An inelastic neutron scattering study has been performed in an $S=3/2$ bilayer honeycomb lattice compound ${\mathrm{Bi}}_3{\mathrm{Mn}}_4{O}_{12}\left({\mathrm{NO}}_3\right)$ at ambient and high magnetic fields. Relatively broad and monotonically dispersive magnetic excitations were observed at ambient field, where no long-range magnetic order exists. In the magnetic-field-induced long-range ordered state at 10 T, the magnetic dispersions become slightly more intense, albeit still broad as in the disordered state, and two excitation gaps, probably originating from an easy-plane magnetic anisotropy and intrabilayer interactions, develop. Analyzing the magnetic dispersions using the linear spin-wave theory, we estimated the intraplane and intrabilayer magnetic interactions, which are almost consistent with those determined by ab initio density functional theory calculations [M. Alaei et al., Phys. Rev. B 96, 140404(R) (2017)], except the third and fourth neighbor intrabilayer interactions. Most importantly, as predicted by the theory, there is no significant frustration in the honeycomb plane but frustrating intrabilayer interactions probably give rise to the disordered ground state.

DOI: https://doi.org/10.1103/PhysRevB.100.134430