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TmGa$_{3}$ (AuCu$_3$ structure) undergoes two phase transitions, anantiferroquadrupolar transition at $\sim$ 4.29 K and long-rangeantiferromagnetic ordering at $\sim$ 4.26 K. Due to the close vicinity of thetwo phase transitions, TmGa$_3$ offers an interesting system to study theinterplay of charge and magnetic degrees of freedom. In order to understandthis interplay we have performed inelastic neutron scattering experiments onTmGa$_{3}$ in the paramagnetic regime ($T >$ 5 K) to redetermine the crystalelectric field level scheme. By fitting our spectra at various temperatures weobtain a new crystal field level scheme with Lea, Leask and Wolf parameters of$x_{\rm LLW}$ = -0.44(2) and $W$ = -0.222(2) K. The total crystal fieldsplitting at 5K amounts to $\sim$ 2.3 meV, about an order of magnitude lessthan found previously, but in good agreement with the splitting extrapolatedfrom the related ErGa$_3$ system.  Our analysis yields a $\Gamma_{2}$ singlet as the crystal field ground statefollowed closely by a (nonmagnetic) $\Gamma_{1}$ singlet at 0.009 meV. The nextexcited states are a $\Gamma_{5}^{(2)}$ triplet at $\sim$0.5 meV, which isalmost degenerate to a $\Gamma_{4}$ doublet. This level scheme is adverse toprevious findings. Subsequent analysis of the magnetisation along severalcrystallographic directions and the temperature dependant susceptibility aswell as of the magnetic contribution to the specific heat are consistent withour new crystal field parameters. Implications for the antiferroquadrupolar andthe antiferromagnetic transition are discussed.

Singlet ground state probed by crystal field inelastic neutron spectroscopy on the antiferroquadrupolar system TmGa_{3}