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Low Temperature Specific Heat of Optimally Doped BaFe$_{2-x}$$TM_x$As$_{2}$ ($TM$ = Co and Ni) Single Crystals: Constraint on the Pairing Gap

Low temperature specific heat has been measured in optimally doped and highly overdoped non-superconducting BaFe$_{2-x}$TM$_x$As$_{2}$ ($TM$ = Co and Ni) single crystals. By using the data of the overdoped samples, we successfully removed the phonon contribution of the optimally doped ones, and derived the electronic specific heat coefficient $γ_e$. Remarkably, we found a continuing temperature dependent $γ_e(T)$ which follows the quadratic relation $γ_e=γ_0+αT^2$ in the low temperature limit. Together with the very small residual term $γ_0$, linear magnetic field dependence of $γ_e$, it is concluded that there are either small segments of nodal lines, or point-like nodes in these samples.