Comparison of Electronic and Magnetic Properties of Fe, Co, and Ni

Sep 18, 2009 - Comparison of Electronic and Magnetic Properties of Fe, Co, and Ni Nanowires Encapsulated in Boron Nitride Nanotubes. Jian-Min Zhang* ...
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J. Phys. Chem. C 2009, 113, 17745–17750

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Comparison of Electronic and Magnetic Properties of Fe, Co, and Ni Nanowires Encapsulated in Boron Nitride Nanotubes Jian-Min Zhang,*,† Su-Fang Wang,† Xiu-Juan Du,† Ke-Wei Xu,‡ and Vincent Ji§ College of Physics and Information Technology, Shaanxi Normal UniVersity, Xian 710062, Shaanxi, People’s Republic of China, State Key Laboratory for Mechanical BehaVior of Materials, Xian Jiaotong UniVersity, Xian 710049, Shaanxi, People’s Republic of China, and ICMMO/LEMHE UMR CNRS 8182, UniVersite´ Paris-Sud 11, 91405 Orsay Cedex, France ReceiVed: July 28, 2009; ReVised Manuscript ReceiVed: September 1, 2009

The electronic and magnetic properties of the three types of ferromagnetic nanowires (FN4’s), Fe4, Co4, and Ni4, encapsulated in boron nitride nanotubes (BNNTs) have been investigated systematically using the firstprinciples projector-augmented wave potential within the density functional theory under the generalized gradient approximation. We find that all three types of the FN4 encapsulated into the narrower (6,6) BNNT are endothermic, whereas if they are encapsulated into the broader (8,8) BNNT, they are exothermic. Both the spin polarization and the magnetic moment of the FN4@(8,8) systems are larger than those of the FN4@(6,6) systems due to weaker restriction of the broader (8,8) BNNT, but those of these two combined systems are smaller than those of the corresponding freestanding FN4. The spin polarization of the Co4@(8,8) system is larger than that of either the Fe4@(8,8) system or the Ni4@(8,8) system, which means that the Co4@(8,8) system can be used as a spin valve in spin-dependent transport nanodevices. I. Introduction Nanotubes (NTs) and nanowires (NWs) have been proved to be promising quasi-one-dimensional (1-D) nanostructures for nanoelectronics, nanolithography, photocatalysis, microscopy, and other fields of modern nanotechnologies.1,2 However, it is difficult to obtain and maintain a homogeneous and pure nanowire due to oxidation and adsorption during fabrication and application processes,3 so the nanowires are usually encapsulated inside carbon nanotubes by using capillarity or wet-chemistry methods.4-9 Novel electronic and magnetic properties of metalfilled carbon nanotubes have been reported,10-13 but the strong coupling between the encapsulated transition-metal (Fe, Co, or Ni) wires and the carbon nanotubes could lead to a few degenerating in electronic and magnetic properties of the nanowires. Therefore, such hybrid carbon nanotube/metal nanowire structures do not appear to have promise as nanocables with conducting properties.14 Recent preparations of novel inorganic nanotubes have provided more candidate materials for nanocables.15-18 Among them, boron nitride nanotubes (BNNTs), one type of groups III-V compounds with a tubular structure, have been of wide interest recently.19-29 In particular, with their band gap as large as 5.5 eV, BNNTs are insulators independent of their chirality and diameter and possess the potential for nanoscale electronic devices owing to their special properties that are useful in many fields.30-32 The BNNTs are especially suitable for the task of shielding a metallic nanowire inside their cavity to protect the encapsulated content from outside interference effectively.33 In fact, this has been achieved experimentally for numerous structures having the encapsulation of Mo clusters, Ni, or Fe-Ni alloy nanorods/nanowires, and potassium halide single crys* To whom correspondence should be addressed. Tel: +862985308456. E-mail: [email protected]. † Shaanxi Normal University. ‡ Xian Jiaotong University. § ICMMO/LEMHE UMR CNRS.

