Transition metal induced magnetism in smaller fullerenes (C_n for n ≤ 36)

Abstract

The magnetic properties of 3d transition metals (TM) encapsulated inside smaller fullerenes ranging from C₂₀ to C₃₆ have been investigated using spin polarized density functional theory. The TM impurities stabilize asymmetrically at an off-center position for n ≥ 28. The total magnetic moment (MM) of TM@C_n complexes are largely contributed by TMs and a small amount of MM of 0.12–0.50 μ_B is induced on the cage carbon atoms. The 3d TM atoms interact with C atoms of C₂₀ and C₂₈ cage ferromagnetically (FM) except for Ni@C₂₈ which shows antiferromagnetic (AFM) interaction. The magnetic interactions change from FM to AFM in C₃₂ cage for Ti, V, Cr and Mn. The MM gets quenched in Ni@C_n for n ≥ 32. The total MM of Mn@C_n does not show any change although the nature of magnetic interactions changes from FM to AFM at n = 32. Ti and V are the only TMs which show positive cohesive energy in all fullerenes considered. The smallest fullerene which can encapsulate all 3d TM are C_n for n ≥ 32, consistent with available experimental and theoretical results.

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I. Introduction

Recent experimental results on magnetism in carbon based materials have renewed interest in carbon systems as possible new magnetic materials due to their technological advantages over conventional magnetic materials,¹ though the origin of the magnetic ordering in the latter systems is still far from clear. The quest for carbon based ferromagnetism has occupied theoreticians for many years and its origin has been proposed to be due to the dislocations, vacancies and impurity atoms.² To date, the focus has been to understand the magnetic properties of metallofullerenes larger than C₆₀^3–5 due to their stability and larger volume available for encapsulation. Among the smaller fullerenes only C₂₀ and C₃₆ have been isolated so far. Lopez et al.⁶ have studied magnetic properties of carbon clusters, clusters inside fullerenes and graphitic nanoribbons. The entrapped atoms bring with them an array of useful physical properties with possible applications in electronic devices,⁷ organic solar cells,⁸ spin-based quantum computing^9,10 and medicine,¹¹ specifically contrast agents for magnetic resonance imaging (MRI) as well as for radiopharmaceutical candidates.¹²

The recent works on the successful synthesis of some endohedral derivations of smaller fullerenes have acquired special significance. The smaller fullerenes violate the isolated pentagon rule and the fused pentagon structures in this class of fullerenes have a strong effect on their stability and electronic properties. Surprisingly, small endohedral metallofullerenes remains to be explored and their magnetic properties have not been investigated in spite of the successful production of many small fullerenes.^13–16 There is a considerable range of carbon clusters, C_n for 20 < n ≤ 30, in which the crossover to fullerene structures have been reported. In the crossover region there are other structures which are energetically competitive such as planar or near-planar sheets and bowls, and monocyclic rings.¹⁷U@C₂₈ films were synthesized in a cationic form by laser vaporization of a UO₂/graphite mixture.¹⁷ Besides U@C₂₈, the signals of U@C₃₆, U@C₄₄ and U@C₅₈ were also observed in the mass spectrum with lower intensities. Thus, the internal uranium atom has apparently stabilized the fullerene cage and made U@C₂₈ the end point of laser shrinking. The presence of Zr, Hf, Ti and Sc inside C₂₈ cage has also been confirmed in the mass spectrum obtained from laser vaporization of graphite/metal-oxide composite discs.¹⁸ Subsequently, none of the experimental groups have been able to isolate the observed metallofullerenes. Following these experiments, many theoretical groups have performed a systematic investigation of a series of M@C₂₈ (M = Mg, Al, Ca, Sc, Ti, Ge, Zr and Sn)¹⁹ and found that only Sc@C₂₈ and Zr@C₂₈ are thermodynamically stable in consequence of their large binding energies. Sun et al.²⁰ studied the encapsulation of thirteen atoms from group IA to group VA (i.e. H, Li, Na, K, Be, Mg, Ca, B, Al, C, Si, N, P) and nine cations from group IA to group IIIA (i.e.H⁺, Li⁺, Na⁺, K⁺, Be²⁺, Mg²⁺, Ca²⁺, _B3+ and Al³⁺) inside C₃₂ cage. Recently, Chen et al.²¹ investigated the stabilities and molecular structures of noble gas atoms (i.e.He, Ne, Ar, and Kr) inside the C₃₂ cage. Subsequently, inspired by the finding of U@C₃₆, Kang²² gave a detailed calculation of the possible encapsulation of alkali metals (i.e.Li, Na, K) inside C₃₆. However, so far there has been no study reported on the trapping of transition metals (TM) inside small fullerene cage structures.

