FIRST PRINCIPLE STUDY OF MAGNETIC BEHAVIOR OF MN ATOMS DOPED IN SILICON NANORING

S. keshavarz* 1, M. Sargolzaei1,2,F. Gudarzi1

1Department of Physics, Iran University of science and Technology, Tehran, Iran 2Computational Physical Science Laboratory, Department of Nano-Science, Institute for Research in Fundamental Sciences (IPM),

Tehran, Iran *E-mail: samara.keshavarz@gmail.com

KEYWORDS

Density functional calculations, Open ended CNT, Hydrogenated CNT, Si-terminated CNT

ABSTRACT We have performed first principles spin polarized density functional theory (DFT) calculations to simulate the transition metal (TM) atoms substitutionally doped in a silicon nanoring that deposited on a short open-ended (8, 0) carbon nanotube (CNT). We found the Si nanoring on CNT substrate shows an antiferromagnetic ground state with a negligible magnetic moment for carbon atoms in the inner wall of the CNT and the Si nanoring. But when two Mn atoms are doped in the Si nanoring the total magnetic moment of the system strongly increases depends on geometric parameter (the angle between two Mn atoms), and the system exhibits ferromagnetic ground state.

INTRODUCTION Low-dimensional electron systems are known to present quantum confinement effects which lead to significant modifications of the electronic, magnetic and optical properties when compared with bulk semiconductor materials. In this context, semiconductor nanostructures such as quantum wells, quantum wires and quantum dots have been the subject of intense investigation in recent years [1]. A particular class of mesoscopic structures, called quantum rings. Semiconductor ring of nanometer range diameters and one atom thickness can be studied to understand of magnetism at the meso and nanoscale, motivated by the search for new physical phenomena [2-4]. This has been simulated and made possible by advances in fabrication of nanodevices. If transition metal atoms are doped in a semiconductor nanoring, this ring exhibits fundamentally new spin states and switching behavior, which can be precisely controlled via geometry, material composition and applied field.

In this overview of our work on Si nanoring, we show the geometric parameter determines the exact magnetic moment and the magnetic ground state of the considered system.

COMPUTATIONAL METHOD The calculations are performed within the framework of generalized gradient approximation (GGA) [5] for the exchange-correlation functional and

using projector augmented wave (PAW) method [6] for describing the interaction of valence electrons and core ions, as implemented in the VASP package [7, 8]. The optimization of the atomic geometry of the Si nanoring is performed via conjugate-gradient minimization of the total energy with respect to the atomic coordinates. Since we used a relatively large suppercell, only the Г point is used in the k-space sampling. The plane wave energy cutoff for structural optimization is taken to be 500 eV in order to achieve total energy convergence in less than 0.001 meV. RESAULTS AND DISCUSSION We simulated the silicon nanoring, composed of 8 Si atoms, and used the finite-length hydrogenated zigzag (8, 0) single walled carbon nanotube (SWCNT) as a substrate (see Fig. 1). Although, it has recently been reported that the spin ordering may occur on the zigzag edges of finite-sized SWCNTs [9, 10], but if one passivates the edges carbon atoms with hydrogen, the magnetization can be considerably reduced [9]. In this extended abstract a short piece of (8, 0) CNT with 8 atomic rings along its axis is included in this simulation. One side of CNT is passivated with hydrogen, while the other is open ended. We used from this structure as a substrate for the considered Si nanoring in the way that each Si atom is bonded to the topest site at the end of CNT. All of the atomic coordinates of Si ring and hydrogen atoms are

Fig. 1 Si nanoring on the CNT substrate. The other edge of CNT is passivated with hydrogen atoms. relaxed and the residue forces are computed to be less than 0.001 eV/Å. The final relaxed structure is shown in Fig. 1. Both spin polarized and nonpolarized calculations were done for this structure and found the anti ferromagnetic (AFM) state is the ground state with total energy less than 5 meV in comparison to the exited state; which is not stable at room temperature. Table 1, lists the magnetic moments for each ring included in the system. It should be noted that the carbon atoms of the first atomic ring away from the Si ring have the highest magnetic moment. The spin density is markedly higher at the Si-terminated end than at the hydrogenated end. Also, the calculation of the adhesion strength of the Si ring to CNT shows the considered structure is highly stable. The adhesion energy of Silicon atoms to CNT is defined as

( ( )) /ad r n r nE E E E N+= − + where Er+n is the energy of the Si ring and CNT, Er is the energy of the Si ring, En is the energy of the CNT and N is the number of Silicons, in which for the presented Si nanoring is N=8. This value was obtained 3.3 eV in our calculations. Table 1 Total magnetic moment of each ring along

the tube axis (top to bottom). )( BSM μ

Si-ring 0.144 5th carbon ring 0.184 1th carbon ring 0.381 6th carbon ring -0.056 2nd carbon ring -0.056 7th carbon ring 0.084 3th carbon ring 0.264 8th carbon ring 0.056 4th carbon ring -0.056 Hydrogen-ring 0.000

Also, having explored the ground state of the considered system when is doped with transition metals (TM) as impurities. First, we replaced two Si atoms by two manganese (Mn) atoms, then, studied different sites that Mn atoms can be substitute. As it is shown in Fig 2, because of the existence of Mn atoms, circular features of the Si-ring is deformed. In Table 2 the magnetic moment and energy difference between ferromagnetic and antiferromagnetic states of the system when two Mn atoms are in different sites, are tabulated. Clearly, the considered system presents the ferromagnetic ordered ground state in all neighbors except the case of two Mn atoms formed the must symmetrical configuration i.e. the last one.