tals.34-38 Theoretically, density functional calculations have provided models for Cu, Fe, Co, and Ni wires encapsulated in the zigzag (n,0) BNNTs,14,33,39,40 in which the interaction between the wire and the BNNT is weak and the electronic structure of the wire is hardly disturbed by the BN coating, thus further proving the efficacy of such an arrangement. However, few theoretical studies have been performed for ferromagnetic nanowires (FNs), such as Fe, Co, and Ni nanowires, in a zigzag square structure, encapsulated in the armchair (m,m) BNNTs; much less information is known on the electronic and magnetic properties of these combined systems. In this paper, the electronic and magnetic properties of a zigzag square structural FN4 (Fe4, Co4, or Ni4) tightly and loosely encapsulated inside armchair (6,6) and (8,8) BNNTs have been comparatively investigated by using the projector-augmented wave (PAW) potential approach to the density functional theory (DFT) within the generalized gradient approximation (GGA) implemented in the Vienna ab initio simulation package (VASP).41-46 The rest of the paper is organized as follows. Section II gives details of our DFT calculation method and model of an Fe4 nanowire encapsulated in the (6,6) BNNT as an example; for simplicity, this model is denoted by Fe4@(6,6), and FN4@(6,6) represents the general FN4 (Fe4, Co4, or Ni4) encapsulated in the (6,6) BNNT. Throughout the paper, a subscript 4 indicates that there are four FN atoms per unit cell. In section III, we first present the binding energies of the FN4@(6,6) and FN4@(8,8) systems to show which one is the most stable and then the results for electronic structures mainly including band structures, total density of states (DOS), projected densities of states (PDOS) onto the FN4, charge and magnetic moments distribution. Finally, the conclusions of the work are given in section IV. II. Calculation Methods and Model All the calculations are performed within the DFT using the plane-wave basis implemented with the VASP code.41-46 The

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Figure 1. Side views for (a) an Fe4 freestanding nanowire and (b) an Fe4 nanowire encapsulated in a (6,6) BNNT.

2s22p1, 2s22p3, 3d74s1, 3d84s1, and 3d94s1 electrons are taken as the valence electrons for B, N, Fe, Co, and Ni atoms, respectively. The electron-ionic core interaction is represented by the PAW potentials,47 which are more accurate than the ultrasoft pseudopotentials. To treat electron exchange and correlation, we chose the Perdew-Burke-Ernzerhof48 formulation of the GGA, which yields the correct ground-state structure of the combined system. The cutoff energy for the plane waves is chosen to be 400 eV, which is much higher than the 250 eV typically used for the PAW potentials, and the supercell is large enough to ensure that the vacuum space is 18 Å to eliminate the interaction between periodic images. The Brillouin zone integration is performed by using the Gamma-centered MonkhorstPack scheme49 with 1 × 1 × 10 k-points. To avoid the numerical instability due to level crossing and quasi-degeneracy near the Fermi level, we use a method of Methfessel-Paxton order N (N ) 1) with a width of 0.2 eV. Geometric structures of both the nanotube and the nanowire wrapped inside are fully relaxed to minimize the total energy of the system until a precision of 10-4 eV is reached. The conjugate gradient minimization is used for optimization of the atom coordinates until the force acting on each atom is smaller than 0.02 eV/Å. Except for a single atom chain and two (or three) atom ribbon, the four atoms in a zigzag square structure, as shown in Figure 1a for Fe4, is the narrowest nanowires cutting directly from a bulk BCC metal. Figure 1b shows such an Fe4 nanowire encapsulated in (6,6) BNNT, in which the yellow, blue, and red balls denote boron, nitrogen, and iron atoms, respectively. The (6,6) BNNT is chosen here because its 6-fold rotation symmetry about its axis can guarantee that each Fe atom be located on the perpendicular of the tube wall through the center of a hexagon by boron-nitrogen bonds, while the 2-fold rotation axis of Fe4 nanowires is coincident to the tube axis. Considering the lattice mismatch between the (6,6) BNNT and Fe4 nanowire along their common axis, we adjust this direction lattice constant of the Fe4 nanowire to 2.494 Å so that the nanotube unit cell with an axis length of 2.494 Å contains two adjacent Fe layers. III. Results and Discussion To determine the stability of the FN4 (Fe4, Co4, or Ni4) encapsulated in the BNNT, we have calculated the binding

energy, Eb, which is defined as the difference between the total energy of the FN4 (Fe4, Co4, or Ni4) encapsulated in the BNNT, EBNNT+FN, and the sum of the total energies of the corresponding pristine BN nanotube, EBNNT, and the isolated FN4, EFN, with the latter assuming the same configuration as the one in the nanocable.33

