Ab initio calculations, the generalized gradient approximations $(\text{GGA}/\text{GGA}+U)$, are used to propose a spin Hamiltonian for the $B$-site ordered double perovskite ${\mathrm{Sr}}_2{\mathrm{NiWO}}_6$. Our results show that the exchange interaction constants between the next-nearest neighbors in both intra- and inter-$ab$ planes $(J_2$ and $J_{2c})$ are an order of magnitude larger than the ones between the nearest neighbors $(J_1$ and $J_{1c})$. Employing the Monte Carlo simulation, we show that the obtained Hamiltonian properly describes the finite-temperature properties of ${\mathrm{Sr}}_2{\mathrm{NiWO}}_6$. Our ab initio calculations also reveal a small magnetic anisotropy and nontrivial biquadratic interaction between the nearest inter-$ab$ plane neighbors, which play essential roles in stabilizing the type-II antiferromagnetic ground state of ${\mathrm{Sr}}_2{\mathrm{NiWO}}_6$.

• Received 25 June 2018
• Revised 12 January 2019

DOI:https://doi.org/10.1103/PhysRevB.99.104411