Ground-state spin dynamics of ErCo2

Abstract

We have studied the ground-state magnetic excitation spectrum of Er${\mathrm{Co}}_{2}$ at 4.2 K using neutron inelastic scattering. Four modes were observed, two which are nondispersive and two which are weakly dispersive. Each of the weakly dispersive modes is degenerate with one of the nondispersive modes at the zone boundary, but falls lower in energy at the zone center. From the dynamic structure factor of the excitations we conclude that the nondispersive modes correspond to out-of-phase precession of the two rare-earth spins in the primitive cell, while the weakly dispersive modes correspond to in-phase precession. The results are described very well by a Green's-function random-phase-approximation theory using standard basis operators to account for the crystalline electric fields, which we find to be comparable in strength to the exchange interactions. The observed excitation modes are associated with transitions from the ${\mathrm{Er}}^{3+}$ ground state to the second and fourth excited states. By fitting the energies and intensities of the modes we determine ${J}_{\mathrm{E}\mathrm{r}\ensuremath{-}\mathrm{E}\mathrm{r}}=0\ifmmode\pm\else\textpm\fi{}0.01$ meV, ${J}_{\mathrm{E}\mathrm{r}\ensuremath{-}\mathrm{C}\mathrm{o}}=\ensuremath{-}0.153$ meV, ${A}_{4}^{0}=4.3$ meV/${\mathit{a}}_{0}^{4}$, and ${A}_{6}^{0}=\ensuremath{-}0.142$ meV/${\mathit{a}}_{0}^{6}$. We did not observe a predominantly Co spin-wave mode predicted by the theory, which may indicate a breakdown of the Heisenberg model when applied to the Co spins. Calculations for the observed modes, however, are nearly independent of the dynamics assumed for the Co sublattice.