A model for coupled $4f-3d$ magnetic spectra: a neutron scattering study of the Yb$-$Fe hybridisation in Yb$_3$Fe$_5$O$_{12}$

TL;DR

This study combines experimental and theoretical approaches to analyze the magnetic excitation spectra in Yb$_3$Fe$_5$O$_{12}$, revealing hybridized Yb and Fe excitations influenced by exchange interactions.

Contribution

It provides a comprehensive model for coupled $4f-3d$ magnetic spectra, including crystal-field effects and hybridization mechanisms in Yb$_3$Fe$_5$O$_{12}$.

Findings

Identification of hybridized Yb and Fe magnetic excitations.

Quantitative analysis framework for coupled spectra.

Detailed characterization of crystal-field splitting and exchange effects.

Abstract

In this work, we explore experimentally and theoretically the spectrum of magnetic excitations of the Fe$^{3+}$ and Yb$^{3+}$ ions in ytterbium iron garnet (Yb$_3$Fe$_5$O$_{12}$). We present a complete description of the crystal-field splitting of the $4f$ states of Yb$^{3+}$, including the effect of the exchange field generated by the magnetically ordered Fe subsystem. We also consider a further effect of the Fe-Yb exchange interaction, which is to hybridise the Yb crystal field excitations with the Fe spin-wave modes at positions in the Brillouin zone where the two types of excitations cross. We present detailed measurements of these hybridised excitations, and propose a framework which can be used in the quantitative analysis of the coupled spectra in terms of the anisotropic $4f-3d$ exchange interaction.