1 2

3 4

Fig. 2 The configurations of two Mn atoms (black balls) doped in Si nanoring in different sites. Table2. Magnetic moment and energy difference between FM and AFM state for the considered system when two Mn atoms are doped in Si nanoring.

Configurartion ( )S BM μ FM AFME E− (meV)

1 0.26 7.5 2 2.00 61 3 3.99 59 4 4.00 -15

The Si nanorings on CNT have antiferromagnetic ground state. Moreover, when two Mn atoms are doped in Si nanorings, the feature of magnetization almost changes to a ferromagnetic state. On the other hand, magnetic moment of the system increases with the distance between two Mn atoms i.e. with increasing the angle between them. It is clear, because the overlap between the electrons of Mn atoms is higher in direct exchange than in superexchange. Our work opens a field to design magnetic nano tweezers. Further studies to stimulate our findings are desirable.

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MAGNETIC ANISOTROPY ENERGY OF 3D TRANSITION METALS (Fe, Co AND Ni) ADSORBED ON GRAPHENE

F. Gudarzi*1, M. Sargolzaei1,2 , S. Keshavarz1

1Department of Physics, Iran University of Science and Technology, Narmak 16345, Tehran, Iran.

2Computational Physical Science Laboratory, Department of Nano-Science, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran.

*E-mail: farideh.gudarzi@gmail.com

KEYWORDS Graphene, Magnetic Data Storage, Magnetic Anisotropy Energy, Density Functional Theory

ABSTRACT

In this work we investigated magnetic behavior of 3d transition metal (TM) atoms (Fe, Co and Ni) add on graphene, by means of density functional calculations. We estimated that hollow site of carbon hexagon of graphene is the most stable geometry for adsorption of TM adatoms. Graphene reduced magnetic moment of TM adatom by a factor of two Bohr magnetons. The largest magnetic anisotropy energy concluded for the Co-graphene system.

INTRODUCTION

Adsorption of metal atoms on the surface of graphene have been investigated both experimentally and theorically [1-5]. Graphene can play the role of quasi two-dimensional substrate to encapsulate magnetic metal nano-particles. These structures are proposed to have potential applications in high-density perpendicular magnetic data storage [1]. One of the most important parameters in nano-magnetism is magnetic anisotropy energy (MAE) which is the intrinsic tendency of the magnetization of the system to lie along a spatial direction, called easy axis. High MAE is crucial for nano-magnetic systems in order to magnetic stability of nano-particles due to thermal fluctuations. As proposed by Van Vleck [6], spin-orbit coupling is the origin of MAE in materials. MAE in the bulk state of elemental ferromagnets, e.g., Fe, Co and Ni, is quit small due to the quenching of the orbital momentum by the crystal field. As the dimension of the system decreases, e. g. on the surface, reduction of symmetry cause enhancement of orbital moment that yield residual magnetic anisotropy effects. Enhancement of MAE up to 1 meV per Co atom, observed in L10 CoPt ordered phase [7] (MAE per Co atom in hcp Co bulk is 0.06 meV). Large MAE of almost 9 meV yields by deposition of single Co atoms on the surface of Pt [8]. Then a challenging issue in nano-magnetic recording is to find a substrate which deserves magnetic moment of adsorbed nano-particles, furthermore show high MAE. In the following we investigate MAE for the adsorption of TM atoms (Fe, Co and N) on graphene.

COMPUTATIONAL METHOD We employed an all-electron full-potential local orbital scheme, FPLO, for the density functional calculations. The presented data were obtained using the generalized gradient approximation (GGA) with a parameterized exchange correlation functional [9]. To approach an upper estimate, an orbital polarization correction (OPC), was applied to the incompletely filled d-shells of TM adatoms [10, 11, 12]. In the considered structure, the x and y directions are parallel and the z direction is perpendicular to the graphene plane. TM adatom is located on an infinite supercell of graphene sheet (See Fig. 1). The distance between TM adatoms is large enough that the interaction of neighboring adatoms is negligible. A mesh of 4×4×8 k-points used in the full Brillouin zone. In order to geometry optimization, coordination of TM adatom and its nearest neighbors carbon atoms are fully relaxed. Residue forces are less than 0.001 eV/A for all of the atoms, which converges the total energy within 0.001 meV. RESULTS AND DISSCUTION Relaxation calculations showed that adsorption of TM atom does not deteriorate the flatness of the graphene and hollow site of the he carbon hexagon of the graphene is the most stable geometry for adsorption of the TM adatom. The distance of the TM adatoms from the plane of the graphene in the z direction,dag, are shown in the Table 1. As it can be seen, dag decreases slightly with atomic number of TM adatom.

