Antichiral spin order, its soft modes, and their hybridization with phonons in the topological semimetal Mn 3 Ge

We report the magnetic structure and spin excitations of ${\text{Mn}}_3\text{Ge}$ , a breathing kagome antiferromagnet with transport anomalies attributed to Weyl nodes. Using polarized neutron diffraction, we show the magnetic order is a $\text{k}=0$ coplanar state belonging to a ${\text{Γ}}_9$ irreducible representation, which can be described as a perfect 120° antichiral structure with a moment of $2.2\left(1\right){\mathrm{micro}}_B/\text{Mn}$ , superimposed with weak collinear ferromagnetism. Inelastic neutron scattering shows three collective $\text{Q}=0$ excitations at ${\text{Δ}}_1=2.9\left(6\right)\text{meV}$ , ${\text{Δ}}_2=14.6\left(3\right)\text{meV}$ , and ${\text{Δ}}_3=17.5\left(3\right)\text{meV}$ . A field theory of $Q\approx 0$ spin waves in triangular antiferromagnets with a 120° spin structure was used to classify these modes. The in-plane mode $\left(\alpha \right)$ is gapless, ${\text{Δ}}_1$ is the gap to a doublet of out-of-plane spin excitations ( ${\beta }_x$ , ${\beta }_y$ ), and ${\text{Δ}}_2$ , ${\text{Δ}}_3$ result from hybridization of optical phonons with magnetic excitations. While a phenomenological spin Hamiltonian including exchange interactions, Dzyaloshinskii-Moriya interactions, and single-ion crystal field terms can describe aspects of the Mn-based magnetism, spin-wave damping [ $\text{Γ}=25\left(8\right)\text{meV}$ ] and the extended range of magnetic interactions indicate itinerant magnetism consistent with the transport anomalies.