  In this paper, we focus on the connection between spin Hall effect and spin
force. Here we investigate that the spin force due to spin-orbit coupling,
which in two-dimensional system is equivalent to forces of Hirsch and
Chudnovsky besides constant factors 3 and 3/2 respectively, is a part of
classic Anandan force, and that the spin Hall effect is an anomalous Hall
effect. Furthermore, we develop the method of AC phase to derive the formula
for the spin force, and find that the most basic spin Hall effect originates
from the AC phase and is therefore an intrinsic quantum mechanical property of
spin. This method differs from approach of Berry phase in the study of
anomalous Hall effect, which is the intrinsic property of the perfect crystal.
On the other hand, we use an elegant skill to show that the Chudnovsky-Drude
model is reasonable, and further have improved the theoretical values of spin
Hall conductivity of Chudnovsky. Compared to the theoretical values of spin
Hall conductivity in the Chudnovsky-Drude model, ours are in better agreement
with experimentation. Finally, we discuss the relation between spin Hall effect
and fractional statistics.
