Spintronic properties of carbon-based one-dimensional molecular structures

In this paper we present an extensive study of the electronic, magnetic, and transport properties of finite and infinite periodic atomic chains composed of carbon atoms and $3d$ transition metal (TM) atoms using first-principles methods. Finite-size, linear molecules made of carbon atomic chains caped with TM atoms, i.e., $\mathrm{TM}\text{−}{\mathrm{C}}_n\text{−}\mathrm{TM}$ structures are stable and exhibit interesting magnetoresistive properties. The indirect exchange interaction of the two TM atoms through a spacer of $n$ carbon atoms determines the type of the magnetic ground state of these structures. The $n$-dependent ($n=1$ to 7) variations of the ground state between ferromagnetic and antiferromagnetic spin configurations exhibit several distinct forms, including regular alternations for Ti, V, Mn, Cr, Fe, and Co, and irregular forms for Sc and Ni cases. We present a simple analytical model that can successfully simulate these variations, and the induced magnetic moments on the carbon atoms. Depending on the relative strengths of the carbon $s$, $p$ and TM $d$ orbital spin-dependent coupling and on the on-site energies of the TM atoms there induces long-range spin polarizations on the carbon atoms which mediate the exchange interaction. While periodically repeated $\mathrm{TM}\text{−}{\mathrm{C}}_n$ atomic chains exhibit half-metallic properties with perfect spin polarization at the Fermi level, finite but asymmetric chains comprising single, double, and triple TM atoms display interesting spin-dependent features. These properties may be altered when these structures are coupled to electrodes. However, when connected to appropriate electrodes the $\mathrm{TM}\text{−}{\mathrm{C}}_n\text{−}\mathrm{TM}$ atomic chains act as molecular spin valves in their ferromagnetic states due to the large ratios of the conductance values for each spin type.

Figure 1

(Color online) Energetics of the formation of $\mathrm{Co}{\mathrm{C}}_7\mathrm{Co}$ and $\mathrm{Cr}{\mathrm{C}}_7\mathrm{Cr}$ atomic chains. Left panels correspond to a TM atom attaching to the left free end of the bare carbon chain; right panels are for the binding of a TM atom to the other end of the $\mathrm{TM}\text{−}{\mathrm{C}}_n$ chain. $d$ is the distance between TM atom and C atom. The total energy of the system for $d\to \infty$ is set to zero in each panel.

Figure 2

(Color online) Optimized interatomic distances (in Å) of $\mathrm{TM}\text{−}{\mathrm{C}}_n\text{−}\mathrm{TM}$ atomic chains in their ferromagnetic (left column) and antiferromagnetic (right column) states. (a) $\mathrm{Co}{\mathrm{C}}_n\mathrm{Co}$; (b) $\mathrm{Cr}{\mathrm{C}}_n\mathrm{Cr}$.

Figure 3

(Color online) Optimized total energy (continuous line) and tensile force (dashed line) vs strain of $\mathrm{Cr}{\mathrm{C}}_3\mathrm{Cr}$ and $\mathrm{Cr}{\mathrm{C}}_4\mathrm{Cr}$ atomic chains. The chain breaks for strain values exceeding the critical point corresponding to the maximum of the force curve indicated by arrows. The total energies in equilibrium are set to zero.

Figure 4

(Color online) The decay of the exchange interaction strength between the Cr atoms in $\mathrm{Cr}{\mathrm{C}}_n\mathrm{Cr}$ as a function of their separation $d$. The curves are the best fits to the $\Delta E_{\mathit{FM}\to \mathit{AF}}$ values in the form $\sim d^{\alpha }$.

Figure 5

(Color online) The energy difference of the AF and the lowest-energy FM states, $\Delta E_{\mathit{FM}\to \mathit{AF}}=E_T\left(\mathit{AF}\right)-E_T\left(\mathit{FM}\right)$ vs the number $n$ of carbon atoms in the chain for different $3d$ transition metal elements.

Figure 6

(Color online) (a) Variation of the atomic magnetic moments in the $\mathrm{TM}\text{−}{\mathrm{C}}_4\text{−}\mathrm{TM}$ atomic chains in their ground (top panels) and excited (down panels) states. Left (right) panels are for $\mathrm{TM}=\mathrm{Co}$ $(\mathrm{TM}=\mathrm{Cr})$. (b) From top to bottom: Variation of spin-up $\rho \uparrow$ and spin-down charge $\rho \downarrow$ densities, atomic magnetic moments, and change in total valance charge $\Delta \rho$ in the $\mathrm{TM}\text{−}{\mathrm{C}}_{15}\text{−}\mathrm{TM}$ atomic chains. Again, left (right) panels are for $\mathrm{TM}=\mathrm{Co}$ $(\mathrm{TM}=\mathrm{Cr})$.

Figure 7

(Color online) Schematic electronic configuration of a $\mathrm{TM}\text{−}{\mathrm{C}}_n\text{−}\mathrm{TM}$ structure in an AF state. TM sites have different on-site energies than the C sites, and the hopping terms are dependent on the magnetic ordering. The energy cost for a spin-up electron of the first C site to hop to the first TM site is different from the energy cost for a spin-down electron to do the same hopping. The energy costs are reversed between the spins of the $n\text{th}$ C site where they are identical for each spin for hopping between different C sites.

Figure 8

(Color online) Energy difference of the AF and the lowest FM states in the $\mathrm{Co}{\mathrm{C}}_n\mathrm{Co}$ and $\mathrm{Cr}{\mathrm{C}}_n\mathrm{Cr}$ atomic chains within the simple tight-binding model. The corresponding DFT results are shown in the inset for comparison.

Figure 9

(Color online) Optimized interatomic distances (in Å) of ${\mathrm{C}}_n\mathrm{Cr}{\mathrm{C}}_m$ atomic chains in their ferromagnetic state.

Figure 10

(Color online) Spin dependent HOMO and LUMO levels of $\mathrm{TM}\text{−}{\mathrm{C}}_n\text{−}\mathrm{TM}$ chains for $\mathrm{TM}=\mathrm{Co}$ and Cr, $n=1–7$, in their ground and excited magnetic states. HOMO levels are set to zero in each case.

Figure 11

(Color online) Left panels: Spin-dependent total density of states of the periodic infinite ${\left(\mathrm{Cr}{\mathrm{C}}_3\right)}_{\infty }$ and ${\left(\mathrm{Cr}{\mathrm{C}}_4\right)}_{\infty }$ atomic chains. Right panels: Same for the ${\left(\mathrm{Cr}{\mathrm{C}}_3\right)}_{\infty }$ and ${\left(\mathrm{Cr}{\mathrm{C}}_4\right)}_{\infty }$. The Fermi energy is set to zero in all systems.

Figure 12

(Color online) Conductance vs energy for the $\mathrm{Cr}{\mathrm{C}}_n\mathrm{Cr}$ $(n=3–5)$ atomic chains between two infinite gold electrodes. The left (right) panels are for the ground (excited) magnetic states of the structures. The Fermi levels are set to zero.

Figure 13

(Color online) Conductance vs energy for the ${\mathrm{CoC}}_n\mathrm{Co}$ $(n=3–5)$ atomic chains between two infinite gold electrodes. The left (right) panels are for the ground (excited) magnetic states of the structures. The Fermi levels are set to zero.