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Magnetic properties of Mg12O12 nanocage doped with transition metal atoms (Mn, Fe, Co and Ni): DFT study
Journal of Magnetism and Magnetic Materials 385 (2015) 138–144
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Magnetic properties of Mg12O12 nanocage doped with transition metal atoms (Mn, Fe, Co and Ni): DFT study Masoud Bezi Javan n Physics Departments, Faculty of Sciences, Golestan University, Gorgan, Iran
art ic l e i nf o
a b s t r a c t
Article history: Received 18 November 2014 Received in revised form 9 February 2015 Accepted 27 February 2015 Available online 3 March 2015
Binding energy of the Mg12O12 nanocage doped with transition metals (TM ¼Mn, Fe, Co and Ni) in endohedrally, exohedrally and substitutionally forms were studied using density functional theory with the generalized gradient approximation exchange-correlation functional along 6 different paths inside and outside of the Mg12O12 nanocage. The most stable structures were determined with full geometry optimization near the minimum of the binding energy curves of all the examined paths inside and outside of the Mg12O12 nanocage. The results reveal that for all stable structures, the Ni atom has a larger binding energy than the other TM atoms. It is also found that for all complexes additional peaks contributed by TM-3d, 4s and 4p states appear in the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) gap of the host MgO cluster. The mid-gap states are mainly due to the hybridization between TM-3d, 4s and 4p orbitals and the cage π orbitals. The magnetic moment of the endohedrally doped TM atoms in the Mg12O12 are preserved to some extent due to the interaction between the TM and Mg12O12 nanocage, in contrast to the completely quenched magnetic moment of the Fe and Ni atoms in the Mg11(TM)O12 complexes. Furthermore, charge population analysis shows that charge transfer occurs from TM atom to the cage for endohedrally and substitutionally doping. & 2015 Elsevier B.V. All rights reserved.
Keywords: Nanocage Metal oxide Transition metals
1. Introduction Magnesium oxide is an advantageous material which can be used in many applications such as catalysts [1,2], ceramics [3], chemical sensors [4] and energy conversion [5]. MgO is also a II–VI compound with wide band gap as its magnetic compounds can be promising material for spintronic applications [6]. Also the doping with transition metal can promote the catalytic behavior of the MgO [7]. With development of nanotechnology, experimental and theoretical studies of tube form of the nanostructures have increased for various organic and inorganic materials [8]. Recently several experimental [9–11] and theoretical [12–22] investigations are performed on the small cluster of MgO. Saunders has studied mass spectroscopy and collision-induced-fragmentation measurements on spattered MgO nanoclusters [9]. Their results indicate that the for small (MgO)n clusters some peaks exist at n ¼6, 9, 12 and 15 which refer to the most stable structures. The same results have been reported with laser-ionization time-of-flight mass spectrometry of the (MgO)n clusters [10]. Theoretical investigation also indicate that the most stable structure of the (MgO)n have the hollow and cage-like shape [12,19]. n
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http://dx.doi.org/10.1016/j.jmmm.2015.02.058 0304-8853/& 2015 Elsevier B.V. All rights reserved.
Doping or adsorption of transition metals (TM) are a common way to tuning the electronic and magnetic properties of materials as so far a number of researches have been concentrated on the interaction between TM and MgO bulk and surface [23–30]. Markovits et al [25] have studied the adsorption of first-row transition metal atoms on MgO (100) in periodic and cluster form with density functional theory (DFT) calculations. Wu et al has done an interesting work from theoretical aspects on the TM doped MgO nanosheets [30]. In other work, Yang et al. have investigated the role of doped transition metal on the sensing CO gas [31]. They have examined the surface doped MgO nanotubes with Ni, Pd and Pt transition metals and found that the CO molecule is more strongly bound to the transition metal atoms with considering of the doping configuration. In this work we have done a theoretical investigation on the different schemes of TM–Mg12O12 nanocage complexes. we studied structural, electronic and magnetic properties of endohedral, exohedral, and substitutional doped Mg12O12 nanocage (Th symmetry) with transition metals (TM¼ Mn, Fe, Co and Ni) which are appropriate candidates for designing magnetic devices and sensors if high spin configuration can be preserved as the ground state or different spins manipulated. The rest of the paper is organized as follows. Section 2 gives an outline of the method. In Section 3 the results and discussion are presented. Conclusions are summarized in Section 4
M.B. Javan / Journal of Magnetism and Magnetic Materials 385 (2015) 138–144
2. Computational details To simulate the endohedrally doped Mg12O12 nanocage with TM atoms first principle approaches using numerical atomic orbitals as a basis set have been implemented. Full geometry optimizations and total energy calculations were performed with ab initio calculations based on the generalized gradient approximation (GGA) with Perdew–Burke–Erenzerhof (PBE) functional [32] in density functional theory and the standard norm-conserving Troulier–Martins pseudopotentials [33]. We have used the OpenMX code that is based on the linear combination of pseudoatomic orbital (LCPAO) basis function for solving the standard Kohn–Sham equations and has been demonstrated to be very efficient for transition metal studied [34–36]. In the calculation with OpenMX, the outer electrons of the TM atoms were treated as valence electrons in the self-consistent field calculations. The pseudo-atomic orbitals have been constructed using two-s, two-p, two-d for TM atoms and two-s and two-p for Mg and O atoms. The cutoff of 150 Ry for the grid integration was utilized to represent the charge density in the real space. The Mg12O12 is constructed from six squares and eight hexagonal rings with Th symmetry. To find the most stable structures of the endohedral and exohedral doped Mg12O12 we have performed single point energy calculations. We select 6 different inner and outer paths as each inner path starts from the cage center and is extended to one of the symmetric key points on the surface of the Mg12O12 cage, such as different atomic sites (“A1” and “A2”), midpoint of the different bonds (“B1” to “B2”) and center of the hexagonal and square rings (“C1” to “C2”). The optimized geometry of Th-Mg12O12 is shown in Fig. 1 and the calculated bond lengths with different schemes of the DFT method are summarized in Table 1. The optimized B1 and B2 bond lengths in GGA method are 1.88 and 1.93 Å respectively which are in agreement with previous studies [37]. Six nonequivalent key points on Mg12O12 surface where determined. We refer to each path with the same designated name to the key point to which the path ends. Each external path starts from symmetry point on the surface toward outside of the cage. For endohedral and exohedral TM-doped Mg12O12, the binding energy variation is studied as a function of distance between the TM atom and the center of the Mg12O12 cage, respectively. The binding energy is taken as the total energy of each complex minus the sum of the total energies of the Mg12O12 cage and the free TM atom at infinite separation. The geometric structure of the complexes is relaxed near the minimum of the binding energy by Hellman–Feynman forces including Pullay-like corrections. Structural optimizations
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Table 1 Structural characteristics of the Mg12O12 nanocage. Bond lengths are in Å. The corresponding sites are labeled in Fig. 1. Mg12O12 Bond Number of bonds GGA-PBE LDA B3LYP/6-31Gn [26]
I (6-4) 24 1.93 1.91 1.95
II (6-6) 8 1.88 1.85 1.89
were performed using the conjugate gradient algorithm until the residual forces were smaller than 0.01 eV/Å. For the substituted TM-doped systems the stable geometry was obtained directly by the full geometry optimization.
