  We establish a general propagation model to describe the spin Hall effect of
light beam in left-handed materials (LHMs). A spin-dependent shift of the beam
centroid perpendicular to the refractive index gradient for the light beam
through an air-LHM interface is demonstrated. For a certain circularly
polarized component, whether the transverse shift is positive or negative
depends on the magnitude of the refractive index gradient. Very surprisingly,
the spin Hall effect in the LHM is unreversed, although the sign of refractive
index gradient is reversed. The physics underlying this counterintuitive effect
is that the spin angular momentum of photons is unreversed. Further, we reveal
that the angular shift in the LHM is reversed due to the negative diffraction.
These findings provide alternative evidence for that the linear momentum of
photons is reversed, while the spin angular momentum is unreversed in the LHM.
