Magnetism in a family of $S=$ 1 square lattice antiferromagnets, Ni$X_{2}$(pyz)$_{2}$ ($X=$ Cl, Br, NCS; pyz $=$ pyrazine)

The crystal structures of Ni$X_{2}$(pyz)$_{2}$ ($X=$ Cl, Br and NCS, henceforth Ni-Cl, Ni-Br and Ni-NCS, respectively), were determined at 298 K from synchrotron powder X-ray diffraction data. All three compounds consist of two-dimensional (2D) [Ni(pyz)$_{2}$]$^{2+}$ square lattices spaced by $X$ ligands, resulting a staggered stacking fashion of 2D layers. Long-range antiferromagnetic order occurs below 1.5 (Ni-Cl) and 1.9 K (Ni-Br and Ni-NCS) as determined by heat capacity and Muon-spin relaxation. The single-ion anisotropy and $g$ factor of Ni-Br and Ni-NCS were measured by electron spin resonance where no zero-field splitting was found. The magnetism of Ni-NCS is interpreted by the 3D simple cubic Heisenberg model with the Ni-pyz-Ni interaction $J_{pyz}=$ 0.70 K. A good overall agreement was found between the pulsed field magnetization data, magnetic susceptibility and $T_{N}$ for Ni-NCS. Ni-Cl and N-Br are characterized as quasi-2D antiferromagnets with the interlayer magnetic coupling significantly suppressed by varying the $X$ ligand.