  Anomalous spin-Hall effects (SHE) and anomalous inverse spin-Hall effects
(ISHE) are predicted when the order parameters are involved in the charge-spin
interconversion. A spin current whose propagation and polarization are
collinear and transverse to an applied charge current can be generated when the
charge current is parallel to the magnetization $\vec M$ in a ferromagnet or to
the Neel order $\vec n$ in an anti-ferromagnet. When the applied charge current
is perpendicular to the order parameter, two spin currents can be generated.
One is the spin current polarized along the order parameter and propagating
along the charge current direction. The other is the one polarized in the
charge current direction and propagating along the order parameter direction.
Charge currents proportional to the order parameter are generated by applied
spin currents in the anomalous ISHE. When a spin current whose propagation and
polarization are collinear is applied, the charge current is along the
perpendicular (to the spin current) component of order parameter, and no
current for order parameter along the spin current. For applied spin current
with propagation and polarization mutually orthogonal to each other, a charge
current along the spin current propagation direction is generated if the order
parameter is collinear with the polarization of the spin current. A charge
current along the polarization of spin current is generated if the order
parameter is collinear with the propagation direction of the spin current.
Experimental verifications are also proposed. In terms of applications, one of
the great advantages of anomalous SHE is that one can control the generated
spin or charge current by controlling the magnetization or the Neel order in
the magnetic materials.
