Cascade of pressure-induced competing charge density waves in the kagome metal FeGe

Electronic ordering is prevalent in correlated systems, which commonly exhibit competing interactions. Here, we use x-ray diffraction to demonstrate a cascade of pressure-induced order-disorder transformations, with propagation vectors ${\mathbf{q}}_{\mathrm{CDW}}=(\frac{1}{2}0\frac{1}{2}), {\mathbf{q}}^{*}=(\frac{1}{3}\frac{1}{3}\frac{1}{2})$, and ${\mathbf{q}}^{\ifmmode\dagger\else\textdagger\fi{}}=(\frac{1}{3}\frac{1}{3}\frac{1}{3})$, in the kagome metal FeGe. In the pressure interval between $4<p<10$ GPa, ${\mathbf{q}}_{\mathrm{CDW}}$ and ${\mathbf{q}}^{*}$ coexist and the spatial extent of the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ order is nearly long range at $\ensuremath{\sim}15$ GPa, $\ensuremath{\sim}30$ unit cells. Above $\ensuremath{\sim}25$ GPa, the periodic lattice distortion has a propagation wave vector of ${\mathbf{q}}^{\ifmmode\dagger\else\textdagger\fi{}}=(\frac{1}{3}\frac{1}{3}\frac{1}{3})$ at room temperature. The cascade of phase transitions is captured by the Ising model of frustrated triangular lattices and modeled by Monte Carlo simulations based on the dimerization of trigonal ${\mathrm{Ge}}_{1}$. The pressure dependence of the integrated intensities and correlation lengths of ${\mathbf{q}}_{\mathrm{CDW}}, {\mathbf{q}}^{*}$, and ${\mathbf{q}}^{\ifmmode\dagger\else\textdagger\fi{}}$ demonstrating a competition between the $2\ifmmode\times\else\texttimes\fi{}2$ and $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ phases prove the tunability of order-disorder phase transitions under pressure and the rich landscape of metastable/fragile phases of FeGe.