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Quantum spin systems such as magnetic insulators usually show magnetic order, but such classical states can give way toquantum liquids with exotic entanglementthrough two known mechanisms of frustration: geometric frustration in lattices with triangle motifs, and spin-orbit-coupling frustration in the exactly solvable quantum liquid of Kitaev’s honeycomb lattice. Here we present the experimental observation of a new kind of frustrated quantum liquid arising in an unlikely place: the magnetic insulator Ba₄Ir₃O₁₀where Ir₃O₁₂trimers form an unfrustrated square lattice. The crystal structure shows no apparent spin chains. Experimentally we find a quantum liquid state persisting down to 0.2 K that is stabilized by strong antiferromagnetic interaction with Curie–Weiss temperature ranging from −766 to −169 K due to magnetic anisotropy. The anisotropy-averaged frustration parameter is 2000, seldom seen in iridates. Heat capacity and thermal conductivity are both linear at low temperatures, a familiar feature in metals but here in an insulator pointing to an exotic quantum liquid state; a mere 2% Sr substitution for Ba produces long-range order at 130 K and destroys the linear-T features. Although the Ir⁴⁺(5d⁵) ions in Ba₄Ir₃O₁₀appear to form Ir₃O₁₂trimers of face-sharing IrO₆octahedra, we propose that intra-trimer exchange is reduced and the lattice recombines into an array of coupled 1D chains with additional spins. An extreme limit of decoupled 1D chains can explain most but not all of the striking experimental observations, indicating that the inter-chain coupling plays an important role in the frustration mechanism leading to this quantum liquid.

The rapidly expanding class of quantum materials known as topological semimetals (TSMs) displays unique transport properties, including a striking dependence of resistivity on applied magnetic field, that are of great interest for both scientific and technological reasons. So far, many possible sources of extraordinarily large nonsaturating magnetoresistance have been proposed. However, experimental signatures that can identify or discern the dominant mechanism and connect to available theories are scarce. Here we present the magnetic susceptibility (χ), the tangent of the Hall angle (${\tan \theta }_H$), along with magnetoresistance in four different nonmagnetic semimetals with high mobilities, NbP, TaP, NbSb₂, and TaSb₂, all of which exhibit nonsaturating large magnetoresistance (MR). We find that the distinctly different temperature dependences,$\chi \left(T\right)$, and the values of${\tan \theta }_H$in phosphides and antimonates serve as empirical criteria to sort the MR from different origins: NbP and TaP are uncompensated semimetals with linear dispersion, in which the nonsaturating magnetoresistance arises due to guiding center motion, while NbSb₂and TaSb₂are compensated semimetals, with a magnetoresistance emerging from nearly perfect charge compensation of two quadratic bands. Our results illustrate how a combination of magnetotransport and susceptibility measurements may be used to categorize the increasingly ubiquitous nonsaturating large magnetoresistance in TSMs.