Magnetic phases at the molecular scale: the case of cylindrical Co nanoparticles

Abstract

The magnetic phases of cobalt nanocylinders at the molecular scale have been studied by means of density functional theory together with micromagnetism. Diameters of the objects are under 1 nm. The magnetic phases resulting from first-principle calculations are far from obvious and quite different from both semiclassical results and extrapolations from what is measured for larger objects. These differences reinforce the importance of the quantum mechanical approach for small nanoscopic particles. One of the main results reported here is precisely the unexpected order in the last filled orbitals, which produce objects with alternating magnetic properties as the length of the cylinder increases. The resulting anisotropy is not obvious. The vortex phase is washed out due to the aspect ratio of the systems and the strength of the exchange constants for Co. Nevertheless, we do a pedagogical experiment by turning gradually down the exchange constants to investigate the kind of vortex states which are hidden underneath the ferromagnetic phases.

Appendix: Nomenclature

Pentagonal tubes

The basic unit is a pentagonal ring of Co atoms. The tube grows by adding these pentagons in an intercalated way thus minimizing energy. A projection of the atoms on any end of the cylinder is presented in Fig. 1b. They are denoted by T₅-N, where N is the total number of atoms in the particle: N = 5 ×R, with R representing the number of rings conforming the tube. We will consider from T₅-10 to T₅-35.

Pentagonal wires

The basic units are a pentagonal ring of Co atoms and a single Co atom over the center of such pentagon. The wires grow intercalating the axial atom in between consecutive rings; a projection of the atoms on any end of the cylinder is presented in Fig. 1c. These wires are denoted by W₅-N, where N is the total number of atoms in the particle: N = 5 ×R + (R −1), with R representing the number of rings conforming the wire. At the ends of the cylinder only pentagons are allowed. We will consider from W₅-11 to W₅-41.

Hexagonal wires

The basic units are hexagonal rings of Co atoms and a single Co atom over the center of such hexagon. The wires grow intercalating the axial atom in between consecutive rings; a projection of the atoms on any end of the cylinder is presented in Fig. 1d. These wires are denoted by W₆-N, where N is the total number of atoms in the particle: N = 6 ×R + (R −1), with R representing the number of rings conforming the wire. At the ends of the cylinders only hexagons are allowed. We will consider from W₆-13 to W₆-48.

Decagonal tubes

The basic units are a pentagonal rings and decagonal rings of Co atoms. These tubes are grown alternating pentagons and decagons along the cylindrical axis; a projection of the atoms on any end of the cylinder is presented in Fig. 1e. These tubes are denoted by T₁₀-N, where N is the total number of atoms in the particle: N = 5 ×R + 10 ×(R −1), with R representing the number of pentagons conforming the tube. We will consider from T₁₀-35 to T₁₀-65. Figure 1a shows a lateral view of T₁₀-50.

Decagonal wires

The basic units are single axial atoms, pentagonal rings and decagonal rings of Co atoms. These tubes are grown similarly to the decagonal tubes but in addition they also have a single atom on the axis at approximately the same height as the external decagon; a projection of the atoms on any end of the cylinder is presented in Fig. 1f. These wires are denoted by W₁₀-N, where N is the total number of atoms in the particle: N = 5 ×R + 10 ×(R −1) + (R −1), with R representing the number of pentagons conforming the tube. We will consider from W₁₀-21 to W₁₀-69.

We should mention that the family of hexagonal tubes (T₆-N) is not included here because we failed to find stable structures for this theoretical conception. When initiations with this symmetry were started from several possible configurations they all collapsed into non cylindrical particles.