Specific Heat in Zero and Applied Magnetic Field of Overdoped Ba$_{\mathrm{1-x}}$K$_{\mathrm{x}}$Fe$_{2}$As$_{2}$: Analysis of The Multigap Behavior and Anisotropies*

Specific heat measurements down to 0.4 K and up to H$_{\mathrm{c2}}$ on single crystals of two different compositions of overdoped Ba$_{\mathrm{1-x}}$K$_{\mathrm{x}}$Fe$_{2}$As$_{2}$ with T$_{\mathrm{c}}$ values of 5.9 K (x$\approx $0.93) and 8.9 K (x$\approx $0.85) are reported. The possibility of mixed/crossover behavior in the pairing symmetry in this composition range has been discussed in the literature. The zero field data analysis for both samples results in essentially the same two gap values: 2$\Delta $/kT$_{\mathrm{c}}=$0.9 and 3.5 while the field data indicate pronounced non-linearity in $\gamma $ vs H both as the lower gap is suppressed by about 1 T but also in higher fields up to H$_{\mathrm{c2}}\approx $5.5 T. Analysis of the field data to investigate the gap anisotropies will be presented.