3. Results and discussion 3.1. Geometric structure, binding energy and population analysis 3.1.1. TM@Mg12O12 (TM ¼Mn, Fe, Co and Ni) The change in the binding energy of TM atoms was calculated with respect to the internal surface of the Mg12O12 nanocage. Binding energies along all the 6 selected paths were computed as a function of the distance from the nanocage center and results for the TM@Mg12O12 case are shown in Fig. 2. As we can see for Mn@Mg12O12 structure the binding energy of the Mn atom varies along different paths inside the nanocage. The minimum of binding energy for Mn atom inside the Mg12O12 structure related to the C1 path with value of the 1.57 eV where the position of the Mn atom is 1.49 Å far from the center. This value is significantly larger than adsorption energy of the Mn atom on the MgO (100) surface which is about 0.596 eV calculated by GGA presented in Morkovits et al work [25]. Some local minimums can be also seen in the binding energy curves. The local minimums of the binding energy for A1, A2, B1, B2 and C2 paths are 1.44., 1.45, 1.52, 1.49 and 1.43 eV respectively at distance about 1.01 Å from the cage center. The negative sing of the binding energy means that the process of the complex formation is exothermic and so the formed complexes are thermodynamically stable. The Hirshfeld charge population analysis show that the Mn atom net charge is about 0.190e while the net charge on O and Mg atom of the cage is 0.507e and 0.497e. Minimum of the binding energy curve for the Fe@Mg12O12
Fig. 1. The optimized (Th)-Mg12O12 (a) and the 6 different more symmetric key points on the Mg12O12 surface, (b) the (“A1”and “A2”), (“B1” and “B2”) and (“C1” and “C2”) sets refer to the different atomic sites, middle of the bonds, center of the hexagonal and square rings, respectively.
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Fig. 2. The binding energy variation of TM atoms with distance of the TM atom from the cage center on some selected paths in which pass at (a) and (b) different atomic sites (“A1” and “A2”); (c) and (d) middle of the different bonds (“B1” and “B2”) and (e) and (f) midpoint of the different hexagonal and pentagonal rings (“C1” and “C2”). The dashed line distinct inside and outside of the Mg12O12 cage.
structure along A1, A2, B1, B2 and C1 and C2 paths are 1.66, 1.64, 1.74, 1.66, 1.64 and 1.65 eV, respectively. As we can see in Fig. 2(c), the global minimum is related to the B1 path (below 6-6 bond) at distance about 1.79 Å from the cage center. In this regard the Fe atom form bond with both Mg and O atoms of the cage with bond length about 1.58 and 2.41 Å respectively. The formed Fe–O bond length is somewhat shorter than Fe–O bond length in free standing cluster about 0.3 Å as reported in the literatures [38]. Although along B1 path we can see a local binding energy minimum about 1.71 eV at 1.03 Å from the cage center that the Fe atom can bind to the cage endohedrally. Regarding to the Markovits et al [25] we can see that the adsorption energy of the Fe atom on the MgO (100) is about 0.805 eV which indicates that the binding of the Fe atom to the Mg12O12 nanocage is higher than MgO (100) surface. According to the Hirshfeld charge population analysis the Fe atom net charge is about 0.105e while the average net charge on O and Mg atoms of the cage is 0.507e and 0.499e. For Co@Mg12O12 structure the minimum of the binding energy along A1, A2, B1, B2 and C1 and C2 paths are 2.12, 1.54, 2.33, 1.91, 1.61 and 1.75 eV, respectively. According to the Fig. 2 (c), the global minimum is related to the B1 path at distance about 1.92 Å from the cage center. The binding energy of the Co atom on the MgO(100) surface is about 0.802 eV [25] which is significantly lower than binding energy of the encapsulated Co atom inside Mg12O12 nanocage. As similar as Fe@Mg12O12 structure along B1 path we can see a local binding energy minimum about 1.66 eV at 1.01 Å from the cage center. According to the Hirshfeld charge population analysis the Co atom net charge is about 0.053e. Both O and Mg atoms have net charges about 507e and 0.505e. The Co–O and Co–Mg bonds for Co@Mg12O12 structure is about 1.58 and 2.57 Å respectively. In generally the Ni atom encapsulated inside Mg12O12 nanocage
has similar binding energy curve to Co atom inside Mg12O12 nanocage but there is some differences for C1 and C2 examined paths. For Ni@Mg12O12 structure the minimum of the binding energy along A1, A2, B1, B2 and C1 and C2 paths are –2.19, –1.36, – 2.38, –2.00, 1.63 and 1.71 eV, respectively. Regarding to the Fig. 2(c) the global minimum is related to the B1 path at distance about 1.99 Å from the cage center. As similar as Mn@Mg12O12, Fe@Mg12O12 and Co@Mg12O12 structures along B1 path we can see a local binding energy minimum about 1.52 eV at 1.01 Å from the cage center. Charge population analysis of the Ni atom show that its net charge is about 0.042e. The O and Mg atoms form bonds with Ni atom as they have net charges about 0.518e and 0.511e. The Ni–O and Ni–Mg bonds for Ni@Mg12O12 structure are about 1.52 and 2.49 Å respectively. 3.1.2. TM: Mg12O12 (TM¼Mn, Fe, Co and Ni) The change in the binding energy of TM atoms with respect to the external surface of the Mg12O12 nanocage was calculated and binding energies along all the 6 selected paths were computed as a function of the distance from the nanocage center. The results for the TM: Mg12O12 cases are shown in Fig. 2 at shady regions. The external surface of the Mg12O12 nanocage has significant differences from binding energy point of view when TM atom interacts with nanocage. In the case of the Mn: Mg12O12, along B2 and C1 paths the binding energy manner show an asymmetric behavior in comparison with inside of the cage. The most stable position outside of the cage for the Mn atom is on the C1 path as the binding energy is 1.42 eV at distance of about 3 Å from the cage center. The binding energy of the Mn: Mg12O12 is somewhat smaller than Mn@Mg12O12 however it is larger than Mn binding energy adsorbed on MgO(100) surface about 1.36 eV [25]. The Hirshfeld charge population analysis show that the Mn atom net charge is about 0.172e while the net charge on nearest O and Mg
