  Magnetism of the $S$ = 1 Heisenberg antiferromagnets on the spatially
anisotropic square lattice has been scarcely explored. Here we report a study
of the magnetism, specific heat, and thermal conductivity on
Ni[SC(NH$_2$)$_2$]$_6$Br$_2$ (DHN) single crystals. Ni$^{2+}$ ions feature an
$S$ = 1 rectangular lattice in the $bc$ plane, which can be viewed as an
unfrustrated spatially anisotropic square lattice. A long-range
antiferromagnetic order is developed at $T \rm_N =$ 2.23 K. Below $T\rm_N$, an
upturn is observed in the $b$-axis magnetic susceptibility and the resultant
minimum might be an indication for the $XY$ anisotropy in the ordered state. A
gapped spin-wave dispersion is confirmed from the temperature dependence of the
magnetic specific heat. Anisotropic temperature-field phase diagrams are mapped
out and possible magnetic structures are proposed.
