  In Mn$_3$X (X=Sn, Ge) antiferromagnets domain walls are thick and remarkably
complex because of the non-collinear arrangement of spins in each domain. A
planar Hall effect (PHE), an electric field perpendicular to the applied
current but parallel to the applied magnetic field, was recently observed
inside the hysteresis loop of Mn$_3$Sn. The sign of the PHE displayed a memory
tuned by the prior orientation of the magnetic field and its history. We
present a study of PHE in Mn$_3$Ge extended from room temperature down to 2 K
and show that this memory effect can be manipulated by either magnetic field or
thermal cycling. We show that the memory can be wiped out if the prior magnetic
field exceeds 0.8 T or when the temperature exceeds $T_\mathrm{N}$. We also
find a detectable difference between the amplitude of PHE with zero-field and
field thermal cycling. The ratio between the PHE and the anomalous Hall effect
(AHE) decreases slightly as temperature is increased from 2 K to $T_{\rm{N}}$,
tracks the temperature dependence of magnetization. This erasable memory effect
may be used for data storage.
