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Magnetism of the $S$ = 1 Heisenberg antiferromagnets on the spatiallyanisotropic square lattice has been scarcely explored. Here we report a studyof the magnetism, specific heat, and thermal conductivity onNi[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 anunfrustrated spatially anisotropic square lattice. A long-rangeantiferromagnetic order is developed at $T \rm_N =$ 2.23 K. Below $T\rm_N$, anupturn is observed in the $b$-axis magnetic susceptibility and the resultantminimum might be an indication for the $XY$ anisotropy in the ordered state. Agapped spin-wave dispersion is confirmed from the temperature dependence of themagnetic specific heat. Anisotropic temperature-field phase diagrams are mappedout and possible magnetic structures are proposed.

Magnetism study on a frustration-free spatially anisotropic $S$ = 1 square lattice antiferromagnet Ni[SC(NH$_2$)$_2$]$_6$Br$_2$