In this paper, we present a systematic investigation of the electronic and magnetic properties of TM@C_n, n = 20, 28, 32, 36 where TM = Ti, V, Cr, Mn, Fe, Co, Ni and Cu using spin polarized density functional theory. Our results show that the magnetic properties of TM@C_n, apart from depending on 3d configuration and charge transfer from the TM atom to carbon cage, also depend on the specific geometric structure of the cage as well as location of the TM atom. The results highlight the possibility of designing magnetic devices if high spin configurations of 3d TMs can be preserved as the ground state or different spin manipulation.

II. Computational details

We have used the spin polarized density functional theory to study the magnetic properties of the TM@C_n complexes as implemented in the Spanish Initiative for Electronic Simulation with Thousands of Atoms (SIESTA) computational code.²³ The electron exchange interactions were considered using generalized gradient approximation (GGA) that implements Perdew, Zunger and Ernzerhof (PBE) exchange–correlation.²⁴ The core electrons are replaced by non-local, norm-conserving pseudo potentials factorized in the Kleinman-Bylander form,²⁵ whereas valence electrons are described using linear combination of numerical pseudo atomic orbitals of the Sankey-Niklewski type²⁶ but generalized for multiple-ζ and polarization functions. In this work, we have used a split valence double-ζ polarized (DZP) basis set. We considered 3d²4s², 3d³4s², 3d⁵4s¹, 3d⁵4s², 3d⁶4s², 3d⁷4s², 3d⁸4s² and 3d¹⁰4s¹ electronic configurations for Ti, V, Cr, Mn, Fe, Co, Ni and Cu, respectively. The structures are obtained by minimization of the total energy using Hellmann-Feynman forces, including Pulay like corrections. Structural optimizations were performed using conjugate gradient algorithm until the residual forces in the optimization are smaller than 0.001 eV/Å. We have studied C₆₀ based heterofullerenes^27,28 and endohedral complexes²⁹ with similar methodology and parameters as described above. This validates the applicability and accuracy of our calculations to investigate smaller carbon fullerene-based systems.

The test calculations were performed on TM dimers and the calculated magnetic moments (MM) and bond lengths of all the clusters are tabulated in Table 1. Our results are in qualitative agreement with the existing experimental and theoretical results for Mn, Fe, Co, Ni and Cu.^30–32 The accuracy of the DFT results for 3d TM are reported to be highly dependent upon the functional employed with pure methods such as BLYP and BP86 performing better than hybrid functionals. No functional gives results directly comparable for all 3d TM species.³³ A choice of other functionals, such as BLYP or BP86, is likely to improve accuracy for some dimer results in qualitative terms but may not change the overall behavior of TM@C_n complexes.

Table 1 Magnetic moments (MM) of single TM atoms and TM–TM bond length with ferromagnetic (FM) and antiferromagnetic (AFM) interactions (in Å)

Atom	MM in μB TM	FM RTM–TM	AFM RTM–TM	Interactions
Ti	4.0	2.15	2.15	AFM
V	5.0	2.51	2.51	AFM
Cr	6.0	3.35	2.98	AFM
Mn	5.0	3.25	3.24	AFM
Fe	4.0	2.12	2.33	AFM
Co	3.0	2.16	2.51	AFM
Ni	2.0	2.25	2.28	AFM
Cu	1.0	2.25	2.25	both

