LETTER TO THE EDITOR: Frustrated quantum-spin system on a triangle coupled with eg lattice vibrations: correspondence to Longuet-Higgins et al' s Jahn Teller model
Abstract
We investigate the frustrated quantum three-spin model (S1,S2,S3) of spin = 1/2 on a triangle, in which spins are coupled with lattice-vibrational modes through the antiferromagnetic exchange interaction depending on distances between spin sites. The present model corresponds to the dynamic Jahn-Teller system {\mathrm {E_g\otimes
e_g}} proposed by Longuet-Higgins et al (1958 Proc. R. Soc. A 244 1). This correspondence is revealed by using the transformation to Nakamura-Bishop's bases used in Phys. Rev. Lett. 54 861 (1985). Furthermore, we elucidate the relationship between a chiral order parameter \hat {\chi }={\mathbf {S}}_{\mathbf {1}}\bdot ({\mathbf {S}}_{\mathbf {2}}\times {\mathbf {S}}_{\mathbf {3}}) in the spin system and the electronic orbital angular momentum \hat {\ell }_z in {\mathrm {E_g\otimes e_g}} vibronic model: the regular oscillatory behaviour of the expectation value \langle \hat {\chi }\rangle with increasing energy can be found as in the case of \langle \hat {\ell }_z\rangle for vibronic structures. The increase of the additional anharmonicity(chaoticity) is found to yield a rapidly decaying irregular oscillation of \langle \hat {\chi }\rangle .- Publication:
-
Journal of Physics Condensed Matter
- Pub Date:
- September 2004
- DOI:
- 10.1088/0953-8984/16/34/L01
- arXiv:
- arXiv:nlin/0312039
- Bibcode:
- 2004JPCM...16L.395Y
- Keywords:
-
- Nonlinear Sciences - Chaotic Dynamics;
- Condensed Matter - Materials Science
- E-Print:
- doi:10.1088/0953-8984/16/34/L01