Origin and dynamics of umbrella states in rare-earth iron garnets

TL;DR

This paper explains the origin of umbrella-shaped magnetic structures in rare-earth iron garnets, showing how crystal-field effects and exchange interactions lead to these non-collinear states, supported by theoretical modeling and experimental comparison.

Contribution

It introduces a general model that accounts for umbrella magnetic states in rare-earth garnets based on crystal-field anisotropies and exchange interactions, advancing understanding of their spin structures.

Findings

Umbrella states naturally emerge from crystal-field anisotropies.

Calculated canting angles match experimental observations.

Provides a basis for future spin wave dynamic studies.

Abstract

Rare-earth iron garnets $R_{3}$Fe$_{5}$O$_{12}$ are fascinating insulators with very diverse magnetic phases. Their strong potential in spintronic devices has encouraged a renewal of interest in the study of their low temperature spin structures and spin wave dynamics. A striking feature of rare-earth garnets with $R$-ions exhibiting strong crystal-field effects like Tb-, Dy-, Ho-, and Er-ions is the observation of low-temperature non-collinear magnetic structures featuring "umbrella-like" arrangements of the rare-earth magnetic moments. In this study, we demonstrate that such umbrella magnetic states are naturally emerging from the crystal-field anisotropies of the rare-earth ions. By means of a general model endowed with only the necessary elements from the crystal structure, we show how umbrella-like spin structures can take place and calculate the canting-angle as a result of the competition between the exchange-interaction of the rare-earth and the iron ions as well as the crystal-field anisotropy. Our results are compared to experimental data, and a study of the polarised spin wave dynamics is presented. Our study improves the understanding of umbrella-like spin structures and paves the way for more complex spin wave calculations in rare-earth iron garnets with non-collinear magnetic phases.