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We present a microscopic magnetic model for the spin-liquid candidatevolborthite Cu3V2O7(OH)2(H2O)2. The essentials of this DFT-based model are (i)the orbital ordering of Cu(1) 3d 3z2-r2 and Cu(2) 3d 3x2-y2, (ii) threerelevant couplings J_ic, J_1 and J_2, (iii) the ferromagnetic nature of J_1 and(iv) frustration governed by the next-nearest-neighbor exchange interactionJ_2. Our model implies magnetism of frustrated coupled chains in contrast tothe previously proposed anisotropic kagome model. Exact diagonalization studiesreveal agreement with experiments.

Coupled frustrated quantum spin-1/2 chains with orbital order in volborthite Cu3V2O7(OH)2(H2O)2