These are the supplementary data to the linked publication. Experimental data are included as .txt files containing the raw data corresponding to the figures in the publication. The DFT calculation of the phonon energies of CsCuCl3 at Gamma can be replicated using the .in file and the Abinit software package (v. 10, www.abinit.org). The _DDB file contains the derivative database which is output by this calculation. All files can be viewed in a standard text editor.