Nanospintronic properties of carbon-cobalt atomic chains

– Periodic atom chains of carbon-cobalt compounds, (CnCo)∞, comprise both conducting and insulating electronic properties simultaneously depending on the spin type of electrons, and hence are half-metals. Their band gap and the net magnetic moment oscillate with the number of carbon atoms in a unit cell. Finite segments of these chains also show interesting magnetic and transport properties. When connected to appropriate metallic electrodes the antiferromagnetic CoCnCo segments behave like molecular spin-valves, which can be conveniently manipulated. In earlier electronic transport studies, the spin-direction of conduction electrons was generally disregarded, in spite of the fact that spin orientation of electrons decays much slower than their momentum and consequently spin-coherence can be maintained relatively easily [1]. Current revolutionary applications using giant magnetoresistance in magnetic recording and nonvolatile memories have been derived from spin-dependent electronic transport (spintronics) [1–3]. Half-metals (HM) are a class of materials which exhibit interesting spintronics properties where electrons distinguished by their different spin orientation can assume different functions in the operation of the same device. This way, not only the capacity of information processing is doubled, but also new functions appear for important technological applications [4, 5]. In HMs a 100% spin polarization is achieved, since the Fermi level (EF ) is populated by states having only one spin direction but the empty states of the electrons of opposite spin are separated from the occupied states by an energy gap Eg. This situation is in contrast to the ferromagnetic metals, where both spins contribute to the state density at EF and spin polarization becomes less than 100%. Even though 3D ferromagnetic Heusler alloys and transition metal oxides exhibit half-metallic properties [6], their stoichiometry cannot be controlled easily and coherent spin transport is destroyed by the defect levels. HMs such as CrAs and CrSb in zincblende structure have been grown only in thin-film forms [7]. In this letter we predict that periodic atom chains of carbon-cobalt compounds, (CnCo)∞, comprise HM properties. Owing to the broken spin degeneracy energy bands split; the bands of one spin direction become semiconducting, but bands of the opposite direction show a c © EDP Sciences Article published by EDP Sciences and available at http://www.edpsciences.org/epl or http://dx.doi.org/10.1209/epl/i2005-10432-4 E. Durgun et al.: Nanospintronic properties in atomic chains 643 metallic character. This way, the difference between the numbers of electrons of different spin orientations in the unit cell, N = N↑ − N↓, is an integer and hence the spins become fully polarized at the Fermi level. In (CnCo)∞ chains the band gap and the net magnetic moment show interesting even-odd disparity depending on the number of carbon atoms in a unit cell. In contrast to those complications found in three-dimensional (3D) structures [8], half-metallicity of (CnCo)∞ chains appear to be rather robust and straightforward. Moreover, the number of carbon atoms in a unit cell provides a structural parameter to engineer the electronic and magnetic properties of these atomic chains, such as their band gap and magnetic moment. Similar half-metallic properties were also recently predicted for (CnCr)∞ chains [9]. While present (CnCo)∞ compounds are metallic for minority spin states and semiconducting for majority spin states when n > 1, in (CnCr)∞ compounds the character of majority and minority states alternate between metallic and semiconducting depending on n being odd or even. The compound chains of other transition metal atoms, such as Ti, Fe, and Mn, do not show half-metallic properties for all n. Finite segments of carbon-cobalt chains show even more interesting properties. The magnetic ground state of the finite CoCnCo chain structures is ferromagnetic for even-n, but antiferromagnetic for odd-n. When connected to appropriate metallic electrodes the antiferromagnetic CoCnCo segments behave like molecular spin valves, which can be conveniently manipulated. We show that these compound atom chains are stable up to 1000K and robust against axial elastic deformation. Their predicted properties are unusual for one-dimensional matter and of fundamental interest in the field of fermionic excitations with spin degree of freedom. Carbon atom strings Cn, which are precursor to CnCo compounds, have been investigated for decades [10]. Finite segments of Cn have already been synthesized [11]. As an ultimate one-dimensional structure having only one atom in the cross-section, carbon strings can form only linear atomic chains and are stabilized by double bonds, which consist of a σ-bond of 2s + 2pz atomic orbitals along the chain axis and π-bonds of 2px and 2py orbitals. Because of cylindrical symmetry of the chain structure, the latter π-orbitals form a doubly degenerate but half-filled band, which crosses the Fermi level. The double-bond structure underlies the unusual properties of Cn, such as its high axial strength, transversal flexibility and strong cohesion. For example, the elastic stiffness of Cn, i.e., the second derivative of the strain energy per atom with respect to the axial strain, dE/dε, was calculated to be 119 eV, which is twice the typical value