Antiferromagnetic Heisenberg model on clusters with icosahedral symmetry
Abstract
The nearest-neighbor antiferromagnetic Heisenberg model is considered for spins si=(1)/(2) and 1 located on the vertices of the dodecahedron and the icosahedron, which belong to the point symmetry group Ih . Taking into account the permutational and spin-inversion symmetries of the Hamiltonian results in a drastic reduction of the dimensionality of the problem, leading to full diagonalization for both clusters. There is a strong signature of the frustration present in the systems in the low-energy spectrum for si=(1)/(2) , where the first excited states are singlets. Frustration also results in a doubly peaked specific heat as a function of temperature for the dodecahedron. Furthermore, there is a discontinuity in the magnetization as a function of magnetic field for the dodecahedron, where a specific total spin sector never becomes the ground state in a field. This discontinuity is accompanied by a magnetization plateau. For si=1 both systems again have singlet excitations. The magnetization of the dodecahedron has now two discontinuities in an external field and also magnetization plateaux, and the specific heat of the icosahedron, a two-peak structure as a function of temperature. The similarities between the two systems suggest that the antiferromagnetic Heisenberg model on a larger cluster with the same symmetry, the 60-site cluster, will have similar properties.
- Publication:
-
Physical Review B
- Pub Date:
- August 2005
- DOI:
- 10.1103/PhysRevB.72.064453
- arXiv:
- arXiv:cond-mat/0503658
- Bibcode:
- 2005PhRvB..72f4453K
- Keywords:
-
- 75.10.Jm;
- 75.50.Xx;
- 75.50.Ee;
- Quantized spin models;
- Molecular magnets;
- Antiferromagnetics;
- Condensed Matter - Strongly Correlated Electrons
- E-Print:
- doi:10.1103/PhysRevB.72.064453