Magnetic Nanowires
Nanotechnology allows structures of a limited number of atoms that may play an important role in future applications, such as spintronics, magneto-optical devices, and quantum computers. The experimental efforts require extensive theoretical support because the results of recent measurements open many questions that remain to be answered. Magnetism in low-dimensional systems such as monatomic nanowires, namely linear chains of magnetic atoms, grown on non-magnetic substrates is particularly interesting. Cobalt chains adsorbed on platinum surfaces display magnetic order which has been studied by ab-initio calculations and experimentally by x-ray magnetic circular dichroism (XMCD) using synchrotron radiation. These systems display the largest orbital magnetic moment ever found in a 3d transition element.
A numerical simulation within the framework of the density functional theory is of great importance in order to interpret these experiments correctly. We apply the super-cell technique, where the nanowires are modeled as a repeat structure, shown in Figure 13. Such a structure with a stepped-substrate surface mimics the real material fairly well. The chosen inter-chain distance is large enough to avoid interactions between different wires. The calculations are performed using the full-potential linearized-augmented-plane-wave (FLAPW) method [2]. The wave functions are calculated in the scalar-relativistic approximation, while the spin-orbit coupling, essential for the XMCD effects, is included as a perturbation with the second-variational method. In the same manner, we optionally include an orbital-polarization (OP) term [3, 4], which takes partial account of the correlation effects associated with Hund’s rule. The local-spin-density approximation (LSDA) is used for the exchange-correlation potential. Figure 14 shows the spin density, calculated as the difference in the charge density for the electrons with up and down spins. Besides the large peaks at the sites of the Co atoms, there are also lower peaks in the spin density at the sites of the Pt atoms. The magnetization is obviously induced in the substrate, which partly explains the existence of ferromagnetism in the quasi one-dimensional wires.
Figure 13. Periodic structure of the cobalt chains (red spheres) on the platinum surface.
Figure 14. Calculated spin density of the cobalt nanowires on platinum.
References
1. Gambardella, P., Dallmeyer, A., Maiti, K, Malagoli, M. C., Eberhardt, W., Kern, K., and Carbone, C. Ferromagnetism in one-dimensional monoatomic metal chains. Nature 416, 301 (2002).
2. Blaha, P., Schwarz, K., Madsen, G., Kvasnicka, D., and Luitz, J. WIEN2k, an augmented plane wave + local orbitals program for calculating crystal properties (Karlheinz Schwarz, Techn. Universitat Wien, Austria), 2001. ISBN 3-9501031-1-2.
3. Komelj, M., Ederer, C., Davenport, J. W., and Fahnle, M. From the bulk to monatomic wires: An ab initio study of magnetism in Co systems with various dimensionality. Phys Rev B 66, 140407 (2002).
4. Ederer, C., Komelj, M., Davenport, J.W., and Fahnle, M. Comment on the analysis of angular-dependent x-ray magnetic circular dichroism in systems with reduced dimensionality. J. Electron Spectroscopy and Related Phenomena 130, 97-100 (2003).