Structures and magnetic properties of iron chains encapsulated in tubal carbon nanocapsules

Abstract

Structures and magnetic properties of ${\mathrm{Fe}}_{n}$ chains encapsulated in tubal carbon nanocages, ${\mathrm{C}}_{10(n+1)}\phantom{\rule{0.3em}{0ex}}(n=1--4)$ and ${\mathrm{C}}_{48}\phantom{\rule{0.3em}{0ex}}(n=1,2)$, are studied by means of the first-principles approach of noncollinear magnetism, in which the atomic and magnetic structures can be optimized simultaneously and self-consistently. The optimizations show that the globular capsule ${\mathrm{FeC}}_{20}$ is energetically unfavorable, while the longer capsule ${\mathrm{Fe}}_{n}{\mathrm{C}}_{10(n+1)}$ for $n=2--4$ becomes favorable and retains the linear structure of the iron chain along the center axis of the cages. The spin magnetic moments of the $\mathrm{Fe}$ atoms align in antiparallel for $n=2$ and 4 in contrast with the parallel magnetic moments in bare ${\mathrm{Fe}}_{n}$ chains. These antiferromagnetic configurations are stabilized by effective antiferromagnetic interactions induced by the carbon cages, where the small magnetic moments appear in the same orientation as those of the adjacent $\mathrm{Fe}$ atoms. For thicker capsules ${\mathrm{Fe}}_{n}{\mathrm{C}}_{48}$, $\mathrm{Fe}$ atoms also settle along the center axis of the cage. Due to the decrease of interaction between $\mathrm{Fe}$ and $\mathrm{C}$ atoms, the parallel alignment of magnetic moments on $\mathrm{Fe}$ atoms is more stabilized than the antiparallel one. For both the cages ${\mathrm{C}}_{10(n+1)}$ and ${\mathrm{C}}_{48}$, terminal effects play a certain role in the settlement of $\mathrm{Fe}$ atoms along the center axis and the antiferromagnetic arrangement.