  Spin is one fundamental property of microscopic particles. A lot of
theoretical work postulated the possible coupling between spin and gravitation,
which could result in the violation of equivalence principle. In a recent joint
mass-and-energy test of weak equivalence principle (WEP) with a 10-meter
$^{85}$Rb-$^{87}$Rb dual-species atom interferometer, the E${\rm
\ddot{o}}$tv${\rm \ddot{o}}$s parameters of four $^{85}$Rb-$^{87}$Rb
combinations with specific atomic spin states were measured to the
$10^{-10}$-level. These experimental results are used to constrain the
postulated spin-gravity coupling effects in a robust way. The bounds on the
spin-independent and spin-dependent anomalous passive gravitational mass
tensors are consistently set to the $10^{-10}$-level, which improve existing
bounds by three orders of magnitude.
