  We construct a nonrelativistic wave equation for spinning particles in the
noncommutative space (in a sense, a $\theta$-modification of the Pauli
equation). To this end, we consider the nonrelativistic limit of the
$\theta$-modified Dirac equation. To complete the consideration, we present a
pseudoclassical model (\`a la Berezin-Marinov) for the corresponding
nonrelativistic particle in the noncommutative space. To justify the latter
model, we demonstrate that its quantization leads to the $\theta$-modified
Pauli equation. Then, we extract $\theta$-modified interaction between a
nonrelativistic spin and a magnetic field from the $\theta$-modified Pauli
equation and construct a $\theta$-modification of the Heisenberg model for two
coupled spins placed in an external magnetic field. In the framework of such a
model, we calculate the probability transition between two orthogonal EPR
(Einstein-Podolsky-Rosen) states for a pair of spins in an oscillatory magnetic
field and show that some of such transitions, which are forbidden in the
commutative space, are possible due to the space noncommutativity.
