Quantum mechanical motion of off-center ion in external magnetic field

TL;DR

This paper investigates the quantum mechanical behavior of off-center ions in crystals under external magnetic fields, revealing how their magnetic moments vary with energy states and aligning with classical current-based models.

Contribution

It introduces a quantum mechanical model for off-center ions in magnetic fields, incorporating the nonlinear Mathieu equation to analyze magnetic responses.

Findings

Magnetic moments increase with higher energy states.

Quantum model aligns with classical current-based theories.

Provides insights into magnetostatic responses of off-center ions.

Abstract

We consider the magnetostatic response to an external magnetic field of a crystal containing off-center ions, such as Li^+ in KCl and KBr or the apical oxygens O(A) in the LaSCO family of layered perovskites. Magnetic dipoles are deduced from the matrix elements of the energy operator of a spinning particle in a magnetic field which particle also satisfies the nonlinear Mathieu equation. The magnetic moments are found to increase in magnitude as the system goes from the lowest energy ground state to the higher lying excited states. Our conclusions are in concert with earlier studies of magnetic dipoles from circular currents based on Ampere's theorem.