Abstract:
Substitutional impurity ions in crystals are known to displace off-center and to perform hindered rotations around the ideal lattice positions. The vibronic theory to describe both the off-center displacements and the hindered rotations by a single angular equation incorporates terms up to 3rd order in the off-center displacement coordinates. When the rotation is confined to a single plane, the corresponding vibronic equation is equivalent to Mathieu's equation. Extending our earlier work, we derive here the dipole-dipole coupling to take into account cooperative phenomena. We also derive the optical absorption band arising from dipolar transitions across “Mexican Hat” surfaces, and we show that hindered rotations gives rise to magnetic moments quantized in rotational bands.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received 18 October 2001 / Received in final form 5 March 2002 Published online 2 October 2002
RID="a"
ID="a"e-mail: allxrose@hotmail.com
Rights and permissions
About this article
Cite this article
Georgiev, M., Mladenova, M., Krastev, V. et al. Off-center Li ions: solid state rotators described by Mathieu's nonlinear-oscillator equation. Eur. Phys. J. B 29, 273–277 (2002). https://doi.org/10.1140/epjb/e2002-00300-1
Issue Date:
DOI: https://doi.org/10.1140/epjb/e2002-00300-1