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{\it Ab initio} calculations, GGA/GGA+$U$, are used to propose a spinHamiltonian for the B-site ordered double perovskite, Sr$_{2}$NiWO$_{6}$. Ourresults show that the exchange interaction constants between the next nearestneighbors in both intra- and inter- $ab$ plane ($J_2$ and $J_{2c}$) are anorder of magnitude larger than the ones between the nearest neighbors ($J_1$and $J_{1c}$). Employing the Monte Carlo simulation, we show that the obtainedHamiltonian properly describes the finite temperature properties ofSr$_{2}$NiWO$_{6}$. Our {\it ab initio} calculations also reveal a smallmagnetic anisotropy and non-trivial bi-quadratic interaction between thenearest inter-$ab$ plane neighbors, which play essential roles in stabilizingthe type-II anti-ferromagnetic ground state of Sr$_{2}$NiWO$_{6}$.

Ab initio investigation of magnetic ordering in the double perovskite Sr$_{2}$NiWO$_{6}$