, CA, USA) software package. Gradient corrected exchange-correlation functional in WC form is adopted to perform the spin-polarized calculations, with the up and down spin states being modeled by different wave-functions according to relativistic Dirac equations [30]. The interactions between atomic-cores and electrons are described by On-the-fly Generation Ultrasoft Pseudopotential, which incorporates the Koelling-Harmon scheme for treating relativistic effects [31]. Electronic wave-functions are expanded by plane-wave basis-set with an energy cutoff of 440.0 eV, in which the Smart algorithm is used to decrease the error of basis-set finiteness to an adequately low level [32]. Self-consistent field (SCF) iterations are carried out with a convergence tolerance of 5 × 10⁻⁷ eV/atom in a FFT grid of 72 × 72 × 216 to ensure the accuracy of electron density calculations, in which the Pulay scheme of density mixing in charge and spin magnitudes of 0.5 and 2.0, respectively, is utilized to realize electron relaxations [33,34]. The k point sampling of integrating on the Brillouin zone (BZ) is carried out on a Monkhorst-Pack 4 × 4 × 1 grid [35]. The geometry optimization for relaxing adsorption configurations is performed by minimizing energy-functionality with the BFGS algorithm in delocalized internal coordinates to reach an energy convergence of 5.0 × 10⁻⁶ eV/atom, with the atomic force and stress being less than 0.02 eV/Å and 0.001 Å, respectively [36].

A monolayer graphene model is constructed in 3-dimensions by setting a sufficiently thick vacuum layer (30 Å) between the periodic-imaged graphene layers so that the actual representation is a two-dimensional system of single-layer graphene. The 4 × 4 × 1 graphene supercell with a larger size along graphene atomic-plane is constructed with one 4d-transition atom being added for a modeling adsorption system, in which no interaction should be considered between the adsorbed atoms in adjacent periodic units. The adsorption binding energy (adsorption energy) is derived by subtracting the total energy of adsorption configuration from the total energy summation of individual 4d-transition atoms and single-layered graphene.

3. Results and Discussion

3.1. Adsorption Energy and Configuration

According to the hexagonal symmetry of graphene, the decoration atoms may be adsorbed on the tops of three positions: a carbon atom, C-C bond middle and carbon-ring center, which are nominated here by atom (A), bridge (B) and central (C) sites, as schematically shown in Figure 1. The space symmetry group of graphene is D_6H-1, which transforms into C_3V-1, C_S-1 and C_6V-1 symmetries while adsorbing atom on A, B and C sites, respectively. The 4d-transition atoms are introduced individually at the three adsorption sites of graphene sheet. The equilibrium adsorption structures are obtained by geometric optimizations of the first-principles total energy minimization to evaluate the adsorption energy and the geometrical distortion of graphene sheet. In order to reveal the charge transfer and Coulomb interaction between the adsorbed atoms and graphene sheet, Mulliken atomic charges are calculated for charge population analyses according to SCF electron density.

Adsorption energy (E_ad) and adsorption distance d_ad = z_ad − z_ave (z_ad and z_ave indicate the z coordinates of adsorbed atoms and the average z coordinates of graphene carbon atoms, the coordinate axis of which is perpendicular to graphene sheet in the initial model), warpage of graphene sheet (∆c), Mulliken charges (q_M/e) of adsorbed atoms and net spin (s_n/(ћ/2)) of adsorption systems are obtained by first-principles calculations with the results being listed in

Table 1. Adsorption energy (E_ad/eV), adsorption distance to the graphene sheet (d_ad/Å), warpage of graphene sheet (∆h/Å), Mulliken charge (q_M/e) populated on transition atom, net spin (s_n/(ћ/2)) of single-layer graphene adsorbing 4d-transition metal atoms on atomic-carbon (A), bridge (B) and center (C) sites, respectively.