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III. Results and discussion

A. Structures and stabilities of TM@C_n complexes

The C₂₀ cage with I_h symmetry (Fig. 1) is considered the starting cage configuration to investigate the effect of 3d TMs. The average diameter and bond length of C₂₀ is found to be 4.14 Å and 1.47 Å which are in agreement with Malolepsza et al.³⁴ The binding energy is 8.32 eV per atom for I_h symmetry which possesses a MM of 2 μ_B in agreement with ref. 35. However, there is a considerable disagreement among theoreticians regarding symmetry and magnetic state of C₂₀. This may be due to the importance of accurate treatment of electron correlation³⁶ in smaller fullerenes. Galli et al.³⁷ used LDA and GGA to predict the C₂₀ cage with D_3d symmetry as the most stable Jahn–Teller distorted cage structure. Wang et al.³⁸ using hybrid DFT predicted the C_2h symmetry as the most stable structure. This may be explained on the basis that C₂₀ with I_h symmetry may undergo Jahn–Teller distortions and its symmetry is reduced to lower groups. Lu et al.³⁹ using tight binding model found that C₂₀ undergoes a magnetic to nonmagnetic transition and nonmagnetic to magnetic transition for I_h and D_3d symmetries, respectively.

Fig. 1 Optimized geometries of pure fullerenes along with their symmetries.

The TMs prefer to stabilize at a central position in C₂₀ and with their encapsulation, the variation in the C–C and C=C bond lengths of all the fullerene cages are tabulated in Table 2. The average C–C bond length in C₂₀ is 1.47 Å and it increases to 1.48–1.54 Å in TM encapsulated complexes. The diameter of TM@C₂₀ complexes increases from 4.21 to 4.27 Å from Ti to Cu. The binding energy per atom shows a maximum value of 8.2 eV for Ti@C₂₀ which decreases with increasing atomic number of 3d TMs to 7.66 eV in Cu@C₂₀. Further, the interaction between the fullerene cage and TMs along with the stabilities of TM@C_n complexes is described by evaluating their cohesive energies. We define the cohesive energy of TM@C_n complexes as follows:

ΔE = E_Total(TM@C_n) − E(C_n) − E(TM) (1)

where E_Total(TM@C_n), E(C_n) and E(TM) are the total energies of the endohedral complex, isolated fullerene and TM atoms, respectively. The cohesive energies “ΔE” calculated using eqn (1) are tabulated in Table 3. The positive values of ΔE indicate the greater stability of TMs inside fullerene cage and are likely to be formed experimentally. The negative values of ΔE indicate that the corresponding TM encapsulated inside the fullerene cage is unstable or less stable and have not been experimentally observed.

Table 2 Average C–C and C=C bond lengths (in Å) for all fullerene cages

TM	C20	C28		C32		C36
	C–C	C–C	C=C	C–C	C=C	C–C	C=C
Ti	1.48–1.51	1.46–1.51	1.43	1.48–1.49	1.43	1.46–1.49	1.44
V	1.51–1.53	1.49–1.52	1.42–1.44	1.46–1.50	1.42–1.43	1.44–1.49	1.44
Cr	1.47–1.51	1.50–1.54	1.44	1.46–1.49	1.42	1.47–1.49	1.46
Mn	1.51–1.54	1.49–1.54	1.44	1.46–1.50	1.45	1.46–1.49	1.44–1.46
Fe	1.52–1.54	1.47–1.53	1.43	1.46–1.49	1.42–1.44	1.46–1.49	1.44–1.46
Co	1.51–1.53	1.46–1.53	1.44	1.47–1.48	1.42–1.45	1.45–1.49	1.44–1.45
Ni	1.51–1.54	1.47–1.53	1.43–1.44	1.46–1.51	1.42–1.44	1.46–1.50	1.45
Cu	1.50–1.54	1.47–1.52	1.44	1.46–1.50	1.42.1.44	1.46–1.50	1.43–1.45

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Table 3 The cohesive energy (ΔE in eV) of TMs encapsulated inside small fullerene cages. The negative values of ΔE corresponds to unstable TMs encapsulated inside the cage

TM	TM@C20	TM@C28	TM@C32	TM@C36
Ti	3.80	2.88	2.69	3.05
V	1.93	2.18	2.11	2.12
Cr	−3.23	−0.60	−0.05	0.52
Mn	−6.31	0.41	0.37	0.85
Fe	−3.47	1.35	0.73	0.99
Co	−4.19	0.27	−0.54	−0.26
Ni	−4.75	0.54	0.25	0.55
Cu	−7.52	−0.59	−0.08	0.21

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From Table 3, it is clear that only Ti and V possess positive values for the C₂₀ cage thereby suggesting the stabilities of these are likely to form complexes with C₂₀.

