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 $Trm_N$, 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.
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