  The present work aims to address the electronic and magnetic properties of
the intermetallic compound GdPd$_2$Bi through a comprehensive study of the
structural, magnetic, electrical and thermal transport on a polycrystalline
sample, followed by theoretical calculations. Our findings indicate that the
magnetic ground state is antiferromagnetic in nature. Magnetotransport data
present prominent hysteresis loop hinting a structural transition with further
support from specific heat and thermopower measurements, but no such signature
is observed in the magnetization study. Temperature dependent powder x-ray
diffraction measurements confirm martensitic transition from the
high-temperature (HT) cubic Heusler $L2_1$ structure to the low-temperature
(LT) orthorhombic $Pmma$ structure similar to many previously reported shape
memory alloys. The HT to LT phase transition is characterized by a sharp
increase in resistivity associated with prominent thermal hysteresis. Further,
we observe robust Bain distortion between cubic and orthorhombic lattice
parameters related by $a_{orth} = \sqrt{2}a_{cub}$, $b_{orth} = a_{cub}$ and
$c_{orth} = a_{cub}/\sqrt{2}$, that occurs by contraction along $c$-axis and
elongation along $a$-axis respectively. The sample shows an unusual
`non-saturating' $H^2$-dependent negative magnetoresistance for magnetic field
as high as 150 kOe. In addition, non-linear field dependence of Hall
resistivity is observed below about 30 K, which coincides with the sign change
of the Seebeck coefficient. The electronic structure calculations confirm
robust metallic states both in the LT and HT phases. It indicates complex
nature of the Fermi surface along with the existence of both electron and hole
charge carriers. The anomalous transport behaviors can be related to the
presence of both electron and hole pockets.
