We report a combined theoretical and experimental investigation devoted to getting deeper insights into the exotic magnetic properties of the low-dimensional ${\mathrm{SeCuO}}_{3}$ system, for which the two inequivalent Cu(1) and Cu(2) sites show different quantum dynamics. First-principles calculations based on the density functional theory were performed to extract the magnetic exchange couplings. Briefly, we notably find that (i) the magnetic structure can be decomposed into two subsystems made of strongly antiferromagnetically coupled Cu(1) singlet state dimers and weak antiferromagnetic Cu(2) spin chains and (ii) weak ferromagnetic interactions between the two subsystems lead to magnetic frustration. The present model allows us to reproduce both magnetic susceptibility and torque magnetometry measurements. In addition, high-magnetic-field experiments and density-matrix renormalization-group simulations evidence a half-magnetization plateau at 40--45 T associated with the polarization of the Cu(2) spin chains, while the Cu(1) dimers are expected to reach the triplet state at 210--220 T.
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