M.B. Javan / Journal of Magnetism and Magnetic Materials 385 (2015) 138–144
Table 2 Bond lengths (in Å) and binding energy of Mg11(TM)O12 structures. Bonds
B1
B2
Binding energy (eV)/atom
Mn–O Fe–O Co–O Ni–O
1.91 1.87 1.84 1.82
2.01 1.95 1.90 1.89
4.18 4.24 4.33 4.27
atoms of the cage is 0.415e and 0.455e. The different behavior can be seen for other TM atom adsorbed on the external surface of the Mg12O12 nanocage. As for Fe: Mg12O12, Co: Mg12O12, Ni: Mg12O12 structures the minimum of the binding energy is in the B2 direction at distance of about 3.74, 3.50 and 3.48 Å from the cage center with values of the 1.39, 1.80 and 1.74 eV, respectively. With this regards the net Hirshfeld charge population of the Fe, Co and Ni atom is about 0.034e, 0.039 and 0.058e. In all considered TM: Mg12O12 structures the TM net charge is negative which means that the charge transfers from cage to the TM atoms. This charge transfer related to the hybridization of the
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4p orbital of the TM atom with π orbitals of the nanocage as it results to partially filling of 4p states. 3.1.3. Mg11(TM)O12 (TM¼ Mn, Fe, Co and Ni) In order to explore the stable structures of the Mg11(TM)O12 (TM¼ Mn, Fe, Co and Ni) we have optimized all the 4 geometries where the Mg atom can be replaced by the considered TM atoms. The binding energy variations of the Mg11(TM)O12 complexes are shown in Table 2. The binding energy of these complexes is taken by the following equation:
Eb = Etot − (11E Mg + ETM + 12EO )
(1)
As the Etot and EX shows the total energy of the system and energy of the isolated X atom. Oxygen substitutionally sites are unstable for TM atoms doping as the cage structure is destroyed due to the optimization. The binding energy is defined as the absolute value of the difference between the total energy of the complexes and the energy sum of the all free atoms constituting the structure of the complexes, which is the essential standard of estimating thermodynamic stability of a complex. One can see that
Fig. 3. The optimized geometry and charge population of the Mg11(TM)O12 structures.
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all TM doped nanocages have negative binding energy which means that the considered structures are stable. Among all examined structures, the Co doped Mg12O12 nanocage has higher binding energy although the differences between all binding energies is not significant. In Table 2 we have also shown that the TM–O bond lengths. In comparison with pure Mg12O12 structure the B1 and B2 bond lengths has a remarkable reduction with increasing the atomic number of the TM atoms. The optimized geometries and charge population of these four structures are shown in Fig. 3. As we can see from the figure, the TM atoms charge is positive as for Mn, Fe, Co and Ni atoms the net charge is 0.193e, 0.154e, 0.120e and 0.104e, respectively. 3.2. Electronic and magnetic properties Now we discuss the effects of the dopant atoms on the electronic structure of the Mg12O12 nanocage. A general feature is that all dopants introduce states in the gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital (HOMO–LUMO gap) of the nanocage. First we discuss the density of states (DOS) of the most stable complexes mentioned above. In Fig. 4 we have plotted the total DOS of the considered structures for up (α) and down (β) spins. Gaussian broadening has been used while plotting the DOS curves and the HOMO level was shifted to zero. The DOS of the Mg12O12 cage for comparison with those of the other complexes is also shown in Fig. 4. As it is seen from the figure the Mg12O12 is a semiconductor material with HOMO–LUMO gap of about 3.44 eV. It is found that for the considered complexes, additional peaks contributed by the TM atomic orbitals appear in the HOMO–LUMO gap of the Mg12O12 nanocage. From PDOS, it is clear
that the mid-gap states are mainly due to the hybridization between TM-3d, 4s and 4p orbitals and the cage π orbitals. At a glance a deformation can be recognized in the DOS, including in shape and shift toward the upper or lower energy region compared with the DOS of the Mg12O12 cage. This substantial shift can be explained by decrease or growth of the effective coulomb potential due to the charge transfer from cage to dopant atom or vice versa. The HOMO and LUMO isosurface of the most stable complexes are shown in Fig. 5. The HOMO, LUMO and HOMO–LUMO gaps for all configurations are also summarized in Table 3. The HOMO of the Mn@Mg12O12 is 3.22 eV higher in energy than the HOMO of Mg12O12, thus the ionization is more easily realized. Also the LUMO of Mn@Mg12O12 is 0.042 eV higher in energy than the LUMO of Mg12O12, so the electron transfer to the LUMO state of the Mn@Mg12O12 is somewhat more difficult than the pure Mg12O12 nanocage. Since the HOMO energies are recognized as an indicator of the first ionization potential (IP), then the order of the first IP of the complexes is as follow: for enstructures we have dohedrally doped (TM@Mg12O12) Fe@Mg12O12 4Mn@Mg12O12 4Co@Mg12O12 4Ni@Mg12O12 4Mg12O12. For exohedrally doped (TM:Mg12O12) structures we have also Mn:Mg12O12 4Ni:Mg12O12 4Co:Mg12O12 4Fe:Mg12O12 4Mg12O12. For substitutionally doped (Mg11(TM)O12) structures we have first IP order as Mg11(Mn)O12 4 Mg11(Fe)O12 4 Mg11(Ni)O12 4Mg11(Co) O12 4Mg12O12. Also the LUMO energies are sometimes considered as an approximation to the electron affinities (EA). So the order of the first EA of these complexes is as follow: for endohedrally doped (TM@Mg12O12) structures we have Fe@Mg12O12 4Mg12O12 4 Mn@Mg12O12 4Co@Mg12O12 4Ni@Mg12O12. For exohedrally doped (TM:Mg12O12) structures we have also Mn:Mg12O12 4Ni:Mg12O12 4 Mg12O12 4Co:Mg12O12 4Fe:Mg12O12. For substitutionally doped
Fig. 4. The spin polarized density of states (DOS) of the TM@Mg12O12, TM:Mg12O12 and Mg11(TM)O12 structures.
