  We report the discovery of a novel giant magnetoresistance (GMR) phenomenon
in a family of BaMn$_{2}$Pn$_{2}$ antiferromagnets (Pn stands for P, As, Sb,
and Bi) with a parity-time symmetry. The resistivities of these materials are
reduced by $60$ times in magnetic fields ($\vec{H}$'s), thus yielding the GMR
of about $-98\%$. The GMR changes systematically along with the Pn elements,
hinting that its origin is the spin orbit coupling (SOC) and/or $d$-$p$ orbital
hybridization. A positive MR component emerging on top of the negative GMR at
low temperatures suggests an orbital-sensitive magnetotransport as $\vec{H}$
suppresses the conduction of the electron-like carriers in the $d$-like band
but enhances those of hole-like ones in the $d$-$p$ hybridized band. The
anisotropy of the GMR reveals that the electrical conductivity is extremely
sensitive to the minute changes in the direction of the antiferromagnetic
moments induced by the parity-time breaking $\vec{H}$, which seems to be
associated with a magnetoelectric effect in the dynamic regime of conduction
electrons. We attribute the observed GMR to the non-trivial low energy band of
BMPn's, which is governed by the parity-time symmetry and an magnetic
hexadecapole ordering.