C₂₈ fullerene with T_d symmetry and zero MM is found to be the most stable geometry compared to the other isomers considered. The TMs have a tendency to occupy off-center positions inside C₂₈ and larger fullerenes as shown in Fig. 2. The average diameter of C₂₈ comes out to be 4.88 Å with a binding energy per atom of 8.67 eV. The average C–C and C=C bond lengths of C₂₈ are 1.45–1.47 Å and 1.42 Å whereas TM@C₂₈ complexes show an increase to 1.49–1.54 Å and 1.44 Å, respectively. The average diameter shows a maximum value of 4.98 Å in Cr@C₂₈. The structural behavior of Sc@C₂₈ and Ti@C₂₈, i.e. the distance of Sc and Ti from the nearest carbon cage atom, is 1.69 Å and 1.75 Å, respectively, in agreement with ref. 18. The binding energy per atom is higher for Sc@C₂₈, Ti@C₂₈ and V @C₂₈, predicting their larger stability over their counterparts. ΔE for all TMs, except Cr and Cu, shows small positive values inside C₂₈.

Fig. 2 Optimized geometries of fullerenes doped with transition metals.

C₃₂ with D_3h symmetry forms a stable cage with zero MM. C₃₂ has an average diameter of 5.08 Å and the binding energy per atom is 8.83 eV with average C–C and C=C bond lengths of 1.47–1.49 Å. As a result of TM substitution inside C₃₂ cage, the average diameter shows a slight increase with a maximum value of 5.16 Å for Co@C₃₂. The average C–C and C=C bond lengths of TM@C₃₂ complexes lie in the range 1.46–1.51 Å (see Table 2). The binding energies show a similar pattern as that shown by C₂₀ and C₂₈, i.e. higher values of 8.65 eV and 8.63 eV for Ti and V respectively and decreasing value for other TMs. The cohesive energies tabulated in Table 3 shows very small negative cohesive energies for Cr, Co, and Cu which suggests their lower stability and that it may not be feasible to encapsulate them inside C₃₂. All the other TMs show positive cohesive energies leading to the fact that they all form stable complexes with C₃₂.

C₃₆ with D_6h symmetry is found to be the most stable geometry with an average diameter of 5.30 Å and 8.89 eV binding energy per atom. The average C–C and C=C bond lengths lies in the range 1.45–1.50 Å and 1.43–1.45 Å, respectively. The TM substitution does not change the diameter to a large extent, rather it remains nearly constant between 5.30–5.33 Å and the average bond lengths are the same for C–C, but C=C changes to 1.44–1.46 Å. The binding energy shows the same trend as shown by other smaller fullerenes. The cohesive energies tabulated in Table 3 shows a positive value for all TMs except for Co which shows a negative value of −0.26 eV. Further, we can conclude that C₃₆ is the smallest fullerene to encapsulate Cr and Cu.

In order to examine the stability of 3d TMs at the surface position in small fullerenes, we performed structure optimization of the C_n−1TM for n = 32 and 36. The total energy calculations suggest TM@C_n is more stable than C_n−1TM complexes. The stability of C_n−1TM complexes increases with an increase in atomic number of TM, consistent with the pattern observed in TMC₅₉ systems⁴⁰ but different from the stability of TM@C_n complexes.