M.B. Javan / Journal of Magnetism and Magnetic Materials 385 (2015) 138–144
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HOMO
Mg11CoO12
LUMO
DOS (arb. Unit)
Ef
Mn@Mg12O12
E (eV)
Fe@Mg12O12
Ni@Mg12O12 DOS (arb. Unit)
Ef
Co@Mg12O12
E (eV)
Ni@Mg12O12
DOS (arb. Unit)
Ni:Mg12O12 Ef
Table 3 The HOMO, LUMO and HOMO–LUMO gap of the complexes and its orbital spin state (spin up (α) and spin down (β) states).
E (eV) Mg11NiO12 DOS (arb. Unit)
Fig. 5. The HOMO and LUMO of TM@Mg12O12, TM:Mg12O12 and Mg11(TM)O12 structures.
Ef
Complexes
HOMO (eV)
LUMO (eV)
Eg
Mg12O12n
5.874 2.652(α) 1.755(β) 3.433(α) 3.498(β) 2.460(β) 3.992(α) 3.106(β) 2.881(α) 3.291(β) 3.667(α) 3.769(β) 3.758(α)
2.430 2.471(β) 1.572(β) 2.888(β) 3.129(β) 2.201(α) 3.593(α) 2.624(α) 2.394(β) 1.997(α) 2.414(β) 2.476(α) 2.996(β)
3.444 0.181 0.183 0.545 0.369 0.259 0.399 0.482 0.486 1.294 1.253 1.293 0.762
Mn@Mg12O12 Fe@Mg12O12 Co@Mg12O12 Ni@Mg12O12 Mn:Mg12O12 Fe:Mg12O12 Co:Mg12O12 Ni:Mg12O12 Mg11MnO12 Mg11FeO12 Mg11CoO12 Mg11NiO12
The HOMO and LUMO orbitals of the structure are doubly degenerate by up and down spin states.
E (eV) Fig. 4. (continued)
(Mg11(TM)O12) structures we have the order of the EA as Mg11(Mn)O12 4 Mg11(Fe)O12 4Mg12O12 4Mg11(Co)O12 4Mg11 (Ni)O12. The different nature of hybridization between the TM-atomic orbitals and the O and Mg-2p orbital is well reflected in the
magnitude of the local magnetic moment on the TM atom, in Table 4. It can be seen that the total magnetic moment of the systems for TM@Mg12O12 are essentially close to the magnetic moment of the dopant atom with small magnetic moment induced on the cage in all cases. In the case of Mn@Mg12O12 a magnetic moment about 0.403 mB is induced on the cage as the negative sign shows the antiparallel spin direction of the cage magnetic moments with magnetic moment of Mn atom. For Fe@Mg12O12, Co@Mg12O12 and Ni@Mg12O12 the induced magnetic moments on cage are 0.409, 0.304 and 0.358 mB, respectively. As it is seen from the table the spin polarization of the 3d, 4s and 4p orbitals of the TM atoms make
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Table 4 The magnetic properties and population analysis of the dopant atoms. The small net magnetic moment for other orbitals are neglected. Complex
Total magnetic moment
TM (mB)
3d (mB)
4s (mB)
4p (mB)
Mn@Mg12O12 Fe@Mg12O12 Co@Mg12O12 Ni@Mg12O12 Mn: Mg12O12 Fe: Mg12O12 Co: Mg12O12 Ni: Mg12O12 Mg11MnO12 Mg11FeO12 Mg11CoO12 Mg11NiO12
5 4 3 2 1 0 1 0.001 1 0 1 0
4.396 3.026 2.174 1.245 1.137 0.006 1.241 0.116 1.036 0 0.97 0
4.442 2.91 1.934 0.954 1.293 0.567 1.59 0.348 0.988 0 0.959 0
0.284 0.463 0.506 0.618 0.168 0.48 0.12 0.315 0.095 0 0.001 0
0.073 0.062 0.038 0.031 0.028 0 0.002 0.012 0.015 0 0.024 0
the magnetization in the TM@Mg12O12 structures. For TM: Mg12O12 structures the total magnetic moments and also the local magnetic moment on each TM atom is reduced significantly due to the strong hybridization with cage orbitals. For Mn: Mg12O12 and Co: Mg12O12 structures the total magnetic moments is very close to the 1 mB while for Fe: Mg12O12 and Ni: Mg12O12 the total magnetic moments is quenched approximately. The same behavior can also seen for Mg11(TM)O12 structures where the total magnetic moment of the Mg11(Fe)O12 and Mg11(Ni)O12 is completely quenched in substituting process. Regarding to the DOS curves we can see also that the all considered Mn-Mg12O12 complexes have the half-metallic behavior as it is seen also in the Mn doped MgO bulk [29]. Full spin polarization on Fermi level and half-metallic behavior is also seen in Fe@Mg12O12, Co@Mg12O12 and Co: Mg12O12 structures.
4. Conclusions In summary, our first principle results show that the transition metal atoms Mn, Fe, Co and Ni may form stable structures with the Mg12O12 nanocage. The full geometry optimization near the minimum of the binding energy curves show that the most stable position of the TM atoms in the TM@Mg12O12 system are below the “B1” site, labeled for (6-6) bonds of the Mg12O12 nanocage, except the Mn atom as its most stable position is below the C1 (center of the hexagonal rings) sites. Although we found that inside the cage is some local minimums that can bind the TM atoms to the cage. The condition for the outside of the cage is somewhat different as the TM atom positions in its most stable state are different from inside. For Mn: Mg12O12 structure the most stable structure related to the systems where the Mn atom locates top of the hexagonal rings on the C1 site while for Fe: Mg12O12, Co: Mg12O12, Ni: Mg12O12 structures the minimum of the binding energy occurs on the B2 (4-6 bonds) site. We found that for Mg11(TM)O12 nanocages all structures have negative binding energy which means that the considered structures are stable. Among them the Co doped structure has higher binding energy although the difference between all binding energies is not significant. For all complexes additional peaks contributed by TM-3d, 4s and 4p states appear in the HOMO–LUMO gap of the Mg12O12 host cluster. The mid-gap states are mainly due to the hybridization between TM-3d, 4s and 4p orbitals and the cage π orbitals.
The magnetic moment of the endohedrally doped TM atoms in Mg12O12 nanocage are preserved where the total magnetic moment of the systems for TM@Mg12O12 are essentially close to the magnetic moment of the dopant TM atom with small magnetic moment induced on the cage in all cases. For TM: Mg12O12 structures the total magnetic moments and also the local magnetic moment on each TM atom is reduced significantly due to the strong hybridization with cage orbitals. For Mn: Mg12O12 and Co: Mg12O12 structures the total magnetic moments is very close to the 1 mB while for Fe: Mg12O12 and Ni: Mg12O12 the total magnetic moments is quenched approximately. The same behavior can also seen for Mg11(TM)O12 structures where the total magnetic moment of the Mg11(Fe)O12 and Mg11(Ni)O12 is completely quenched in substituting process.