Fig. 1 TM adatom (larger ball) on the hollow site of continuous supercell of graphene. In order to evaluate the relative stability of the TM-graphene structure we calculated adsorption energy as:

Eadsorption= Ecomplex – Egraphene – ETM ,

where Ecomplex is the total energy of the optimized TM-graphene structure, Egraphene is the total energy of an isolated graphene sheet (in considered supercell) and ETM is the total energy of isolated considered TM atom. The results of calculated adsorption energies are presented in Table 1., that show the conferment of the studied TM atom on graphene sheet. Table 1 dag is the distance of TM adatom from the plane of graphene in angstrom (Å). Adsorption energy is defined in the text.

An important aspect of TM adsorption on the surface of graphene is magnetic moment of the TM adatom as it bound to the surface of graphene. When TM adatoms add on the surface of graphene, 3d and 4s orbitals of the TM adatom hybridize with six Π orbitals of carbon hexagon of graphene to form the valence orbitals of TM-graphene. Magnetic calculations revealed that magnetic moment of TM adatoms reduced approximately by the factor of two Bohr magnetons, in comparison with isolated TM atoms. Another crucial parameter of TM-graphene is magnetic anisotropy energy, that is a characteristic of magnetization stability of the system. MAE for TM-graphene structure is defined as:

MAE = E|| - E┴ , that E|| and E┴ are the total energy of the structure in parallel and perpendicular quantization axis of the TM adatom with respect to the plane of the graphene. MAE is obtained in full-relativistic calculations, with and without OPC correction. The values for calculated MAE

Table 2 M is magnetic moment of the TM adatom in Bohr magneton (µB). MAE is magnetic anisotropy energy that is defined in the text and is obtained in full-relativistic (FR) and full-relativistic with OPB correction (FR+OPB) calculations.

are shown in Table 2. Positive (negative) value of MAE means the magnetization axis is perpendicular (parallel) to the plane of grapheme. Fe-graphene shows a small negative MAE which means that magnetic moment of Fe adatom lies along the graphene plane, with small different energy with perpendicular state, which makes this structure useless to be applied in magnetic data storage. Co-graphene shows the highest value of MAE with perpendicular magnetization with respect to the plane of graphene, that makes this structure a promising building block medium to perpendicular magnetic data storage. Small, positive MAE concluded for Ni-graphene, is indicated magnetic unstability of this system due to thermal fluctuations. In conclusion we investigated magnetic properties of TM-graphene system. This structure showed relative stability. Graphene reduced magnetic moment of TM adatoms by the factor 2 Bohr magneton in comparison with free state. The largest MAE concluded for Co-graphene system with perpendicular magnetization to the plane of graphene, that confirms high magnetic stability of this nano-magnet. We propose that this structure have potential to be applied as a promising medium for two dimensional magnetic data storage. REFERENCES [1] H. Cao, R. Li, Q. J. Gui, X. H. Wang, X. Bin, Nanoscience, 12, (2007) 35. [2] H. Sevincli, M. Topsakal, E. Durgun, and S. Giraci, Phys. Rev. B 77, (2008) 195434. [3] K. T. Chan, J. B. Neaton, and M. L. Cohen, Phys. Rev. B 77, (2008) 235430. [4] P. A. Khomyakof, G. Giovannetti, P. C. Rusu, G. Brocks, J. van den Brink, and P. J. Kelly, Phys. Rev. B 79, (2009) 195425. [5] H. Johll and H. Chuan Kang, Phys. Rev. B. 79, (2009) 245416. [6] J. H. Van Vleck, phys. Rev. 52, (1937) 1178. [7] P. Ravindran, A. Kjekshus, H. Fjellvaag, P. James, L. Nordstrom, B. Johansson, and O. Eriksson, Phys. Rev. B 63, (2001) 144409. [8] P. Gambardella et al, Science 300, (2003) 1130. [9] J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, (1996) 3865. [10] Brooks. M. S. S, Physica. B, 1306 (1985). [11] Eriksson. O,,Brooks M. S. S, and Johansson B., Phys. Rev. B 41, (1990) 7311. [12] H. Eschrig, M. Sargolzaei, K. Koepernik and M. Richter, Europhys. Lett, 72, (2005) 611.

TM adatom dag(Å) Adsorption

energy (eV) Fe 1.419 -0.78 Co 1.414 -0.71 Ni 1.404 -1.23

TM adatom M ( µB)

MAE (meV)

FR FR+OPB

Fe 2.22 -0.61 -3.23 Co 1.30 2.95 19.90 Ni 0.00 0.00 0.19