Antiferromagnetic Heisenberg Model on the Icosahedron: Influence of Connectivity and the Transition from the Classical to the Quantum Limit

Abstract

The antiferromagnetic Heisenberg model on the icosahedron, which consists of 20 edge-sharing triangles and belongs to the icosahedral $I_h$ symmetry group, presents unconventional properties at the classical and quantum level. These originate in the frustrated nature of the interactions between the spins. For classical spins the magnetization is discontinuous in a magnetic field. Here we examine the importance of the connectivity of the icosahedron for the appearance of the magnetization discontinuity, and also investigate the transition from the classical to the quantum limit. The influence of connectivity on the magnetic properties is revealed by considering the cluster as being made up of a closed strip of a triangular lattice with two additional spins attached. The classical magnetization discontinuity is shown to evolve continuously from the discontinuity effected by these two spins when they are uncoupled to the cluster. In the second part the transition from the classical to the quantum limit is examined by focusing on the low energy spectrum taking fully into account the spatial and the spin symmetry of the model in the characterization of the states. A symmetry analysis of the highly degenerate due to the connectivity lowest energy classical manifold identifies as its direct fingerprint the low energy quantum states for spin magnitude as low as $s=1$, with the latter following a tower of states behavior which relates to the icosahedron having a structure reminiscent of a depleted triangular lattice. The classical character of the AHM for small $s$ is also detected on the ground state energy and correlation functions. On the other hand the classical magnetization discontinuity in a field eventually disappears for small $s$, after a weak reentrant behavior.

13 pages, 2 tables, 11 figures

References in corpus (6)

• Highly Frustrated Magnetic Clusters: The kagome on a sphere
• Metamagnetic phase transition of the antiferromagnetic Heisenberg icosahedron
• Calculating the energy spectra of magnetic molecules: application of real- and spin-space symmetries
• The even-odd effect in short antiferromagnetic Heisenberg chains
• Magnetization Process of the S=1/2 Heisenberg Antiferromagnet on the Cairo Pentagon Lattice
• Singular field response and singular screening of vacancies in antiferromagnets

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• Symmetry-Induced Universal Momentum-Transfer Dependencies for Inelastic Neutron Scattering on Anisotropic Spin Clusters
• $\mathbf{\Delta }$S${}^z$=2 quantum magnetization discontinuities proportional in number to the spin s in C${}_{60}$: Origin and the role of symmetry
• Simultaneous Spin and Point-Group Adaptation in Exact Diagonalization of Spin Clusters
• Energy Scale Deformation on Regular Polyhedra
• Ground-state magnetic properties of spin ladder-shaped quantum nanomagnet: Exact diagonalization study
• Origin of the classical magnetization discontinuities of the dodecahedron