The nuclear and magnetic structure and full magnon dispersions of yttrium iron garnet ${\mathrm{Y}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}$ have been studied using neutron scattering. The refined nuclear structure is distorted to a trigonal space group of $R\overline{3}$. 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 $16a$ (octahedral) and $24d$ (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 at low energies. The magnon density of state is estimated from ${\chi }^{″}(E$) obtained on an absolute scale. The value is consistent with the single chirality mode for the magnon branch expected theoretically.

• Received 8 May 2017
• Revised 11 December 2017

DOI:https://doi.org/10.1103/PhysRevB.97.054429