Eur. Phys. J. B 29, 273-277 (2002)
https://doi.org/10.1140/epjb/e2002-00300-1

Off-center Li⁺ ions: solid state rotators described by Mathieu's nonlinear-oscillator equation

¹ Institute of Solid State Physics, Bulgarian Academy of Sciences, 72 Tsarigradsko Chaussee, 1784 Sofia, Bulgaria
² Department of Condensed Matter Physics, Physics Faculty, Sofia University, 5 James Bourchier Blvd., 1126 Sofia, Bulgaria
³ Institute of General and Inorganic Chemistry, Bulgarian Academy of Sciences, Block 11, Acad. G. Bonchev Street, 1113 Sofia, Bulgaria
⁴ Central Laboratory of Photoprocesses, Bulgarian Academy of Sciences, Block 109, Acad. G. Bonchev Street, 1113 Sofia, Bulgaria

Corresponding author: ^a allxrose@hotmail.com

Received: 18 October 2001
Revised: 5 March 2002
Published online: 2 October 2002

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.