  We report magnetic dipole field investigation at the atomic scale in a single
crystal of quasi-one-dimensional (Q1D) paramagnetic conductor
Li$_{0.9}$Mo$_{6}$O$_{17}$, using a paramagnetic electron model and
$^{7}$Li-NMR spectroscopy measurements with an externally applied magnetic
field $B_{0}$ = 9 T. We find that the magnetic dipole field component
($B_{||}^{\text{dip}}$) parallel to $B_{0}$ at the Li site from the Mo
electrons has no lattice axial symmetry; it is small around the middle between
the lattice $c$ and $a$ axes in the $ac$-plane with the minimum at the field
orientation angle $\theta$ = +52.5$^{\circ}$, while the $B_{||}^{\text{dip}}$
maximum is at $\theta$ = +142.5$^{\circ}$ when $B_{0}$ is applied perpendicular
to $b$ ($B_{0}$ $\perp$ $b$), where $\theta$ = 0$^{\circ}$ represents the
direction of $B_{0}$ $\parallel$ $c$. Further estimate indicates that
$B_{||}^{\text{dip}}$ has a maximum value of 0.35 G at $B_{0}$ = 9 T, and the
Mo ions have a possible effective magnetic dipole moment 0.015 $\mu_{\text{B}}$
per ion, which is significantly smaller than that of a spin 1/2 free electron.
By minimizing potential magnetic contributions to the NMR spectrum satellites
with the NMR spectroscopy measurements at the direction where the value of the
magnetic dipole field is the smallest, the behavior of the independent charge
contributions is observed. This work demonstrates that the magnetic dipole
field from the Mo electrons is the dominant source of the local magnetic fields
at the Li site, and it suggests that the mysterious "metal-insulator" crossover
at low temperatures is not a charge effect. The work also reveals valuable
local field information for further NMR investigation which is suggested
recently [Phys. Rev. B $\bf{85}$, 235128 (2012)] to be key important to the
understanding of many mysterious properties of this Q1D material of particular
interest.
