Unconventional magnetic properties of the icosahedral symmetry antiferromagnetic Heisenberg model

The antiferromagnetic Heisenberg model on icosahedral symmetry $I_h$ fullerene clusters exhibits unconventional magnetic properties despite the lack of anisotropic interactions. At the classical level, and for number of sites $n⩽720$, the magnetization has two discontinuities in an external magnetic field, except from the dodecahedron where it has three, emphasizing the role of frustration introduced by the pentagons in the unusual magnetic properties. For spin magnitude $s_i=\frac{1}{2}$, there is a discontinuity of quantum character close to saturation for $n⩽80$. This common magnetic behavior indicates that it is a generic feature of $I_h$ fullerene clusters, irrespective of $n$.

Figure 1

Classical energy per site $\frac{E}{n}$ as a function of the number of sites $n$. The unfrustrated hexagon-only value is $-\frac{3}{2}$.

Figure 2

Reduced magnetization $\frac{M}{n}$ for a number of sites $n=540$, as a function of the magnetic field $h$ over its saturation value $h_{\mathit{sat}}$. The insets show the details of the low- and high-field magnetization discontinuities, which occur at magnetic fields $h_c$ such that $\frac{h_c}{h_{\mathit{sat}}}=0.04722$ and $0.99355$ respectively.

Figure 3

Reduced magnetization $\frac{M}{n}$ for a number of sites $n=720$, as a function of the magnetic field $h$ over its saturation value $h_{\mathit{sat}}$. The insets show the details of the low- and high-field magnetization discontinuities, which occur at magnetic fields $h_c$ such that $\frac{h_c}{h_{\mathit{sat}}}=0.04082$ and $0.99516$ respectively.

Figure 4

Difference $\Delta S$ between the total spin in the ground state for $s_i=\frac{1}{2}$, $S$, and its saturated value $S_{\mathit{sat}}=\frac{n}{2}$, with $n$ the number of sites, as a function of the magnetic field $h$ over its saturation value $h_{\mathit{sat}}$. Solid line, $n=20$; dotted line, $n=60$; and dashed line, $n=80$. The discontinuities occur at magnetic fields $h_c$ such that $\frac{h_c}{h_{\mathit{sat}}}=0.75177$, 0.941 79, and 0.961 42, respectively.

Figure 5

Correlation functions $⟨\vec{s}\bullet {\vec{s}}_i⟩$ between a spin $\vec{s}$ and the rest of the spins ${\vec{s}}_i$ for $s_i=\frac{1}{2}$ as a function of distance $r_i$ (the unit of distance is the distance between nearest neighbors, taken equal for all their pairs). $엯$, $S=\frac{n}{2}-6$ and $\times$, $S=\frac{n}{2}-4$ ($S$ is the total spin, $n$ the number of sites). Upper left, $n=20$; upper right, $n=60$; lower left, $n=80$, site belonging only to hexagons; and lower right, $n=80$, site belonging to a pentagon.