Eb ) EBNNT+FN - (EBNNT + EFN)

(1)

The calculated binding energies per unit cell for the Fe4@(6,6), Co4@(6,6), and Ni4@(6,6) systems are 0.20, 0.21, and 0.31 eV, respectively. The positive values of the binding energy indicate a repulsive interaction between the FN4 and (6,6) BNNT. The combining processes of all these FN4@(6,6) systems are endothermic. The calculated binding energies per unit cell for the Fe4@(8,8), Co4@(8,8), and Ni4@(8,8) systems are -0.37, -0.06, and -0.05 eV, respectively. The negative values of the binding energy indicate an attractive interaction between the FN4 and (8,8) BNNT, and the combining processes of all these FN4@(8,8) systems are exothermic. Therefore, the FN4@(8,8) systems are more stable than the FN4@(6,6) systems and we expect that more complex configurations of FNs would be pulled spontaneously into broader BNNTs by forces amounting to a fraction of a nanonewton. Better insight into the distribution of the electrons with energy can be gained from the analyses of electronic band structures and density of states (DOS). The band structures of both the majority spin (left panel) and the minority spin (right panel) for the (a) Fe4@(6,6), (b) Fe4@(8,8), (c) Co4@(6,6), (d) Co4@(8,8), (e) Ni4@(6,6), and (f) Ni4@(8,8) systems are shown in Figure 2. The Fermi level is set to zero energy and indicated by the horizontal red dashed lines. From Figure 2, one can see that, first, a similar band structure is obtained for the FN4@(6,6) and FN4@(8,8) systems. Second, after inserting a FN4 into either a (6,6) BNNT or a (8,8) BNNT, the combined system becomes a metallic character, although a pristine BNNT has a large band gap of about 5 eV, as is shown in Figure 3a for a (6,6) BNNT. Third, comparing the band structure of the majority spin (left panel) with that of the minority spin (right panel) for each combined system, one readily identifies an asymmetry in the

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Figure 2. Band structures (left, majority spin; right, minority spin) for the (a) Fe4@(6,6), (b) Fe4@(8,8), (c) Co4@(6,6), (d) Co4@(8,8), (e) Ni4@(6,6), and (f) Ni4@(8,8) combined systems. The Fermi level is set to zero energy and indicated by the horizontal red dashed lines.

proximity of the Fermi level (red dashed lines). That is, there are more bands crossing the Fermi level for the minority spin than those for the majority spin. This indicates that a spin polarization transport process can be achieved in these FN4@(m,m) systems. Fourth, the π band across the Fermi level in the majority spin of the FN4@(8,8) system is broader than that of the FN4@(6,6) system, which may be due to a larger diameter and thus a weaker restriction of (8,8) BNNT. The total density of states (DOS) with the upper (lower) panel representing the majority (minority) spin for the pristine (6,6) BNNT and the Fe4, Co4, and Ni4 freestanding nanowires are shown in Figure 3a-d, respectively. The following features can be seen by comparing. First, as expected, the pristine (6,6) BNNT is an insulator and nonmagnetic, as indicated by about a 5 eV band gap and symmetry DOS curves between the

majority and minority spins, respectively, whereas all Fe4, Co4, and Ni4 freestanding nanowires are metallic and ferromagnetic with asymmetry DOS curves. In detail, only the majority d-band is filled below the Fermi level and the exchange splitting values of Fe4, Co4, and Ni4 freestanding nanowires are 2.27, 2.51, and 0.71 eV, respectively. Second, comparing the DOS at the Fermi level of the majority spin (upper panel) with that of the minority spin (lower panel) in Figure 3b-d, one readily identifies that the Fe4, Co4, and Ni4 freestanding nanowires have a high spin polarization and magnetic moment. Both the total density of states (DOS) (black lines) and the projected density of states (PDOS) onto the FN4 nanowires (blue lines) are shown in Figure 4 for the (a) Fe4@(6,6), (b) Co4@(6,6), (c) Ni4@(6,6), and (d) Fe4@(8,8) systems, where the upper and lower panels represent the majority and minority

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Wang et al. TABLE 1: Spin Polarization (%) and Magnetic Moment per FN4 Atom (µB/atom) for the Freestanding FN4, FN4@(6,6), and FN4@(8,8) Combined Systems characters Fe Co Ni

Figure 3. Total density of states (upper, majority spin; lower, minority spin) for (a) a pristine (6,6) BNNT and a (b) Fe4, (c) Co4, and (d) Ni4 freestanding nanowire. The vertical red dashed lines denote the Fermi level shifted to zero energy.

