Magnetization of armchair carbon tori

Abstract

Magnetoelectronic states of armchair carbon tori are studied by the tight-binding model. They strongly depend on the magnitude and the direction of the magnetic field $(\mathbf{B})$. $\mathbf{B}$ induces the destruction of state degeneracy, the change of energy spacing, and the semiconductor-metal transition (SMT). SMT's happen more frequently when $\mathbf{B}$ is relatively close to the toroid axis. Such characteristics are directly reflected in magnetic properties. Magnetization $(\mathbf{M})$ exhibits special jump structures at $T=0$, mainly owing to SMT's. Magnitude of $\mathbf{M}$ and magnetism are mainly determined by the toroid radius $(R)$, the temperature, the angle $(\ensuremath{\alpha})$ between the magnetic field and the symmetry axis, and the chirality. The dependence of $M$ on radius (temperature) is strong at $\ensuremath{\alpha}=0\ifmmode^\circ\else\textdegree\fi{}$, but weak at $\ensuremath{\alpha}=90\ifmmode^\circ\else\textdegree\fi{}$. Most of armchair carbon tori are paramagnetic for $\ensuremath{\alpha}>30\ifmmode^\circ\else\textdegree\fi{}$. The critical angle in determining magnetism is ${\ensuremath{\alpha}}_{c}\ensuremath{\simeq}30\ifmmode^\circ\else\textdegree\fi{}$. Armchair carbon tori quite differ from carbon tori near zigzag configuration (or armchair carbon nanotubes) in magnetoelectronic structures and magnetism.