# Neutron-scattering study of yttrium iron garnet

## TL;DR

This neutron scattering study reveals the detailed nuclear and magnetic structures, magnon dispersions, and exchange interactions in yttrium iron garnet, providing insights into its magnetic excitations and structure distortions.

## Contribution

The paper provides the first comprehensive neutron scattering analysis of yttrium iron garnet, including refined structure, magnon dispersions, and exchange parameters, with a simple model explaining the observed data.

## Key findings

- Nuclear structure is distorted to trigonal space group R-3.
- Magnon dispersions extend up to 86 meV.
- Exchange integrals are estimated as J_aa=0, J_ad≈-2.90, J_dd≈-0.35 meV.

## Abstract

The nuclear and magnetic structure and full magnon dispersions of yttrium iron garnet Y$_3$Fe$_5$O$_{12}$ have been studied by neutron scattering. The refined nuclear structure is distorted to a trigonal space group of $R\bar{3}$. The highest-energy dispersion extends up to 86 meV. The observed dispersions are reproduced by a simple model with three nearest-neighbor-exchange integrals between 16$a$ (octahedral) and 24$d$ (tetrahedral) sites, $J_{aa}$, $J_{ad}$, and $J_{dd}$, which are estimated to be 0.00$\pm$0.05, $-$2.90$\pm$0.07, and $-$0.35$\pm$0.08 meV, respectively. The lowest-energy dispersion below 14 meV exhibits a quadratic dispersion as expected from ferromagnetic magnons. The imaginary part of $q$-integrated dynamical spin susceptibility $\chi$"($E$) exhibits a square-root energy-dependence in the low energies. The magnon density of state is estimated from the $\chi$"($E$) obtained on an absolute scale. The value is consistent with a single polarization mode for the magnon branch expected theoretically.