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Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Magnetic properties of Mg12O12 nanocage doped with transition metal atoms (Mn, Fe, Co and Ni): DFT study Masoud Bezi Javan n Physics Departments, Faculty of Sciences, Golestan University, Gorgan, Iran
art ic l e i nf o
a b s t r a c t
Article history: Received 18 November 2014 Received in revised form 9 February 2015 Accepted 27 February 2015 Available online 3 March 2015
Binding energy of the Mg12O12 nanocage doped with transition metals (TM ¼Mn, Fe, Co and Ni) in endohedrally, exohedrally and substitutionally forms were studied using density functional theory with the generalized gradient approximation exchange-correlation functional along 6 different paths inside and outside of the Mg12O12 nanocage. The most stable structures were determined with full geometry optimization near the minimum of the binding energy curves of all the examined paths inside and outside of the Mg12O12 nanocage. The results reveal that for all stable structures, the Ni atom has a larger binding energy than the other TM atoms. It is also found that for all complexes additional peaks contributed by TM-3d, 4s and 4p states appear in the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) gap of the host MgO cluster. The mid-gap states are mainly due to the hybridization between TM-3d, 4s and 4p orbitals and the cage π orbitals. The magnetic moment of the endohedrally doped TM atoms in the Mg12O12 are preserved to some extent due to the interaction between the TM and Mg12O12 nanocage, in contrast to the completely quenched magnetic moment of the Fe and Ni atoms in the Mg11(TM)O12 complexes. Furthermore, charge population analysis shows that charge transfer occurs from TM atom to the cage for endohedrally and substitutionally doping. & 2015 Elsevier B.V. All rights reserved.
Keywords: Nanocage Metal oxide Transition metals
1. Introduction Magnesium oxide is an advantageous material which can be used in many applications such as catalysts [1,2], ceramics [3], chemical sensors [4] and energy conversion [5]. MgO is also a II–VI compound with wide band gap as its magnetic compounds can be promising material for spintronic applications [6]. Also the doping with transition metal can promote the catalytic behavior of the MgO [7]. With development of nanotechnology, experimental and theoretical studies of tube form of the nanostructures have increased for various organic and inorganic materials [8]. Recently several experimental [9–11] and theoretical [12–22] investigations are performed on the small cluster of MgO. Saunders has studied mass spectroscopy and collision-induced-fragmentation measurements on spattered MgO nanoclusters [9]. Their results indicate that the for small (MgO)n clusters some peaks exist at n ¼6, 9, 12 and 15 which refer to the most stable structures. The same results have been reported with laser-ionization time-of-flight mass spectrometry of the (MgO)n clusters [10]. Theoretical investigation also indicate that the most stable structure of the (MgO)n have the hollow and cage-like shape [12,19]. n
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http://dx.doi.org/10.1016/j.jmmm.2015.02.058 0304-8853/& 2015 Elsevier B.V. All rights reserved.
Doping or adsorption of transition metals (TM) are a common way to tuning the electronic and magnetic properties of materials as so far a number of researches have been concentrated on the interaction between TM and MgO bulk and surface [23–30]. Markovits et al [25] have studied the adsorption of first-row transition metal atoms on MgO (100) in periodic and cluster form with density functional theory (DFT) calculations. Wu et al has done an interesting work from theoretical aspects on the TM doped MgO nanosheets [30]. In other work, Yang et al. have investigated the role of doped transition metal on the sensing CO gas [31]. They have examined the surface doped MgO nanotubes with Ni, Pd and Pt transition metals and found that the CO molecule is more strongly bound to the transition metal atoms with considering of the doping configuration. In this work we have done a theoretical investigation on the different schemes of TM–Mg12O12 nanocage complexes. we studied structural, electronic and magnetic properties of endohedral, exohedral, and substitutional doped Mg12O12 nanocage (Th symmetry) with transition metals (TM¼ Mn, Fe, Co and Ni) which are appropriate candidates for designing magnetic devices and sensors if high spin configuration can be preserved as the ground state or different spins manipulated. The rest of the paper is organized as follows. Section 2 gives an outline of the method. In Section 3 the results and discussion are presented. Conclusions are summarized in Section 4
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2. Computational details To simulate the endohedrally doped Mg12O12 nanocage with TM atoms first principle approaches using numerical atomic orbitals as a basis set have been implemented. Full geometry optimizations and total energy calculations were performed with ab initio calculations based on the generalized gradient approximation (GGA) with Perdew–Burke–Erenzerhof (PBE) functional [32] in density functional theory and the standard norm-conserving Troulier–Martins pseudopotentials [33]. We have used the OpenMX code that is based on the linear combination of pseudoatomic orbital (LCPAO) basis function for solving the standard Kohn–Sham equations and has been demonstrated to be very efficient for transition metal studied [34–36]. In the calculation with OpenMX, the outer electrons of the TM atoms were treated as valence electrons in the self-consistent field calculations. The pseudo-atomic orbitals have been constructed using two-s, two-p, two-d for TM atoms and two-s and two-p for Mg and O atoms. The cutoff of 150 Ry for the grid integration was utilized to represent the charge density in the real space. The Mg12O12 is constructed from six squares and eight hexagonal rings with Th symmetry. To find the most stable structures of the endohedral and exohedral doped Mg12O12 we have performed single point energy calculations. We select 6 different inner and outer paths as each inner path starts from the cage center and is extended to one of the symmetric key points on the surface of the Mg12O12 cage, such as different atomic sites (“A1” and “A2”), midpoint of the different bonds (“B1” to “B2”) and center of the hexagonal and square rings (“C1” to “C2”). The optimized geometry of Th-Mg12O12 is shown in Fig. 1 and the calculated bond lengths with different schemes of the DFT method are summarized in Table 1. The optimized B1 and B2 bond lengths in GGA method are 1.88 and 1.93 Å respectively which are in agreement with previous studies [37]. Six nonequivalent key points on Mg12O12 surface where determined. We refer to each path with the same designated name to the key point to which the path ends. Each external path starts from symmetry point on the surface toward outside of the cage. For endohedral and exohedral TM-doped Mg12O12, the binding energy variation is studied as a function of distance between the TM atom and the center of the Mg12O12 cage, respectively. The binding energy is taken as the total energy of each complex minus the sum of the total energies of the Mg12O12 cage and the free TM atom at infinite separation. The geometric structure of the complexes is relaxed near the minimum of the binding energy by Hellman–Feynman forces including Pullay-like corrections. Structural optimizations
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Table 1 Structural characteristics of the Mg12O12 nanocage. Bond lengths are in Å. The corresponding sites are labeled in Fig. 1. Mg12O12 Bond Number of bonds GGA-PBE LDA B3LYP/6-31Gn [26]
I (6-4) 24 1.93 1.91 1.95
II (6-6) 8 1.88 1.85 1.89
were performed using the conjugate gradient algorithm until the residual forces were smaller than 0.01 eV/Å. For the substituted TM-doped systems the stable geometry was obtained directly by the full geometry optimization.
