(n = 1, 2, and ∞)**

Quantum spin liquids are among the most intensively sought states of matter.  Our work revealed an anomalously strong frustration in an unlikely place, the trimer lattice Ba₄Ir₃O₁₀ [1]. These findings suggest an important role of Ir₃O₁₂ trimers in producing spin entanglement and point to a new pathway to the search of new phases of matter in trimer lattices [1-3]. We have recently synthesized and studied single crystals of a series of such trimer lattices Ba_3n+1Ir_3nO_9n+1 (n = 1, 2, ∞), i.e., Ba₄Ir₃O₁₀ (n=1), Ba₇Ir₆O₁₉ (n=2), and 9R-BaIrO₃ (n=∞), where n represents the number of the trimer planes per unit cell.  This new series of trimer iridates hosts Ir⁴⁺(5d⁵) ions, which support the spin-orbit-coupled Mott state. These iridates adopt a similar crystal structure with different trimer connectivity and yet cover the extreme ends of a magnetic spectrum: the delicate quantum liquid (n=1) on one end and an antiferromagnet with T_N = 183 K with a possible charge density wave (n=∞) on the other [4]. Situated between the two is Ba₇Ir₆O₁₉ (n=2), whose ground state is the focus of this talk.