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

Zheng, X.-G.*; Yamauchi, Ichihiro*; Hagihara, Masato   ; Nishibori, Eiji*; Kawae, Tatsuya*; Watanabe, Isao*; Uchiyama, Tomoki*; Chen, Y.*; Xu, C.-N.*

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(OH)Cl. 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 ____$. 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.