	Site	Ead/eV	dad/Å	∆c/Å	qM/e	sn/(ћ/2)		Site	Ead/eV	dad/Å	∆c/Å	qM/e	sn/(ћ/2)
Y	A	2.763	1.687	−0.555	1.32	0	Ru	A	3.213	1.652	−0.320	0.65	0
	B	1.735	2.055	−0.212	0.76	0		B	2.095	2.063	−0.032	0.41	2.00
	C	3.028	1.727	−0.214	1.42	0		C	3.817	1.542	−0.126	0.58	0
Zr	A	4.313	1.496	−0.473	1.25	1.23	Rh	A	2.169	1.863	−0.110	0.47	0
	B	2.026	2.088	−0.148	0.60	3.87		B	1.663	2.091	−0.031	0.34	1.00
	C	4.770	1.586	−0.205	1.37	0		C	2.249	1.666	−0.068	0.46	0
Nb	A	2.670	1.652	−0.480	0.99	1.87	Pd	A	1.956	2.202	−0.070	0.34	0
	B	1.830	2.184	−0.018	0.48	4.89		B	1.452	2.151	−0.051	0.25	0
	C	3.363	1.520	−0.224	1.06	0		C	1.570	2.019	−0.026	0.34	0
Mo	A	1.840	1.770	−0.298	0.74	2.58	Ag	A	0.729	2.605	−0.067	0.27	0
	B	1.793	2.290	−0.029	0.35	5.18		B	0.242	3.083	−0.004	0.05	1.00
	C	2.148	1.469	−0.210	0.69	0		C	0.484	2.501	−0.030	0.24	0
Tc	A	2.095	1.541	−0.477	0.55	0	Cd	A	0.505	3.526	−0.044	0.01	0
	B	1.936	2.144	−0.038	0.39	3.01		B	0.207	3.569	−0.009	0.07	0
	C	3.147	1.470	−0.176	0.56	0		C	0.508	3.541	−0.031	0.01	0

. All the 4d-transition atoms represent the highest and lowest adsorption energies at C and B sites, respectively. Pd, Ag and Cd atoms adsorbed on various sites show lower relative adsorption energies than other 4d-transition atoms, which are below the lower limit of ~1.6 eV of typical chemisorptions and hereby imply the physical interactions through van der Waals force [37]. Significant electron transfers between the adsorbed Y, Zr and Nb atoms and graphene adsorbent, as indicated by large q_M, manifest the chemical adsorption through ionic bonding which is more consistent with the higher adsorption energies than with 1.7 eV, even at the B site. In contrast, Mo, Tc, Ru and Rh atoms are adsorbed on graphene by forming a covalent bond with graphene carbon atoms through orbital hybridization, as manifested by the apparently smaller q_M and the high adsorption energy that is similar to for Y, Zr and Nb atoms, which agree well with the recent reports of first-principle calculations [19]. Furthermore, adsorption energy rises with the increase of the atomic number for Mo,Tc,Ru/graphene adsorptions. A larger q_M identifies more charge transfers and indicates a stronger Coulomb interaction of ion bonding, while a longer adsorption distance indicates a weaker adsorbing action. In comparison with the Y element, the q_M and d_ad of the Zr atom adsorbed on A or C sites are smaller when reaching the highest adsorption energy in all 4d-transistion elements, thereby suggesting that q_M and d_ad coordinately affect adsorption strength. Pd, Ag and Cd atoms are adsorbed on graphene in a distance that is remarkably longer than the chemical bonding distance between atoms, especially exceeding 3.0 Å for Ag and Cd. For chemisorptions, the longest adsorption distance coincides with the lowest adsorption energy at the B site compared with the other two adsorption sites. The adsorbed atoms on the graphene surface causes the deviation of the nearby carbon atoms out to the other side of the graphene adsorption surface, resulting in warping deformation of the fully planar graphene, which can be described by the graphene sheet warpage ∆c = z_min − z_ave (z_min and z_ave denote the minimum and averaged coordinates of the z-axis vertical to the graphene sheet). Additionally, 4d-transition atomic-adsorptions on the A site distort the largest warpage of the graphene sheet, thereby approaching the highest ∆c value of 0.555 Å. A larger ∆c implies more covalent components in adsorption bonding, which is basically consistent with q_M results.