3. Results and discussion 3.1. Geometric structure, binding energy and population analysis 3.1.1. TM@Mg12O12 (TM ¼Mn, Fe, Co and Ni) The change in the binding energy of TM atoms was calculated with respect to the internal surface of the Mg12O12 nanocage. Binding energies along all the 6 selected paths were computed as a function of the distance from the nanocage center and results for the TM@Mg12O12 case are shown in Fig. 2. As we can see for Mn@Mg12O12 structure the binding energy of the Mn atom varies along different paths inside the nanocage. The minimum of binding energy for Mn atom inside the Mg12O12 structure related to the C1 path with value of the 1.57 eV where the position of the Mn atom is 1.49 Å far from the center. This value is significantly larger than adsorption energy of the Mn atom on the MgO (100) surface which is about 0.596 eV calculated by GGA presented in Morkovits et al work [25]. Some local minimums can be also seen in the binding energy curves. The local minimums of the binding energy for A1, A2, B1, B2 and C2 paths are 1.44., 1.45, 1.52, 1.49 and 1.43 eV respectively at distance about 1.01 Å from the cage center. The negative sing of the binding energy means that the process of the complex formation is exothermic and so the formed complexes are thermodynamically stable. The Hirshfeld charge population analysis show that the Mn atom net charge is about 0.190e while the net charge on O and Mg atom of the cage is 0.507e and 0.497e. Minimum of the binding energy curve for the Fe@Mg12O12
Fig. 1. The optimized (Th)-Mg12O12 (a) and the 6 different more symmetric key points on the Mg12O12 surface, (b) the (“A1”and “A2”), (“B1” and “B2”) and (“C1” and “C2”) sets refer to the different atomic sites, middle of the bonds, center of the hexagonal and square rings, respectively.
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Fig. 2. The binding energy variation of TM atoms with distance of the TM atom from the cage center on some selected paths in which pass at (a) and (b) different atomic sites (“A1” and “A2”); (c) and (d) middle of the different bonds (“B1” and “B2”) and (e) and (f) midpoint of the different hexagonal and pentagonal rings (“C1” and “C2”). The dashed line distinct inside and outside of the Mg12O12 cage.
structure along A1, A2, B1, B2 and C1 and C2 paths are 1.66, 1.64, 1.74, 1.66, 1.64 and 1.65 eV, respectively. As we can see in Fig. 2(c), the global minimum is related to the B1 path (below 6-6 bond) at distance about 1.79 Å from the cage center. In this regard the Fe atom form bond with both Mg and O atoms of the cage with bond length about 1.58 and 2.41 Å respectively. The formed Fe–O bond length is somewhat shorter than Fe–O bond length in free standing cluster about 0.3 Å as reported in the literatures [38]. Although along B1 path we can see a local binding energy minimum about 1.71 eV at 1.03 Å from the cage center that the Fe atom can bind to the cage endohedrally. Regarding to the Markovits et al [25] we can see that the adsorption energy of the Fe atom on the MgO (100) is about 0.805 eV which indicates that the binding of the Fe atom to the Mg12O12 nanocage is higher than MgO (100) surface. According to the Hirshfeld charge population analysis the Fe atom net charge is about 0.105e while the average net charge on O and Mg atoms of the cage is 0.507e and 0.499e. For Co@Mg12O12 structure the minimum of the binding energy along A1, A2, B1, B2 and C1 and C2 paths are 2.12, 1.54, 2.33, 1.91, 1.61 and 1.75 eV, respectively. According to the Fig. 2 (c), the global minimum is related to the B1 path at distance about 1.92 Å from the cage center. The binding energy of the Co atom on the MgO(100) surface is about 0.802 eV [25] which is significantly lower than binding energy of the encapsulated Co atom inside Mg12O12 nanocage. As similar as Fe@Mg12O12 structure along B1 path we can see a local binding energy minimum about 1.66 eV at 1.01 Å from the cage center. According to the Hirshfeld charge population analysis the Co atom net charge is about 0.053e. Both O and Mg atoms have net charges about 507e and 0.505e. The Co–O and Co–Mg bonds for Co@Mg12O12 structure is about 1.58 and 2.57 Å respectively. In generally the Ni atom encapsulated inside Mg12O12 nanocage
has similar binding energy curve to Co atom inside Mg12O12 nanocage but there is some differences for C1 and C2 examined paths. For Ni@Mg12O12 structure the minimum of the binding energy along A1, A2, B1, B2 and C1 and C2 paths are –2.19, –1.36, – 2.38, –2.00, 1.63 and 1.71 eV, respectively. Regarding to the Fig. 2(c) the global minimum is related to the B1 path at distance about 1.99 Å from the cage center. As similar as Mn@Mg12O12, Fe@Mg12O12 and Co@Mg12O12 structures along B1 path we can see a local binding energy minimum about 1.52 eV at 1.01 Å from the cage center. Charge population analysis of the Ni atom show that its net charge is about 0.042e. The O and Mg atoms form bonds with Ni atom as they have net charges about 0.518e and 0.511e. The Ni–O and Ni–Mg bonds for Ni@Mg12O12 structure are about 1.52 and 2.49 Å respectively. 3.1.2. TM: Mg12O12 (TM¼Mn, Fe, Co and Ni) The change in the binding energy of TM atoms with respect to the external surface of the Mg12O12 nanocage was calculated and binding energies along all the 6 selected paths were computed as a function of the distance from the nanocage center. The results for the TM: Mg12O12 cases are shown in Fig. 2 at shady regions. The external surface of the Mg12O12 nanocage has significant differences from binding energy point of view when TM atom interacts with nanocage. In the case of the Mn: Mg12O12, along B2 and C1 paths the binding energy manner show an asymmetric behavior in comparison with inside of the cage. The most stable position outside of the cage for the Mn atom is on the C1 path as the binding energy is 1.42 eV at distance of about 3 Å from the cage center. The binding energy of the Mn: Mg12O12 is somewhat smaller than Mn@Mg12O12 however it is larger than Mn binding energy adsorbed on MgO(100) surface about 1.36 eV [25]. The Hirshfeld charge population analysis show that the Mn atom net charge is about 0.172e while the net charge on nearest O and Mg