Furthermore, from the structural analysis of TM@C_n, we find that all the TMs prefer to place themselves at a central position for n = 20 and nearly off-center positions for n ≥ 28 within the cage by distorting the cage symmetry. The distortion in fullerene cages due to TM encapsulation is maximum for n = 20 and minimum for n = 36. The binding energy of TM@C_n decreases with increasing atomic number from Ti to Cu in all the fullerenes considered, although the rate of decrease falls with increasing diameter. The average bond lengths and diameters also show an increase due to TM encapsulation. The positive or negative ΔE values indicate the feasibility of formation of these endohedral complexes. Ti and V are the only two TMs which show positive values for all the fullerene cages which suggest a strong possibility for their formation experimentally. Only Cr and Cu show negative values for C₂₈ and all the other TMs form stable complexes with C₂₈. Similarly, in C₃₂, Cr and Cu show small negative values which suggest that these complexes can be formed but with somewhat less stability. However, Co shows a comparatively higher negative value which indicates its unstable nature inside C₃₂ cage. Further, in C₃₆, except Co, the cohesive energies show positive values which suggest the stability of all TMs inside this cage.

B. Electronic and magnetic properties of TM@C_n

The electronic properties of TM@C_n complexes are investigated in terms of the HOMO (highest occupied molecular orbital)–LUMO (lowest unoccupied molecular orbital) gap as well as the electronic density of states (EDOS).

The HOMO–LUMO gap for both spin up (↑) and spin down (↓) states as a function of 3d TMs with increasing atomic number is plotted in Fig. 3. The spin ↑ gap shows a sharp decrease from V to Cr and vice versa in the spin ↓ gap, with an oscillatory pattern thereafter in C₂₀. For the TM@C₂₈ complexes, the spin ↑ gap shows a sharp increase from Cr to Mn and is nearly constant thereafter, whereas the spin ↓ gap decreases sharply from Mn to Fe and shows an oscillatory pattern after that but decreases to 0.36 eV for Cu. For C₃₂, the spin ↑ gap decreases from 1.41 eV in pure C₃₂ to 0.68 eV in Fe@C₃₂ and shows sharp increase from Fe to Co and then decrease for Cu. The spin ↓ gap shows a similar pattern as the spin ↑ gap but it increases sharply from Mn to Fe and then decreases for Co, with a further increase for Cu. In C₃₆, the spin ↑ gap decreases from 0.83 eV for pure C₃₆ to 0.41 eV for V@C₃₆, then increases to 0.76 eV (Cr) and then gradual decreases to 0.73 eV (Cu). The spin ↓ gap shows a similar behavior as the spin ↑ gap with the only exception being Co which has a very small gap of 0.12 eV.

Fig. 3 HOMO–LUMO gaps for spin up and spin down states for all TM@C₂₀, C₂₈, C₃₂ and C₃₆.

The EDOS of TM@C_n complexes are plotted in Fig. 4(a) which shows a polarized EDOS for C₂₀ at the Fermi level (E_f) even without encapsulating TMs. On encapsulation with Ti and V, the EDOS is modified significantly near E_f with the spin ↓ EDOS greater than the spin ↑ EDOS. The EDOS of C₂₀ shows occupied states within the range −4.0 to −2.0 eV in contrast to Ti and V which shows unoccupied states. In the Cr@C₂₀ complex, spin ↑ and spin ↓ EDOS are almost equal with 0.85 eV for the HOMO–LUMO gap.

Fig. 4 Electronic density of states (EDOS) for C₂₀, Ti@C₂₀, V@C₂₀, and Cr@C₂₀. The dotted line shows the position of the Fermi level (E_f).

The Mulliken charge analysis shows an interesting pattern for the charge redistribution in TM@C₂₀ complexes. Ti, V, and Cr donates ∼0.36–0.55 electrons to the C₂₀ cage structure, Mn and Fe gain 0.12 electrons from nearby C atoms, whereas Co, Ni and Cu show no charge transfer. Apart from the external charge transfer in all the complexes, the internal transfer of electrons takes place from 4s to 3d and 4p orbitals significantly.

The EDOS for TM@C₂₈ complexes are plotted in Fig. 5. EDOS for C₂₈ is equal for both spin ↑ and spin ↓ electrons. However, with the encapsulation of TMs the EDOS show significant change at and below the E_f. Ti shows finite spin ↑ states at E_f and modified spin ↑ and ↓ EDOS up to −4.0 eV below E_f. V shows a similar behavior as Ti with the only difference being the finite spin ↑ EDOS near E_f. For Mn, there is an equal HOMO–LUMO gap for spin ↑ and spin ↓ electrons with unoccupied states at E_f. For Fe and Ni, the EDOS show a similar behavior at and near E_f with an equal HOMO–LUMO gap.

