Strong relevance of zinc impurities in spin- 12 kagome quantum antiferromagnets: A variational study

Copper hydroxyhalide materials herbertsmithite ZnCu₃(OH)₆Cl₂ and Zn-barlowite ZnCu₃(OH)₆FrBr are thought to be the best realizations of the spin-1/2 kagome quantum antiferromagnetic Heisenberg model and are widely believed to host a spin liquid ground state. However, the exact nature of such a novel state of matter is still under strong debate, partly due to the complication related to the occupation disorder between the zinc and the copper ions in these systems. More specifically, some nonmagnetic Zn²⁺ ions in the system may occupy the Cu²⁺ site within the kagome plane and some spin-1/24pt0exCu²⁺ ions may occupy the Zn²⁺ site between the kagome planes. Both types of impurity can have a nontrivial effect on the dynamical behavior of the antiferromagnetically coupled Cu²⁺ spins on the kagome planes. Recent nuclear magnetic resonance measurements indicate that the magnetic response of the kagome plane is significantly spatial inhomogeneous, even though the content of the misplaced zinc or copper ions is very small. Here we use extensive variational optimization to show that the well-known U(1) Dirac spin liquid state is extremely sensitive to the introduction of the nonmagnetic Zn²⁺ impurity in the kagome plane. More specifically, we find that the zinc impurities can significantly reorganize the local spin correlation pattern around them and induce strong spatial oscillation in the magnetic response of the system. We argue that this is a general trend in highly frustrated quantum magnet systems, in which the nonmagnetic impurity may act as a strongly relevant perturbation on the emergent resonating valence bond structure in their spin liquid ground state. We also argue that the strong spatial oscillation in the magnetic response should be attributed to the free moment released by the doped Zn²⁺ ions and may serve as the smoking-gun evidence for the Dirac node in the U(1) Dirac spin liquid state on the kagome lattice.