  In this study, we investigate the Pauli oscillator in a noncommutative space.
In other words, we derive wave function and energy spectrum of a spin half
non-relativistic charged particle that is moving under a constant magnetic
field with an oscillator potential in noncommutative space. We obtain critical
values of the deformation parameter and the magnetic field, which counteract
the normal and anomalous Zeeman effects. Moreover, we find that the deformation
parameter has to be smaller than $2.57\times 10^{-26}m^2$. Then, we derive the
Helmholtz free energy, internal energy, specific heat, and entropy functions of
the Pauli oscillator in the noncommutative space. With graphical methods, at
first, we compare these functions with the ordinary ones, and then, we
demonstrate the effects of magnetic field on these thermodynamic functions in
the commutative and noncommutative space, respectively
