Spin Waves in Ferromagnetic CrBr3Studied by Inelastic Neutron Scattering

Abstract

Neutron scattering measurements of spin waves in a nonmetallic ferromagnetic material are reported here for the first time. Cr${\mathrm{Br}}_3$ is a rhombohedral two-sublattice ferromagnet below $T_C=32.5\mathrm{}$° K, and we have observed acoustical and optical spin waves at 6° K as well as investigated their temperature behavior. The dispersion relation is found to be highly directionally dependent, being very flat along the hexagonal $c$ direction, thus verifying directly previous conclusions obtained from magnetization data. The intralayer ferromagnetic coupling is dominated by the nearest-neighbor interaction, and the much weaker interlayer coupling results from competing ferromagnetic and antiferromagnetic interactions. The use of a two-parameter model is only qualitatively correct, except for the low-energy part, where quantitative description to within 5% accuracy is possible by two parameters only. In the study of the temperature effects, the particularly interesting observation was made that the spin-wave energy renormalization is also directionally dependent. Such an effect has not been observed previously since it is negligibly small for cubic or nearly cubic systems. The effect represents the first direct evidence in favor of Dyson's dynamical spin-wave theory. In fact, energy shifts calculated using this theory were found to be in quantitative agreement with observations up to a temperature of about 0.8 $T_C$. As $T_C$ is approached, the widths of the spin-wave peaks increase, and the peaks disappear at $T_C$ by broadening out at finite energies. Well-defined spin waves were not seen above $T_C$.