# Dynamical splitting of cubic crystal field levels in rare-earth cage compounds

## TL;DR

This paper explores how the spatial movement of rare-earth ions in cage compounds affects their crystal field levels, leading to unique thermal and magnetic behaviors, including a Schottky anomaly and phonon softening.

## Contribution

It introduces a position-dependent CEF model for cage compounds, revealing how ion excursions cause level splitting and influence low-temperature properties.

## Key findings

- Identification of a cage-split ground multiplet causing a Schottky anomaly.
- Observation of a centrifugal Jahn-Teller effect expanding ion distribution.
- Altered magnetic and thermal properties in rare-earth cage materials.

## Abstract

The Crystalline Electric Field (CEF) influence is usually described by considering an ideally symmetrical rare-earth site. In the case of cage compounds, ample excursions of the rare-earth inside the cage require an adapted CEF description. A corrective, position dependent, CEF term accounts for the deviation from the perfect symmetry. In the paramagnetic range, a CEF level with orbital degeneracy thus acquires a width reflecting the rare-earth spatial distribution. In the case, frequent in cubic systems, of an orbitally degenerate CEF ground state at the center, this width introduces an additional energy scale, influential at low temperature. A spherical simplification allows to identify the major consequences of a cage-split ground multiplet: a Schottky-like anomaly appears in the specific heat with associated reduction of the magnetic entropy and alteration of the magnetic properties. Concomitantly, a centrifugal Jahn-Teller effect develops that expands the distribution of the magnetic ion and softens the rattling phonons. These effects are confronted with anomalous paramagnetic properties of rare-earth cage compounds, notably rare-earth filled skutterudites and hexaborides.