M.B. Javan / Journal of Magnetism and Magnetic Materials 385 (2015) 138–144
Table 2 Bond lengths (in Å) and binding energy of Mg11(TM)O12 structures. Bonds
B1
B2
Binding energy (eV)/atom
Mn–O Fe–O Co–O Ni–O
1.91 1.87 1.84 1.82
2.01 1.95 1.90 1.89
4.18 4.24 4.33 4.27
atoms of the cage is 0.415e and 0.455e. The different behavior can be seen for other TM atom adsorbed on the external surface of the Mg12O12 nanocage. As for Fe: Mg12O12, Co: Mg12O12, Ni: Mg12O12 structures the minimum of the binding energy is in the B2 direction at distance of about 3.74, 3.50 and 3.48 Å from the cage center with values of the 1.39, 1.80 and 1.74 eV, respectively. With this regards the net Hirshfeld charge population of the Fe, Co and Ni atom is about 0.034e, 0.039 and 0.058e. In all considered TM: Mg12O12 structures the TM net charge is negative which means that the charge transfers from cage to the TM atoms. This charge transfer related to the hybridization of the
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4p orbital of the TM atom with π orbitals of the nanocage as it results to partially filling of 4p states. 3.1.3. Mg11(TM)O12 (TM¼ Mn, Fe, Co and Ni) In order to explore the stable structures of the Mg11(TM)O12 (TM¼ Mn, Fe, Co and Ni) we have optimized all the 4 geometries where the Mg atom can be replaced by the considered TM atoms. The binding energy variations of the Mg11(TM)O12 complexes are shown in Table 2. The binding energy of these complexes is taken by the following equation:
Eb = Etot − (11E Mg + ETM + 12EO )
(1)
As the Etot and EX shows the total energy of the system and energy of the isolated X atom. Oxygen substitutionally sites are unstable for TM atoms doping as the cage structure is destroyed due to the optimization. The binding energy is defined as the absolute value of the difference between the total energy of the complexes and the energy sum of the all free atoms constituting the structure of the complexes, which is the essential standard of estimating thermodynamic stability of a complex. One can see that
Fig. 3. The optimized geometry and charge population of the Mg11(TM)O12 structures.
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all TM doped nanocages have negative binding energy which means that the considered structures are stable. Among all examined structures, the Co doped Mg12O12 nanocage has higher binding energy although the differences between all binding energies is not significant. In Table 2 we have also shown that the TM–O bond lengths. In comparison with pure Mg12O12 structure the B1 and B2 bond lengths has a remarkable reduction with increasing the atomic number of the TM atoms. The optimized geometries and charge population of these four structures are shown in Fig. 3. As we can see from the figure, the TM atoms charge is positive as for Mn, Fe, Co and Ni atoms the net charge is 0.193e, 0.154e, 0.120e and 0.104e, respectively. 3.2. Electronic and magnetic properties Now we discuss the effects of the dopant atoms on the electronic structure of the Mg12O12 nanocage. A general feature is that all dopants introduce states in the gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital (HOMO–LUMO gap) of the nanocage. First we discuss the density of states (DOS) of the most stable complexes mentioned above. In Fig. 4 we have plotted the total DOS of the considered structures for up (α) and down (β) spins. Gaussian broadening has been used while plotting the DOS curves and the HOMO level was shifted to zero. The DOS of the Mg12O12 cage for comparison with those of the other complexes is also shown in Fig. 4. As it is seen from the figure the Mg12O12 is a semiconductor material with HOMO–LUMO gap of about 3.44 eV. It is found that for the considered complexes, additional peaks contributed by the TM atomic orbitals appear in the HOMO–LUMO gap of the Mg12O12 nanocage. From PDOS, it is clear
that the mid-gap states are mainly due to the hybridization between TM-3d, 4s and 4p orbitals and the cage π orbitals. At a glance a deformation can be recognized in the DOS, including in shape and shift toward the upper or lower energy region compared with the DOS of the Mg12O12 cage. This substantial shift can be explained by decrease or growth of the effective coulomb potential due to the charge transfer from cage to dopant atom or vice versa. The HOMO and LUMO isosurface of the most stable complexes are shown in Fig. 5. The HOMO, LUMO and HOMO–LUMO gaps for all configurations are also summarized in Table 3. The HOMO of the Mn@Mg12O12 is 3.22 eV higher in energy than the HOMO of Mg12O12, thus the ionization is more easily realized. Also the LUMO of Mn@Mg12O12 is 0.042 eV higher in energy than the LUMO of Mg12O12, so the electron transfer to the LUMO state of the Mn@Mg12O12 is somewhat more difficult than the pure Mg12O12 nanocage. Since the HOMO energies are recognized as an indicator of the first ionization potential (IP), then the order of the first IP of the complexes is as follow: for enstructures we have dohedrally doped (TM@Mg12O12) Fe@Mg12O12 4Mn@Mg12O12 4Co@Mg12O12 4Ni@Mg12O12 4Mg12O12. For exohedrally doped (TM:Mg12O12) structures we have also Mn:Mg12O12 4Ni:Mg12O12 4Co:Mg12O12 4Fe:Mg12O12 4Mg12O12. For substitutionally doped (Mg11(TM)O12) structures we have first IP order as Mg11(Mn)O12 4 Mg11(Fe)O12 4 Mg11(Ni)O12 4Mg11(Co) O12 4Mg12O12. Also the LUMO energies are sometimes considered as an approximation to the electron affinities (EA). So the order of the first EA of these complexes is as follow: for endohedrally doped (TM@Mg12O12) structures we have Fe@Mg12O12 4Mg12O12 4 Mn@Mg12O12 4Co@Mg12O12 4Ni@Mg12O12. For exohedrally doped (TM:Mg12O12) structures we have also Mn:Mg12O12 4Ni:Mg12O12 4 Mg12O12 4Co:Mg12O12 4Fe:Mg12O12. For substitutionally doped
Fig. 4. The spin polarized density of states (DOS) of the TM@Mg12O12, TM:Mg12O12 and Mg11(TM)O12 structures.
M.B. Javan / Journal of Magnetism and Magnetic Materials 385 (2015) 138–144
143
HOMO
Mg11CoO12
LUMO
DOS (arb. Unit)
Ef
Mn@Mg12O12
E (eV)
Fe@Mg12O12
Ni@Mg12O12 DOS (arb. Unit)
Ef
Co@Mg12O12
E (eV)
Ni@Mg12O12
DOS (arb. Unit)
Ni:Mg12O12 Ef
Table 3 The HOMO, LUMO and HOMO–LUMO gap of the complexes and its orbital spin state (spin up (α) and spin down (β) states).
