The recent discovery of a charge density wave order at the wave vector $P(\frac{1}{3},\frac{1}{3},\frac{1}{3})$ in the kagome metal ${\mathrm{ScV}}_6{\mathrm{Sn}}_6$ has created a mystery because subsequent theoretical and experimental studies show a dominant phonon instability instead at another wave vector $H(\frac{1}{3},\frac{1}{3},\frac{1}{2})$. In this paper, I use first-principles total energy calculations to map out the landscape of the structural distortions due to the unstable phonon modes at $H$, $L(\frac{1}{2},0,\frac{1}{2})$, and $P$ present in this material. In agreement with previous results, I find that the distortions due to the $H$ instability cause the largest gain in energy relative to the parent structure, followed in order by the $L$ and $P$ instabilities. However, only two distinct structures occur due to this instability, which are separated by 6 meV/f.u. The instability at $L$ results in three distinct structures separated in energy by 5 meV/f.u. In contrast, six different distorted structures are stabilized due to the instability at $P$, and they all lie within 2 meV/f.u. of each other. Hence, despite a lower-energy gain, the condensation at $P$ could be favorable due to a larger entropy gain associated with the fluctuations within a manifold with larger multiplicity via the order-by-disorder mechanism.

• Received 22 August 2023
• Accepted 3 January 2024

DOI:https://doi.org/10.1103/PhysRevMaterials.8.014006