Origin of Orbital Ferromagnetism and Giant Magnetic Anisotropy at the Nanoscale

The origin of orbital magnetism recently observed in different nanostructured films and particles is discussed as a consequence of spin-orbit coupling. It is shown that contact potentials induced at the thin film surface by broken symmetries, as domain boundaries in self-assembled monolayers, lead to orbital states that in some cases are of large radius. The component of the angular momentum normal to the surface can reach very high values that decrease the total energy by decreasing spin-orbit interaction energy. Intraorbital ferromagnetic spin correlations induce orbital momenta alignment. The estimated values of the magnetic moments per atom are in good agreement with the experimental observations in thiol capped gold films and nanoparticles.

Figure 1

(a)–(c) Orbital energy $\epsilon$ of the electron in the localized orbit as a function of $L_z$ for different radius.

Figure 2

Magnetic moment, in number of Bohr magnetons, per surface atom [Au (111)] as a function of the orbit radius for different values of ${\alpha }_r$. Experimental results reported and measured [9] are also plotted as horizontal lines: (dashed line) fresh samples; (dashed-dotted line) aged 5 days; (dotted line) aged 10 days. The effect of aging is a decrease of the domain size as observed in Ref. 12. If we consider ${\alpha }_r$ ${\hslash }^2=0.4\mathrm{eV}$, the average domain radius decreases from 70 nm in fresh samples to 45 and 30 nm after for samples aged for 5 and 10 days, respectively.