Figure 4. Total DOS (black lines) and PDOS onto the FN4 nanowires (blue lines) (upper, majority spin; lower, minority spin) for the (a) Fe4@(6,6), (b) Co4@(6,6), (c) Ni4@(6,6), and (d) Fe4@(8,8) systems. The vertical red dashed lines denote the Fermi level shifted to zero energy.

spins, respectively. The vertical red dashed lines denote the Fermi level shifted to zero energy. It can be seen that, first, the energy states near the Fermi level are mainly attributed to the Fe4, Co4, and Ni4 nanowires. Second, that only the majority d-bands of these combined systems are all fully filled below the Fermi level implies that these combined systems have a strong ferromagnetism. The PDOSs onto the FN4 nanowires (blue lines) shown in Figure 4a-c for the Fe4@(6,6), Co4@(6,6), and Ni4@(6,6) combined systems are not completely similar to the DOSs for their corresponding freestanding nanowires shown in Figure 3b-d, respectively, which may be resulted from the stronger restriction of the narrower (6,6) BNNT. In Figure 4d, however, the PDOS onto the Fe4 nanowire for the Fe4@(8,8) combined system is similar to the DOS of the Fe4 freestanding nanowire shown in Figure 3b. This indicates that the FN4’s loosely wrapped in the broader BNNT have the similar electronic and magnetic properties of the corresponding FN4. The enhancement of the spin polarization is important for spin-dependent electronic transport. The spin polarization (P) is defined as

P)

NV(EF) - Nv(EF) NV(EF) + Nv(EF)

(2)

spin polarization (%)

magnetic moment per FN4 atom (µB/atom)

FN4 FN4@(6,6) FN4@(8,8) FN4 FN4@(6,6) FN4@(8,8) 99 87 89 2.78 2.68 2.77 97 82 95 1.81 1.77 1.80 90 88 89 0.80 0.70 0.79

where Nv(EF) and NV(EF), respectively, represent the total DOS of the majority and minority spins at the Fermi level. Determined values of the spin polarization (%) for the freestanding FN4, FN4@(6,6), and FN4@(8,8) combined systems are listed in Table 1. It can be seen that the spin polarization of FN4@(8,8) is larger than that of FN4@(6,6) due to weaker restriction of the broader (8,8) BNNT but that of these two combined systems is smaller than that of the corresponding freestanding FN4. This means that a FN4 encapsulated inside a BNNT will lead to a decreasing in the spin polarization, especially for the narrower BNNT. In detail, the spin polarizations of the Ni4@(6,6) and Ni4@(8,8) systems reduce only about 2% and 1%, respectively, compared with that of Ni4 freestanding nanowire, whereas the spin polarizations of both the Fe4@(6,6) and the Co4@(6,6) systems decrease significantly; that is, they are 12% and 15% lower than those of the Fe4 and Co4 freestanding nanowires, and the spin polarizations of the Fe4@(8,8) and Co4@(8,8) systems increase about 2% and 16% compared with those of their corresponding Fe4@(6,6) and Co4@(6,6) systems, respectively. The spin polarization of 95% for the Co4@(8,8) system is larger than those of the Fe4@(8,8) and Ni4@(8,8) systems and slightly smaller than that of 97% for the Co4 freestanding nanowire. This means that the Co4 nanowire loosely encapsulated inside a (8,8) BNNT can be used as a spin valve in spin-dependent transport nanodevices. Similar results are also obtained for the magnetic moment per FN4 atom (µB/atom), as listed in Table 1, for the FN4, FN4@(6,6), and FN4@(8,8) systems. That is, the magnetic moment per FN4 atom of FN4@(8,8) is larger than that of FN4@(6,6), but that of these two combined systems is smaller than that of the corresponding freestanding FN4. In detail, the magnetic moment of 0.79 µB/atom for Ni atoms in the Ni4@(8,8) system increases about 13% compared with that of 0.70 µB/ atom in the Ni4@(6,6) system, whereas the magnetic moments of the Fe4@(8,8) and Co4@(8,8) systems increase only about 3% and 2% compared with those of the Fe4@(6,6) and Co4@(6,6) systems, respectively. The magnetic moments of all these FN4@(8,8) systems decrease 0.01 µB/atom from the values of the corresponding freestanding FN4. This indicates that the FN4’s loosely encapsulated inside the broader (8,8) BNNT have larger magnetic moments than the corresponding nanowires tightly encapsulated inside the narrower (6,6) BNNT due to the weaker restriction of the broader (8,8) BNNT. Charge distribution in real space can be a help to ulteriorly visualize the interaction characteristics between FN4’s and BNNTs. Taking the Fe4@(6,6) and Fe4@(8,8) systems as examples, the charge density on layer A (see Figure 1) is compared in Figure 5a,b, respectively. The red, orange, yellow, green, blue, and purple colors represent the magnitude of electron density in an increasing order, where one isodensity curve of 0.14 (electrons/Å3) is denoted by the black solid line. Compared with Figure 5b for the Fe4@(8,8) system, Figure 5a shows not only a slight counterclockwise rotation of the Fe4 wire relative to outside (6,6) BNNT after relaxation but also a small overlap of the charges between the Fe atom and its nearest-

