Physical properties and \textbf{spin excitations in the lacunar spinels AV}$_{\mathrm{\mathbf{4}}}$\textbf{S}$_{\mathrm{\mathbf{8}}}$\textbf{ (A }$=$\textbf{ Ga, Ge)}

In the lacunar spinels AV$_{\mathrm{4}}$S$_{\mathrm{8}}$ (A $=$ Ga, Ge), the interplay of spin, charge, and orbital degrees of freedom results in a complex phase diagram which includes: ferroelectric, orbitally ordered, and N\'{e}el type skyrmion phases. Below 12.7 K GaV$_{\mathrm{4}}$S$_{\mathrm{8}}$ exhibits cycloidal and ferromagnetic order and the application of a magnetic field results in a N\'{e}el type skyrmion spin structure. On the other hand, GeV$_{\mathrm{4}}$S$_{\mathrm{8}}$ orders antiferromagentically below 18 K. To illuminate the underlying physics driving the formation of these novel phases, we have measured the magnetization, resistivity, thermal conductivity, and inelastic neutron scattering spectrum of these spinels. The inelastic neutron scattering data shows broadened spin excitations which extend to 6 meV within the magnetically order phases for both GaV$_{\mathrm{4}}$S$_{\mathrm{8}}$ and GeV$_{\mathrm{4}}$S$_{\mathrm{8}}$. The similarity of the spectra for ferromagnetic GaV$_{\mathrm{4}}$S$_{\mathrm{8}}$ and antiferromagnetic GeV$_{\mathrm{4}}$S$_{\mathrm{8}}$ reflects the close balance of ferromagnetic and antiferromagnetic interactions in these materials.