  It is widely believed that the skyrmion Hall effect is absent in
antiferromagnets because of the vanishing topological charge. However, the
Aharonov-Casher theory indicates the possibility of topological effects for
neutral particles. In this work, we predict the skyrmion Hall effect in
emerging altermagnets with zero net magnetization and zero skyrmion charge. We
first show that the neutral skyrmion manifests as a magnetic quadrupole in
altermagnets. We reveal a hidden gauge field from the magnetic quadrupole,
which induces the skyrmion Hall effect when driven by spin transfer torque.
Interestingly, we identify a sign change of the Hall angle when one swaps the
anisotropic exchange couplings in altermagnets. Furthermore, we demonstrate
that both the velocity and Hall angle of altermagnetic skyrmions sensitively
depend on the current direction. Our findings real the critical role of
magnetic quadrupole in driving the skyrmion Hall effect with vanishing charge,
and pave the way to discovering new Hall effect of neutral quasiparticles
beyond magnetic skyrmions.
