Off-center impurity in alkali halides: reorientation, electric polarization and pairing to F center. II. In-plane rotation and polarizability

TL;DR

This paper investigates the reorientation and polarizability of off-center impurities in alkali halides, using Mathieu equations for in-plane rotation and analyzing electric dipole interactions with F centers.

Contribution

It provides an exact solution overview for impurity reorientation using Mathieu functions and compares them with harmonic approximations, enhancing understanding of impurity behavior.

Findings

Mathieu functions accurately describe impurity reorientation.

Harmonic approximation with renormalized frequency offers a practical alternative.

In-plane polarizability is influenced by dipole-dipole coupling with F centers.

Abstract

Because of its inherent 2-D character, the eigenvalue equation for the hindered rotation around a normal cation site of an off-center impurity nearest-neighboring an F center is the well-known Mathieu equation. We present an overview of literature data on Mathieu's periodic functions providing exact solutions to the Li+ reorientational problem. We compare them with bottom-well approximating solutions by harmonic-oscillator functions at an effective vibrational frequency renormalized by both first- and third- order electron-mode coupling. We finally discuss the in-plane inversion polarizability of an off-center impurity assumed to form a dipole-dipole coupling with a nearby F center.