Using combination of first-principles density-functional theory and quantum Monte Carlo technique we study the magnetic behavior of $S=1$ spin chain compound ${\mathrm{SrNi}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}$. The magnetic model, derived in a first-principles Wannier function basis, shows the presence of finite next-neighbor intrachain coupling, in addition to interchain couplings, thereby deviating from the ideal Haldane chain description. The computed single-ion anisotropy turns out to be of easy axis type and of appreciable magnitude. Solution of the first-principles derived spin model confirms the spin-gapped ground state of the compound. The spin gap is found to close at a critical value of magnetic field, which is estimated to be much reduced compared to that of an ideal Haldane chain. Our study highlights the effectiveness of the next-nearest-neighbor intrachain coupling in reducing the spin gap from the ideal Haldane chain limit. Further study on the effect of biaxial strain on the magnetic behavior predicts that the application of tensile strain should enable the closing of the spin gap in the ground state.
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