Antiferromagnetic Order and Possible Quantum Spin Liquid in Kagome Antiferromagnet LuCu₃(OH)₆Br₂Br_x(OH)_1-x

Recent studies on the kagome lattice YCu₃(OH)_6+xX_3-x (X = Cl, Br) have provided promising evidence for the existence of Dirac quantum spin liquids. In this study, we synthesized a new compound, LuCu₃(OH)₆Br₂Br_x(OH)_1-x, which has two types of structures with two different space groups, P \overline3 m 1 and R \overline3. The type-I sample with a space group of P \overline3 m 1 had undistorted Cu²⁺ kagome planes and orders magnetically below approximately 1.5 K. The type-II sample had a larger unit cell with a space group of R \overline3 and distorted kagome planes. No magnetic ordering was observed, and the low-temperature specific heat behaved like a Dirac quantum spin liquid, including a quadratic temperature dependence at zero field and an additional linear T term under magnetic fields. By comparing the structures with those of YCu₃(OH)_6+xX_3-x (X = Cl, Br), we show that the quantum spin liquid ground state may have a deep connection with the J_\bigcirc-J-J^\prime Heisenberg model in the kagome lattice.