Intertwined Charge and Spin Density Waves in a Topological Kagome Material

Using neutrons and x-rays we show the topological kagome antiferromagnet Mn$_3$Sn for $T<285$~K forms a homogeneous spin and charge ordered state comprising a longitudinally polarized spin density wave (SDW) with wavevector $\textbf{k}_{\beta}=k_\beta {\bf \hat{c}}$, a helical modulated version of the room temperature anti-chiral magnetic order with $\textbf{k}_{\chi}=k_\chi{\bf \hat{c}}$, and charge density waves with wave vectors $2\textbf{k}_\beta, 2\textbf{k}_\chi$, and $\textbf{k}_\beta+\textbf{k}_\chi$. Though $\textbf{k}_{\chi}$ and $\textbf{k}_\beta$ coincide for $200~{\rm K}<T<230$~K, they exhibit distinct continuous $T-$dependencies before locking to commensurate values of $\textbf{k}_{\beta} = \frac{1}{12}\textbf{c}^{*}$ and $\textbf{k}_{\chi} = \frac{5}{48}\textbf{c}^{*}$ at low$-T$. Density functional theory indicates this complex modulated state may be associated with the nesting of Fermi surfaces from correlated flat kagome bands, which host Weyl nodes that are annihilated as it forms.