Magnetic excitation in the hyperkagome antiferromagnet Mn3RhSi

In a paramagnetic state of a hyperkagome lattice antiferromagnet ${\mathrm{Mn}}_3\mathrm{RhSi}$, magnetic diffuse scattering by magnetic short-range order is observed over a wide temperature range of approximately 500 K above the Néel temperature of 190 K. We have studied the magnetic excitation with a single crystal in a wide energy range from 0.3 to 140 meV by inelastic neutron scattering, where the prominent inelastic neutron-scattering signal is observed at $\mathbf{Q}=(2,0,0)$. The inelastic scattering intensity integrated for two of twelve magnon modes leads to a localized magnetic moment of about 5 ${\mu }_{\mathrm{B}}$ per Mn site, although the long-range ordered magnetic moment is only 2.61 ${\mu }_{\mathrm{B}}$ at 4 K. The result suggests that a large part of the magnetic moment does not order in ${\mathrm{Mn}}_3\mathrm{RhSi}$, possibly due to the geometrical spin frustration of the hyperkagome lattice.