Fe, Co, and Ni NWs Encapsulated in BNNTs

J. Phys. Chem. C, Vol. 113, No. 41, 2009 17749 the Co4@(8,8) system can be used as a spin valve in spindependent transport nanodevice. Acknowledgment. The authors would like to acknowledge the State Key Development for Basic Research of China (Grant No. 2004CB619302) for providing financial support for this research. References and Notes

Figure 5. Charge density on layer A (see Figure 1) for the (a) Fe4@(6,6) and (b) Fe4@(8,8) systems. Red, orange, yellow, green, blue, and purple colors represent the magnitude of electron density in increasing order, where one isodensity curve of 0.14 (electrons/Å3) is denoted by the black solid line.

neighbor N atom, indicating the stronger interaction between the Fe4 wire and the narrower (6,6) BNNT as well. Similar results are also obtained for the other FN4@(6,6) and FN4@(8,8) systems. More importantly, the FN4’s encapsulated inside the BNNT are under the protection of the BNNT to prevent from oxidation and thus may stably exist in the atmosphere for long time. This is a good progress because the bare metal nanowires with a 10 Å diameter approximately were reported to exist only transiently in even ultrahigh vacuum.50,51 Therefore, the FN4’s encapsulated inside the broader (8,8) BNNT have a high spin polarization and magnetic moment and stably exist in the atmosphere for long time and thus can be expected to have potential applications in building nanodevices. IV. Conclusions The electronic and magnetic properties of FN4’s (Fe4, Co4, and Ni4) with a zigzag square structure tightly and loosely encapsulated inside armchair (6,6) and (8,8) BNNTs have been investigated systematically using the first-principles PAW potential within DFT under GGA. The following conclusions are obtained: (1) Binding energy analyses show all the FN4’s encapsulated into the narrower (6,6) BNNT are endothermic, whereas if they are encapsulated into the broader (8,8) BNNT, they are exothermic. We expect more complex configurations of FNs would be pulled spontaneously into the broader BNNTs by force amounting to a fraction of a nanonewton. (2) The asymmetry in the energy bands between the majority spin and minority spin near the Fermi level, that is, there are more bands crossing the Fermi level for the minority spin than those for the majority spin, indicates that the spin polarization transport process can be achieved in these FN4@(m,m) systems. (3) Comparing the total density of states (DOS) of both the combined systems and the freestanding FN4 with projected densities of states (PDOS) onto the FN4, we find that the energy states near the Fermi level are mainly attributed to the FN4, and the FN4’s loosely encapsulated into the broader (8,8) BNNT have the similar electronic and magnetic properties of the corresponding FN4. (4) The spin polarization and magnetic moment of the FN4@(8,8) systems are larger than those of the FN4@(6,6) systems due to the weaker restriction of the broader (8,8) BNNT, but those of these two combined systems are smaller than those of the corresponding freestanding FN4. The spin polarization of the Co4@(8,8) system is larger than that of either the Fe4@(8,8) system or the Ni4@(8,8) system, which means that

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