Spin-Orbit Locking and Scissors Modes in rare earth crystals with uniaxial symmetry

TL;DR

This paper investigates the possibility of spin-orbit locking in rare-earth crystals with uniaxial symmetry, proposing experiments to test the standard assumptions about spin-orbit and crystal-field strength ratios through Scissors Modes.

Contribution

It introduces the concept of spin-orbit locking in rare-earth systems and suggests experimental methods to verify this phenomenon via Scissors Modes.

Findings

Standard values of crystal field strength are inconsistent with the Single Ion Model.

Spin-orbit force may be much larger than the crystal field in some systems.

Proposed experiments could confirm spin-orbit locking in rare-earth crystals.

Abstract

A recent experiment has questioned the standard relative value of spin-orbit and crystal-field strengths in rare-earth $4f$ electron systems, according to which the first should be one order of magnitude larger that the second. We find it difficult to reconcile the standard values of crystal field strength with the Single Ion Model of magnetic anisotropy. If in rare-earth systems the spin-orbit force is much larger than the crystal field, however, spin and orbit of $4f$ electrons should be locked to each other. For rare earths with non-vanishing spin, an applied magnetic field should rotate both spin and charge density profile. We suggest experiments to investigate the possible occurrence of such Spin-Orbit Locking, thus making a test of the standard picture, by studying the Scissors Modes in such systems.