Fig. 5 EDOS for C₂₈, Ti@C₂₈, V@C₂₈, Mn@C₂₈, Fe@C₂₈, and Ni@C₂₈. The dotted line shows the position of E_f.

To further elucidate the origin of FM, the projected density of states (PDOS) for both Ti and Ni inside C₂₈ cage are plotted in Fig. 6, as the former behaves as the acceptor and the latter behaves as the donor with respect to neighboring carbon atoms. Fig. 6(a) represents PDOS for Ti, which shows that the electronic states in the vicinity of E_f come mainly from up 3d states with empty down 3d states. In Ni, spin ↓ DOS are finite and gives significant contribution at and near E_f, whereas up 3d states show finite contribution within the region −3.0 to −1 eV. For both Ti and Ni, 4s and 4p states do not show any contribution near E_f, whereas all 3d up and 3d down components lie in its vicinity.

Fig. 6 Projected density of states (PDOS) for Ti@C₂₈ and Ni@C₂₈ with their 4s and 3d contributions. The dotted line shows the position of E_f.

For TM@C₂₈ complexes, Ti gains ∼0.30 electrons from C₂₈ cage and Ni loses ∼0.72 electrons to surrounding C atoms. The 4s orbital of Ni has lost 0.2 electrons to the 3d orbital, 0.7 electrons to the 4p orbital and 0.7 electrons to the C₂₈ cage, with 0.32 electrons remaining in the 4s orbital. Therefore, there is an internal conversion as well as donation of electron that takes place from 4s.

For the C₃₂ cage, the spin ↑ and spin ↓ EDOS are equal with unoccupied states at E_f. Ti shows an increased spin ↑ EDOS whereas V shows more contribution from spin ↓ EDOS, as shown in Fig. 7. At E_f, Mn and Fe show similar behavior and below E_f, up to −4.0 eV, there is a significant change in EDOS. For Ni, the complex shows half-metallic behavior with finite spin ↓ EDOS and very small spin ↑ EDOS near E_f. Inside the C₃₂ cage, all the 3d TMs behave as donors by donating ∼0.11–0.86 electrons to the surrounding cage C atoms. Like all the other cages considered, the 4s orbital loses charge to the cage as well as undergoing internal conversion of electrons with 3d and 4p orbitals.

Fig. 7 EDOS for C₃₂, Ti@C₃₂, V@C₃₂, Mn@C₃₂, Fe@C₃₂ and Ni@C₃₂. The dotted line shows the position of E_f.

EDOS for TM@C₃₆ complexes show a similar behavior as shown by TM@C₃₂ complexes with a small change in the EDOS at the E_f which is depicted in the HOMO–LUMO gap (Fig. 3). The difference in the spin ↑ and spin ↓ EDOS for TM@C_n complexes is because of the presence of strong electronic polarization arising due to transfer of charges. The Mulliken charge analysis predicts that V, Cr and Cu inside the C₃₆ cage act as donors by losing ∼0.4–0.76 electrons to the surrounding C atoms.

To study the evolution of magnetic properties of C_nfullerenes, we calculated the total MMs of TM@C_n complexes and the local magnetic moments (LMM) of TMs (see Fig. 8). The local MM at the 3d TM site along with the individual contributions of 3d, 4p and 4s orbitals are tabulated in Table 4. Due to the Jahn–Teller distortion and strong hybridization C₂₀ with I_h symmetry has an intrinsic MM of 2 μ_B which is consistent with ref. 33 and in TM@C₂₀ complexes, the MM varies from 2 μ_B for Ti@C₂₀ to 5 μ_B in Cu@C₂₀, whereas for Cr@C₂₀, the MM gets quenched (Fig. 8). In TM@C₂₀ complexes, the LMM is not fully localized at the TM site but also a significant amount is induced at the nearest neighboring C atoms. The magnetic interaction between TM impurities at the endo position and the surface C atoms is ferromagnetic (FM) in nature. 20–60% of the total MM is contributed by TM which is due to unpaired 3d electrons.