The adsorption characteristics can also be explained by electron ionization potentials of metal atoms on graphene surface. The first electron ionization potential (IP) of 4d-transition atoms are calculated with the same first-principles method as for graphene adsorbing systems by E⁺-E (E⁺ and E represent the total energies of the positively charged cations with +e and the neutral atoms respectively in vacuum). The IP values of Pd, Ag and Cd atoms are 8.62, 8.97, 9.05 eV, respectively, which are appreciably higher than 5.66, 5.92 and 6.57 eV of Y, Zr and Nb, respectively, while Mo, Tc, Ru and Rh atoms possess medium IP values of 7.15, 7.50, 7.73 and 7.82 eV, respectively. Therefore, 4d-orbital electrons of Pd, Ag and Cd atoms can hardly transfer to or participate in covalent bonding with graphene carbon, leading to a physical adsorption, while the other 4d-transition atoms show a possible capacity for chemisorptions by forming ionic or covalent bonds with the graphene sheet. In comparison with the adsorption energies of three sites on the graphene sheet for adsorbing 4d-transition atoms, the C site can present the highest adsorption energy to form the most stable adsorption configuration the highest locating probability, while showing a zero net spin. Therefore, we only consider the chemical absorption on the C site in the following analyses of adsorption bonding characteristics and band-structures without spin-splitting in the next section. Nevertheless, Zr, Nb, Mo and Tc/graphene B-site adsorptions present a substantial net spin higher than 3.0(ћ/2) resulting from 4d-orbital sin-polarization, which is specifically investigated with the spin-dependent partial density of states (PDOS) in the following Section 3.3 to elucidate their dominant attributes of spin magnetism.

3.2. Adsorption Bonding Characteristics

To reveal the bonding characteristics of 4d-transition atoms adsorbed on graphene, electron density differences (EDD) are derived from SCF electron density in space distributions being contoured on the over-atomic plane perpendicular to graphene sheet, as shown by the color maps in Figure 2. For Y and Zr atoms being adsorbed at the C site, the lowest negative EDD appears around the adsorbed atoms along the direction towards the carbon ring center (the C site center), implying that a significant electron transfer from Y and Zr to the graphene sheet occurs as a manifestation of the ionic bonding character. For Nb atoms, the lowest negative EDD region shift to the route towards carbon atoms of the benzene ring at the C site, thereby undertaking a certain orientation of electron transfer as a trend towards covalent bond characteristics. In contrast, Mo, Tc, Ru and Rh atoms adsorbed at the C site present the highest positive and lowest negative EDD regions, respectively, along the ways to the benzene center and the adjacent carbon atoms of the C-site, therefore showing an obvious directionality of the characteristic covalent bonding in the localized electronic states. The charge population analyses based on the Muliken algorithm verify that the oxidation states of Mo, Tc, Ru and Rh atoms adsorbed on the graphene sheet are much less than the lowest oxidation states of oxide compounds, as listed in Table 1, therefore confirming their covalent characteristics of chemisorptions.

