  The half-Heusler compounds YPdBi and TbPdBi, while having similar band
structure, exhibit different magnetic properties. YPdBi is a diamagnet, while
TbPdBi shows antiferromagnetic order below 5.5 K. Both are superconductors with
T${_c}\approx$1 K for YPdBi and T${_c}\approx$1.75 K for TbPdBi. Such a
contrast in properties between these two compounds opens a question about the
effects of band structure or magnetic correlations on superconductivity. Using
the combination of a tunnel diode oscillator (TDO) and a commercial dilution
refrigerator, we measured temperature dependent magnetic penetration depth
$\Delta\lambda(T)$ in single crystals of YPdBi and TbPdBi, down to temperatures
as low as 0.1K. We found that penetration depths of both compounds do not show
exponential temperature dependence and saturation at low temperatures, as
expected for conventional BCS superconductors. Instead, in both compounds, the
penetration depth can be described by a power law $\Delta\lambda(T) = A\times
T^{n}$. The coefficient A was found to be about 50$\%$ smaller in TbPdBi, but
the exponents are very similar, $n = 2.76\pm 0.04$ in YPdBi and $n = 2.6\pm
0.3$ in TbPdBi, respectively. Our results suggest unconventional
superconductivity in both YPdBi and TbPdBi.