Fig. 8 Total magnetic moments and local MMs at the TM site with respect to the 3d TMs for all fullerenes, i.e.C₂₀, C₂₈, C₃₂ and C₃₆.

Table 4 The magnetic moments in Bohr magnetons at the TM site (μ_TM), and the individual contributions of 3d, 4p, 4s orbitals of TM atoms, μ_3d, μ_4p and μ_4s, respectively, are tabulated

TM	C20				C28				C32				C36
	μ TM	μ 3d	μ 4p	μ 4s	μ TM	μ 3d	μ 4p	μ 4s	μ TM	μ 3d	μ 4p	μ 4s	μ TM	μ 3d	μ 4p	μ 4s
Ti	0.24	0.18	0.04	0.02	1.36	1.33	0.01	0.01	2.00	1.99	0.05	0.03	2.13	2.03	0.06	0.04
V	0.20	0.17	0.02	0.01	2.66	2.60	0.03	0.01	3.24	3.08	0.09	0.06	3.43	3.38	0.10	0.08
Cr	0.00	0.00	0.00	0.00	3.99	3.88	0.04	0.05	4.65	4.43	0.12	0.09	4.82	4.60	0.12	0.09
Mn	3.08	3.08	0.06	0.02	4.87	4.64	0.09	0.10	5.04	4.80	0.12	0.11	5.10	4.86	0.12	0.12
Fe	3.45	3.33	0.14	0.04	3.82	3.71	0.05	0.06	3.92	3.76	0.07	0.08	3.93	3.80	0.07	0.06
Co	2.51	2.47	0.12	0.04	2.73	2.65	0.03	0.05	2.42	2.34	0.04	0.04	2.77	2.69	0.05	0.04
Ni	1.39	1.54	0.11	0.04	2.29	1.61	0.02	0.08	1.17	1.11	0.02	0.04	0.00	0.00	0.00	0.00
Cu	0.27	0.45	0.12	0.04	0.20	0.01	0.00	0.00	0.03	0.03	0.02	0.02	0.00	0.00	0.00	0.00

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The C₂₈ cage structure possesses zero MM, however, when encapsulated with TMs, it acquires finite MM. In TM@C₂₈ complexes, MM is mainly localized at the TM site (see Fig. 8) with a small amount of MM induced on surrounding C atoms. The total MM ranges from 2 μ_B in Ti@C₂₈ to 1 μ_B in Cu@C₂₈. However, the total MM of Cr@C₂₈ increases to 4 μ_B from 0 μ_B in C₂₈ cage. In Cu@C₂₈, 0.2 μ_B of a total MM of 1 μ_B is localized at the Cu atom. The magnetic interaction of Ti, V, Mn, Fe, Co and Cu with the surrounding C atoms is of FM nature except for Ni which shows antiferromagnetic (AFM) interactions.

The C₃₂ and C₃₆fullerene structures are non-magnetic in their ground state. However, when encapsulated with TMs, the resultant complex becomes magnetic. Similar to the trend observed in the smaller fullerenes, C₃₂ and C₃₆ also have MM localized mainly at the TM sites, as shown in Table 4, except for Co, Ni and Cu (see Fig. 8). Interestingly, Ni@C₃₂ and Ni@C₃₆ show zero MM. The LMM at the Ni site in Ni@C₃₂ is 1.17 μ_B with a major contribution from 3d orbital electrons, whereas in Ni@C₃₆ complex, LMM is zero. The surrounding C atoms interact AFM with Ti, V, Cr, Mn, Co and Ni. The Cu@C₃₂ complex shows a MM of 1 μ_B but with nearly no contribution from TM and all the MM is contributed by the cage C atoms.

Inside C₃₆, the TMs show a mixed behavior as Ti, V, and Mn show AFM interactions, whereas Cr, Fe, Co and Cu show FM interactions with the cage C atoms. In TM@C₃₆ complexes, the majority contribution to MM is localized at the TM site with a maximum contribution from 3d orbitals, apart from Cr and Cu (see Table 4).

