Unique magnetic transition process demonstrating the effectiveness of bond percolation theory in a quantum magnet

Like the crystallization of water to ice, magnetic transition occurs at a critical temperature after the slowing down of dynamically fluctuating short-range correlated spins. Here, we report a unique type of magnetic transition characterized by a linear increase in the volume fraction of unconventional static short-range-ordered spin clusters, which triggered a transition into a long-range order at a threshold fraction perfectly matching the bond percolation theory in a new quantum antiferromagnet of pseudo-trigonal Cu 4 (OH) 6 Cl 2 . Static short-range order appeared in its Kagome lattice plane below ca. 20 K from a pool of coexisting spin liquid, linearly increasing its fraction to 0.492(8), then all Kagome spins transitioned into a stable two-dimensional spin order at T N = 5.5 K. Inspection on the magnetic interactions and quantum magnetism revealed an intrinsic link to the spin liquid material Herbertsmithite, ZnCu 3 (OH) 6 Cl 2 . The unconventional static nature of the short-range order was inferred to be due to a pinning effect by the strongly correlated coexisting spin liquids. This work presents a unique magnetic system to demonstrate a complete bond percolation process toward the critical transition. Meanwhile, the unconventionally developed magnetic order in this chemically clean system should shed new light on spin-liquid physics. Magnetic transitions are a paradigmatic example of phase transitions, but the effectiveness of universal percolation theory has not been proven in magnetic systems. Zheng et al. report a magnetic transition in the new pseudo-trigonal structure of Cu 4 (OH) 6 Cl 2 , which can be described by the bond percolation theory.