Ground-state order and spin-lattice coupling in tetrahedral spin systems ${\mathrm{Cu}}_2{\mathrm{Te}}_2{\mathrm{O}}_5{X}_2$ $(X=\mathrm{Br}$ or Cl)

High-resolution ac susceptibility and thermal conductivity measurement on ${\mathrm{Cu}}_2{\mathrm{Te}}_2{\mathrm{O}}_5{X}_2(X=\mathrm{Br},\mathrm{Cl})$ single crystals are reported. For Br-sample, sample dependence prevents one from distinguishing between possibilities of magnetically ordered and spin-singlet ground states. In Cl-sample a three-dimensional transition at 18.5 K is accompanied by almost isotropic behavior of susceptibility and almost switching behavior of thermal conductivity. Thermal conductivity studies suggest the presence of a tremendous spin-lattice coupling characterizing Cl- but not Br-sample. Below the transition Cl-sample is in a complex magnetic state involving AF order but also the elements consistent with the presence of a gap in the excitation spectrum.