At this point, we would like to present the magnetic behavior of complexes when 3d TM is substituted on the surface of the fullerenes for assessment, although total energy calculations have suggested larger stability of the endohedral complexes. The total magnetic moment and local magnetic moment of C_n−1TM for n = 32 and 36 are presented in the Table 5.

Table 5 The total magnetic moment (μ_T in Bohr magneton) and local magnetic moment (μ_TM) for C_n−1TM for n = 32 and 36

TM	C32		C36
	μ T	μ TM	μ T	μ TM
Sc	1.0	0.00	1.0	0.01
Ti	0.0	0.00	0.0	0.01
V	1.0	2.90	1.0	2.93
Cr	2.0	4.03	2.0	4.01
Mn	3.0	4.64	3.0	4.87
Fe	4.0	4.18	2.0	4.08
Co	1.0	1.11	1.0	1.13
Ni	0.0	0.00	2.0	2.26
Cu	1.0	0.00	1.0	0.01

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From Table 5, the 3d TMs towards the left of Mn in the periodic table shows distinct magnetic behavior when substituted on the surface with a different value of total MM as compared to endohedral metallofullerene complexes. Towards the right of Mn in the 3d series, the MM of the surface doped fullerene complexes shows a similar pattern to TM@C_n complexes.

The MMs of TM@C_n complexes are dependent on nature of TM and the size of encapsulating fullerenes. The atomic MMs of 3d TMs are altered to a large extent inside the fullerene cage. For Cr, the MM increases from 0.0 μ_B in C₂₀ to 5.99 μ_B in C₃₆. Interestingly for Mn, the MM is constant in all fullerenes from C₂₀ to C₃₆. For Fe, the MM decreases from 8 μ_B in C₂₀ to 3.99 μ_B in C₃₆. For Co, the MM decreases from 7.0 μ_B in C₂₀ to 1.0 μ_B in C₃₂ and then increases to 3.0 μ_B in C₃₆. There is a small induced MM on the nearest C atoms in all fullerenes which aligns FM for n < 32 and AFM for n ≥ 32, with some exceptional cases.

IV. Conclusions

We have investigated a possibility of inducing magnetism in small carbon fullerenes by encapsulating magnetic 3d TM impurities using spin polarized DFT. The average diameters of the fullerene cages show a small increase on TM encapsulation. The cohesive energy describes reliably the element’s ability to be trapped inside fullerene but do not tell us much about the energetics of the formation process. The cohesive energy of TM@C_n complexes suggest that Ti and V are stable inside all cage structures, therefore indicating a strong possibility of their production. The C₂₈ cage is the smallest fullerene which can encapsulate all 3d TMs except Cr and Cu which can only be encapsulated inside the C₃₆ cage. Cu is found to be least stable for encapsulation. The stability of substitutional metallofullerenes is found to improve with higher atomic number TMs, which is contrary to the pattern observed in similar sized endohedral fullerenes. The MM is induced in all fullerene cages with the introduction of TM impurity at the endohedral site. There is a significant MM of the order 0.12–0.50 μ_B induced on the carbon cage atoms. All the 3d TMs in C₂₀ and C₂₈ cages interact with C atoms ferromagnetically except Ni@C₂₈ which interacts antiferromagnetically. Ti, V, Cr, and Mn show AFM interactions with C atoms of C₃₆ cage. Therefore, it may be concluded that there is a transition of magnetic interactions from FM to AFM for n = 32. The MM is quenched for Ni beyond C₃₂. It does not show any change for Mn@C_n, although a FM to AFM change does take place at n = 32. Thus, the magnetic behavior of TM@C_n complexes is dependent on the size of the fullerene cages, configuration of 3d metals and the type of magnetic interactions between TMs and surrounding C atoms. The fullerene molecule acquires spin and charge and becomes magnetic due to the spin and charge transfer from transition metal dopants. Therefore, the choice of TM and host fullerenes provides a novel possibility to control the magnetic behavior of carbon systems. Further, given suitable experimental conditions, these small metallofullerenes should therefore be producible in abundance, facilitating the production of fullerene-based magnetic materials.

Acknowledgements

Authors are thankful to SIESTA group for providing their computational code. Isha Garg is thankful to University Grant Commission for providing financial support.

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