for carbon nanotubes. Despite its low coordination number of two as compared to four in diamond or three in graphite, the cohesive energy of Cn is as large as 90% of that of diamond [10]. Mechanical, electronic and magnetic properties of CnCo compounds are derived from those of Cn strings. Now our prime concern is to demonstrate that they are stable and they can, in fact, be synthesized without major difficulty. To this end, we carry out a state-of-the art, firstprinciples analysis based on quantum mechanics within density functional theory (DFT) [12] at zero and high temperatures [13]. Together with generalized gradient approximation, we used ultrasoft pseudopotentials and plane waves with cut-off energy of 350 eV. The finite and infinite atomic chains have been treated in supercell geometries using a tetragonal cell with lattice parameters of asc = bsc = 10 Å and csc = c, where c is the lattice parameter of the chain. For finite chains an additional 10 Å vacuum space in the axial direction is left in the supercell. Brillouin zone is sampled by 25-special k-points for the CCo chain. The number of k-points is scaled according to the size of the unit cell for other periodic chains. Atomic positions (hence the geometric structure) and the lattice parameter c are optimized by minimizing the total energy, as well as Hellmann-Feynman forces on the atoms and the strain. The convergence criteria adopted for the total energy and atomic forces are 10−5 eV and 10−3 eV/Å, respectively. The calculations for finite chains are also compared and 644 EUROPHYSICS LETTERS Table I – Summary of results of spin-polarized first-principles calculations for (CnCo)∞ (1 ≤ n ≤ 6) atomic chains. ∆ET is the difference between spin-paired (non-magnetic) and spin-unpaired (magnetic) total energies; ∆ET > 0 indicates that the compound has a magnetic ground state. c is the optimized 1D lattice parameter. μ is the net magnetic moment per unit cell. In the last two columns, M denotes the metallic character, and the numerals are the band gaps in eV for semiconducting (or insulating) band structures. Structure ∆ET (eV) c (Å) μ (μB) Majority spin (↑) Minority spin (↓) (CCo)∞ 0.11 3.04 1.0 M 0.70 (C2Co)∞ 1.22 4.96 3.0 3.70 M (C3Co)∞ 0.71 6.18 1.0 1.52 M (C4Co)∞ 0.99 7.52 3.0 2.80 M (C5Co)∞ 1.20 8.76 1.0 1.81 M (C6Co)∞ 1.02 10.1 3.0 2.29 M confirmed with those of gaussian 03 code [14] which utilizes local basis sets instead of plane waves. B3LYP and BPW91 DFT parametrization with cep31-g basis sets have been used. The reliability of gaussian 03 results have been further tested by performing wave function stability analysis. It is well documented that these calculations have been extremely successful in predicting novel nanostructures, such as carbon nanotubes, monatomic chains of carbon and transition metal atoms, even before these structures were synthesized [15]. Since all the atomic positions and the lattice parameter c along the chain axis are optimized by minimizing the total energy of the whole system at T = 0K, as well as the forces on the atoms and the stress, the predicted geometric structures have a close bearing to the actual systems. Transition state analysis performed for different reaction paths provides us with conclusive evidences showing that the linear CnCo chains are stable and can be synthesized. The CnCo compound chains can conveniently grow from a finite Cn chain by attaching first Co and then n C atoms sequentially to one of its free ends, where individual Co and C atoms are attracted to their equilibrium bound state positions. No energy barrier is involved in the course of the growth and hence the process is exothermic. The minimum energy barrier to remove one Co atom from the (CnCo)∞ chain in the transverse direction is calculated to be 1.1 eV, that is significantly high and renders stability. The energetics of the growth clearly demonstrates that CnCo linear compounds are not simply a theoretical construct of fundamental interest, but they can also be realized experimentally. In fact, stable CnCo atom chains can be fabricated starting from one end of the finite-length Cn string which has been found at the center of a carbon nanotube [11]. In that geometry the carbon nanotube itself encapsulates the compound and protects it from oxidation and chemisorption of foreign atoms. Atomic manipulations using atomic force microscopy can be proposed as a potential technique for the fabrication of the prototypes of CnCo atom chains. While first-principles total energy calculations at T = 0K determines optimized structures by the conjugate gradient method, the stability of a (CnCo)∞ compound is assured by stringent tests. For example, if a (CnCo)∞ linear compound is stable, it corresponds to a local minimum of energy in the configuration space and this minimum shall be separated from other lower-energy local minima (or the global minimum) by sizable energy barriers. Such a case is examined first by displacing individual atoms of the compounds along various directions and then by allowing them to relax. In the present case all displaced atoms of (CnCo)∞ have returned to their original configuration upon relaxation. A similar process is carried out by ab initio molecular-dynamics calculations performed at high temperatures where individual atoms are moved in random directions resulting in sizable displacements. If the structure E. Durgun et al.: Nanospintronic properties in atomic chains 645