We have investigated the effects of spatial-inversion and time-reversal symmetry breaking on the acoustic phonon branches in chiral MnSi using high-resolution inelastic x-ray scattering and first-principles calculations. We find a momentum-transfer-dependent ( $q$ -dependent) splitting between transverse phonon bands having angular momentum parallel or antiparallel to $q$ . This is understood by a phenomenological theory using a gyrotropic tensor. We observed no significant impact from the time-reversal symmetry breaking induced by a magnetic field (energy shifts < 0.3 meV). This suggests the effect of time-reversal symmetry breaking is small or is restricted to a very-low-energy regime in this material, possibly due to small spin-orbit interaction.

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• Acoustic phonons
• First-principles calculations
• Lattice dynamics
• Magnetism
• Magnetoacoustic effect
• Magnetoelastic effect
• Spin-orbit coupling
• Chiral magnets
• Transition metal alloys
• X-ray techniques