  Magnetic fields are ubiquitous in the interstellar medium, including extended
objects such as supernova remnants and diffuse halos around Pulsars. Its
turbulent characteristics govern the diffusion of cosmic rays and the
multi-wavelength emission from PWNe. However, the geometry and turbulence
nature of the magnetic fields in the ambient region of PWN is still unknown.
Recent gamma-ray observations from HAWC and synchrotron observations suggest a
highly suppressed diffusion coefficient compared to the mean interstellar
value. In this study, we present the first direct observational evidence of the
orientation of the mean magnetic field and turbulent characteristics by
employing a recently developed statistical parameter `Y$_{turb}$' in the
extended halo around the Monogem pulsar. Our study points two possible
scenarios: nearly aligned toward the line of sight (LoS) with compressible
modes dominance or high inclination angle toward LoS and characterized by
Alfv\'enic turbulence. The first scenario appears consistent with other
observational signatures. Furthermore, we report that the magnetic field has an
observed correlation length of approximately $3 \pm 0.6 {\rm pc}$ in the
Monogem halo. Our study highlights the pivotal role of magnetic field and
turbulence in unraveling the physical processes in TeV halos and cosmic ray
transport.
