Zero-temperature magnetic response of small fullerene molecules at the classical and full quantum limit

Abstract

The ground-state magnetic response of fullerene molecules with up to 36 vertices is calculated, when spins classical or with magnitude $s=\frac{1}{2}$ are located on their vertices and interact according to the nearest-neighbor antiferromagnetic Heisenberg model. The frustrated topology, which originates in the pentagons of the fullerenes and is enhanced by their close proximity, leads to a significant number of classical magnetization and susceptibility discontinuities, something not expected for a model lacking magnetic anisotropy. This establishes the classical discontinuities as a generic feature of fullerene molecules irrespective of their symmetry. The largest number of discontinuities have the molecule with 26 sites, four of the magnetization and two of the susceptibility, and an isomer with 34 sites, which has three each. In addition, for several of the fullerenes the classical zero-field lowest energy configuration has finite magnetization, which is unexpected for antiferromagnetic interactions between an even number of spins and with each spin having the same number of nearest-neighbors. The molecules come in different symmetries and topologies and there are only a few patterns of magnetic behavior that can be detected from such a small sample of relatively small fullerenes. Contrary to the classical case, in the full quantum limit $s=\frac{1}{2}$ there are no discontinuities for a subset of the molecules that was considered. This leaves the icosahedral symmetry fullerenes as the only ones known supporting ground-state magnetization discontinuities for $s=\frac{1}{2}$. It is also found that a molecule with 34 sites has a doubly-degenerate ground state when $s=\frac{1}{2}$.

12 pages, 5 tables, 5 figures

References in corpus (12)

• Metamagnetic phase transition of the antiferromagnetic Heisenberg icosahedron
• Polyradical character and spin frustration in fullerene molecules: An ab initio non-collinear Hartree--Fock study
• The even-odd effect in short antiferromagnetic Heisenberg chains
• Enhanced magnetocaloric effect in a proximity of magnetization steps and jumps of spin-1/2 XXZ Heisenberg regular polyhedra
• The Schottky-type specific heat as an indicator of relative degeneracy between ground and first-excited states: the case study of regular Ising polyhedra
• Magnetization Process of the S=1/2 Heisenberg Antiferromagnet on the Cairo Pentagon Lattice
• Antiferromagnetic Heisenberg Model on the Icosahedron: Influence of Connectivity and the Transition from the Classical to the Quantum Limit
• Spin-Flop Phenomenon of Two-Dimensional Frustrated Antiferromagnets without Anisotropy in Spin Space
• Thermalization away from Integrability and the Role of Operator Off-Diagonal Elements
• Estimates of Effective Hubbard Model Parameters for C20 isomers
• Magnetic spectra in the tridiminished-icosahedron \{Fe${}_9$\} nano-cluster by inelastic neutron scattering
• Isothermal Entropy Change and Adiabatic Change of Temperature of the Antiferromagnetic Spin-1/2 Ising Octahedron and Dodecahedron

Cited by in corpus (7)

• Discontinuous quantum and classical magnetic response of the pentakis dodecahedron
• Noncoplanar and chiral spin states on the way towards Néel ordering in fullerene Heisenberg models
• $\mathbf{\Delta }$S${}^z$=2 quantum magnetization discontinuities proportional in number to the spin s in C${}_{60}$: Origin and the role of symmetry
• Theory of ground states for classical Heisenberg spin systems II
• Origin of the classical magnetization discontinuities of the dodecahedron
• Entropic selection of magnetization in a frustrated 2D magnetic model
• The magnetization process of classical Heisenberg magnets with non-coplanar cuboc ground states