3.3. Band Structure and Magnetism

Since the influence of physically adsorbed atoms on the graphene electronic structure is negligible, the electronic structure calculations are merely performed for Y, Zr, Nb, Mo, Tc, Ru and Rh/graphene chemisorptions on the most stable C-site, as shown by the band-structure results in Figure 3. No spin-polarization has been found in the band structure of pristine graphene with a zero density of states at the Fermi-level, which confirms the non-magnetic semi-metallic character of graphene which is consistent with the results reported in other research [36,37]. The band-structures of Y, Zr and Nb/graphene C-site adsorptions retain the Dirac point of graphene, while the Fermi-level has been shifted to a higher energy due to the electron transfer from the adsorbed atoms, which also introduces the unoccupied σ* localized states above the Fermi-level. It is noted that the energy level of the lowest energy σ* state moves closer to the Fermi-level with the increase of the atomic-number. After individually adsorbing Y, Zr and Nb atoms at the C-site, the band-structure of graphene alters from semi-metallic to metallic characteristics, after which the electron transfer from the adsorbed atoms to graphene matrix leads to the π* band crossing the Fermi-level as a manifestation of n-type doping characteristics. By contrast, the occupied σ states below the Fermi-level are introduced into the band-structures of Mo,Tc,Ru,Rh/graphene adsorptions, implying that the adsorption atom has formed a covalent bond with graphene.

For the B-site chemisorptions of 4d-transition atoms on graphene sheet, spin polarization breaks the spatial symmetry distribution between the up (α) and down (β) spin states, which leads to electronic energy splitting (spin splitting) and a net spin magnetic moment, as shown in Table 1. Zr, Nb, Mo and Tc/graphene B-site adsorptions represent the substantial net spins of 3.87, 4.89, 5.18 and 3.01(ћ/2), respectively, which originate from the spin-polarization of 4d and 5s orbitals in the adsorbed atoms, as illustrated by spin-the resolved partial density of states (SPDOS) in Figure 4. For Zr and Nb/graphene adsorptions, the energy levels of β-states from 5s and 4d orbitals have been increased above the Fermi-level while the remaining α-states from 4d orbital are occupied below the Fermi-level, thereby indicating that spin polarization splits the energy levels of α and β spin-states, which leads to a higher density of α-state electrons than β-state electrons and thus produces a net spin. In Mo and Tc/graphene adsorptions, the α-states and β-states are respectively dominated by Mo-5s and Tc-4d orbitals located at the Fermi-level that are partially occupied, while the exacerbation of spin-polarization further splits the majorities of 4d-orbital α and β states to be respectively lower and higher than the Fermi-level by 0.3 eV. Therefore, B-site Mo and Tc atoms are adsorbed on graphene by forming s-p and d-p covalent bonds respectively with the conjugated π bond derived from C-2p orbitals, as indicated by the minorities of Mo-5s α-states and Tc-4d β states just below the Fermi-level with the net spin being increased and decreased, respectively. To this end, the Zr, Nb, Mo and Tc/graphene B-site adsorptions represent a substantial magnetic moment that is essentially contributed to by the spin-polarized electrons from 5s and 4d orbitals of the adsorbed atoms.

4. Conclusions

The atomic geometry, electronic structure and magnetic properties of 4d-transition atoms adsorbed on graphene sheet are studied by using first principle calculations. Except for the physical adsorptions of Pd, Ag and Cd atoms on graphene, Y, Zr, Nb and Mo, Tc, Ru and Rh atoms could be chemically adsorbed with the most stable configuration at the central site of graphene by ionic and covalent bonds, respectively. The adsorptions of 4d-transition atoms by ionic bonds are similar to the n-type doping in graphene, leading to a fundamental transformation of the electronic structure from semi-metallic to metallic band characters, which is attributed to the significant elevation of the Fermi-level caused by the effective electron transfer from adsorbed atoms to graphene. The C-cite chemisorptions of 4d-transition atoms represent a clear Dirac point in the band-structure, while the significant net spin magnetism can only be acquired by B-site chemisorptions. Spin-resolved partial density of states indicate that the net spin essentially derives from the spin-splitting of 5s-orbital in ionic Coulomb adsorption and 4d-orbital in covalent bonding adsorption. The present study demonstrates that the electronic and magnetic properties of graphene can be effectively regulated by doping 4d-transition atoms of Y, Zr, Nb, Mo, Tc, Ru and Rh to form stable chemisorptions, which provides a theoretical basis for applying the atomic-decorated graphene in nanoelectronics.