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We report on the microscopic magnetic model of a spin-1/2 magnetBaV$_3$O$_8$. In contrast to earlier phenomenological analysis, ourdensity-functional band-structure calculations combined with quantumMonte-Carlo simulations establish a relatively simple and non-frustrated modelof weakly coupled spin chains with the intrachain coupling of $J\sim$ 38 K andthe Neel temperature of $T_N\sim$ 6 K, both in excellent agreement with theexperiment. The intrachain coupling between the spin-1/2 V$^{+4}$ ions takesplace via two contiguous V$^{+5}$O$_4$ tetrahedra forming an extendedsuperexchange pathway with the V$^{+4}$--V$^{+4}$ distance of 7.44 A.Surprisingly, this pathway is preferred over shorter V$^{+4}$--V$^{+4}$connections, owing to peculiarities in the interacting orbitals of the magneticV$^{+4}$ ions and V$^{+5}$ ions that are non-magnetic, but feature low-lying$3d$ states contributing to the superexchange process. We also note that thecrystal structure of BaV$_3$O$_8$ supports the long-sought uniform arrangementof Dzyaloshinsky-Moriya (DM) couplings on a spin-1/2 chain. While ourcalculations yield only a weak DM anisotropy in BaV$_3$O$_8$, the crystalstructure of this compound provides a suitable framework for the search of spinchains with the uniform DM anisotropy in other compounds of the vanadatefamily.

Spin-chain magnetism and uniform Dzyaloshinsky-Moriya anisotropy in BaV$_3$O$_8$