Magnetoelastic coupling and effects of uniaxial strain in $\alpha$-RuCl$_3$ from first principles.

We present first-principles results on the magnetoelastic coupling in $\alpha$-RuCl$_3$ and uncover a striking dependence of the magnetic coupling constants on strain effects. Different magnetic interactions are found to respond very unequally to variations in the lattice, with the Kitaev interaction being the most sensitive. Exact diagonalization results on our magnetoelastic model reproduce recent measurements of the structural Gr\"uneisen parameter and explain the origin of the negative magnetostriction of $\alpha$-RuCl$_3$, disentangling contributions related to different anisotropic interactions and g factors. Uniaxial strain perpendicular to the honeycomb planes is predicted to reorganize the relative coupling strengths, strongly enhancing the Kitaev interaction while simultaneously weakening the other anisotropic exchanges under compression. Uniaxial strain may therefore pose a fruitful route to experimentally tune $\alpha$-RuCl$_3$ nearer to the Kitaev limit.