E (eV) Mg11NiO12 DOS (arb. Unit)
Fig. 5. The HOMO and LUMO of TM@Mg12O12, TM:Mg12O12 and Mg11(TM)O12 structures.
Ef
Complexes
HOMO (eV)
LUMO (eV)
Eg
Mg12O12n
5.874 2.652(α) 1.755(β) 3.433(α) 3.498(β) 2.460(β) 3.992(α) 3.106(β) 2.881(α) 3.291(β) 3.667(α) 3.769(β) 3.758(α)
2.430 2.471(β) 1.572(β) 2.888(β) 3.129(β) 2.201(α) 3.593(α) 2.624(α) 2.394(β) 1.997(α) 2.414(β) 2.476(α) 2.996(β)
3.444 0.181 0.183 0.545 0.369 0.259 0.399 0.482 0.486 1.294 1.253 1.293 0.762
Mn@Mg12O12 Fe@Mg12O12 Co@Mg12O12 Ni@Mg12O12 Mn:Mg12O12 Fe:Mg12O12 Co:Mg12O12 Ni:Mg12O12 Mg11MnO12 Mg11FeO12 Mg11CoO12 Mg11NiO12
The HOMO and LUMO orbitals of the structure are doubly degenerate by up and down spin states.
E (eV) Fig. 4. (continued)
(Mg11(TM)O12) structures we have the order of the EA as Mg11(Mn)O12 4 Mg11(Fe)O12 4Mg12O12 4Mg11(Co)O12 4Mg11 (Ni)O12. The different nature of hybridization between the TM-atomic orbitals and the O and Mg-2p orbital is well reflected in the
magnitude of the local magnetic moment on the TM atom, in Table 4. It can be seen that the total magnetic moment of the systems for TM@Mg12O12 are essentially close to the magnetic moment of the dopant atom with small magnetic moment induced on the cage in all cases. In the case of Mn@Mg12O12 a magnetic moment about 0.403 mB is induced on the cage as the negative sign shows the antiparallel spin direction of the cage magnetic moments with magnetic moment of Mn atom. For Fe@Mg12O12, Co@Mg12O12 and Ni@Mg12O12 the induced magnetic moments on cage are 0.409, 0.304 and 0.358 mB, respectively. As it is seen from the table the spin polarization of the 3d, 4s and 4p orbitals of the TM atoms make
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Table 4 The magnetic properties and population analysis of the dopant atoms. The small net magnetic moment for other orbitals are neglected. Complex
Total magnetic moment
TM (mB)
3d (mB)
4s (mB)
4p (mB)
Mn@Mg12O12 Fe@Mg12O12 Co@Mg12O12 Ni@Mg12O12 Mn: Mg12O12 Fe: Mg12O12 Co: Mg12O12 Ni: Mg12O12 Mg11MnO12 Mg11FeO12 Mg11CoO12 Mg11NiO12
5 4 3 2 1 0 1 0.001 1 0 1 0
4.396 3.026 2.174 1.245 1.137 0.006 1.241 0.116 1.036 0 0.97 0
4.442 2.91 1.934 0.954 1.293 0.567 1.59 0.348 0.988 0 0.959 0
0.284 0.463 0.506 0.618 0.168 0.48 0.12 0.315 0.095 0 0.001 0
0.073 0.062 0.038 0.031 0.028 0 0.002 0.012 0.015 0 0.024 0
the magnetization in the TM@Mg12O12 structures. For TM: Mg12O12 structures the total magnetic moments and also the local magnetic moment on each TM atom is reduced significantly due to the strong hybridization with cage orbitals. For Mn: Mg12O12 and Co: Mg12O12 structures the total magnetic moments is very close to the 1 mB while for Fe: Mg12O12 and Ni: Mg12O12 the total magnetic moments is quenched approximately. The same behavior can also seen for Mg11(TM)O12 structures where the total magnetic moment of the Mg11(Fe)O12 and Mg11(Ni)O12 is completely quenched in substituting process. Regarding to the DOS curves we can see also that the all considered Mn-Mg12O12 complexes have the half-metallic behavior as it is seen also in the Mn doped MgO bulk [29]. Full spin polarization on Fermi level and half-metallic behavior is also seen in Fe@Mg12O12, Co@Mg12O12 and Co: Mg12O12 structures.
4. Conclusions In summary, our first principle results show that the transition metal atoms Mn, Fe, Co and Ni may form stable structures with the Mg12O12 nanocage. The full geometry optimization near the minimum of the binding energy curves show that the most stable position of the TM atoms in the TM@Mg12O12 system are below the “B1” site, labeled for (6-6) bonds of the Mg12O12 nanocage, except the Mn atom as its most stable position is below the C1 (center of the hexagonal rings) sites. Although we found that inside the cage is some local minimums that can bind the TM atoms to the cage. The condition for the outside of the cage is somewhat different as the TM atom positions in its most stable state are different from inside. For Mn: Mg12O12 structure the most stable structure related to the systems where the Mn atom locates top of the hexagonal rings on the C1 site while for Fe: Mg12O12, Co: Mg12O12, Ni: Mg12O12 structures the minimum of the binding energy occurs on the B2 (4-6 bonds) site. We found that for Mg11(TM)O12 nanocages all structures have negative binding energy which means that the considered structures are stable. Among them the Co doped structure has higher binding energy although the difference between all binding energies is not significant. For all complexes additional peaks contributed by TM-3d, 4s and 4p states appear in the HOMO–LUMO gap of the Mg12O12 host cluster. The mid-gap states are mainly due to the hybridization between TM-3d, 4s and 4p orbitals and the cage π orbitals.
The magnetic moment of the endohedrally doped TM atoms in Mg12O12 nanocage are preserved where the total magnetic moment of the systems for TM@Mg12O12 are essentially close to the magnetic moment of the dopant TM atom with small magnetic moment induced on the cage in all cases. For TM: Mg12O12 structures the total magnetic moments and also the local magnetic moment on each TM atom is reduced significantly due to the strong hybridization with cage orbitals. For Mn: Mg12O12 and Co: Mg12O12 structures the total magnetic moments is very close to the 1 mB while for Fe: Mg12O12 and Ni: Mg12O12 the total magnetic moments is quenched approximately. The same behavior can also seen for Mg11(TM)O12 structures where the total magnetic moment of the Mg11(Fe)O12 and Mg11(Ni)O12 is completely quenched in substituting process.
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