Evidence for the topological order in a kagome antiferromagnet (1710.02991v3)

Abstract: A Z2 quantum spin liquid hosts one of the simplest topological orders and exhibits many exotic properties due to long-range quantum entanglements. Its elementary excitations are anyons such as spinons carrying fractionalized spin quantum number and visons carrying emergent Z2 gauge flux. However, experimental detection of these anyons remains elusive. The difficulties lie not only in the fact that there exists few candidates for Z2 quantum spin liquids but also in that visons are magnetically inert hence immune to available experimental techniques. Here we have studied the spin excitations and specific heats of kagome-lattice antiferromagnet Cu$_4$(OH)$_6$FBr and Cu$_3$Zn(OH)$_6$FBr, which consists of two-dimensional Cu$^{2+}$ kagome layers with either Cu$^{2+}$ or Zn$^{2+}$ ions in between. By combining the first principle calculations and inelastic neutron scattering data in the former, we show that the dominate couplings in Cu$_4$(OH)$_6$FBr are between the nearest neighbor spins within the kagome planes, and the kagome and interlayer spin systems are essentially decoupled above the antiferromagnetic transition temperature. The intrinsic spin excitations and specific heats of the kagome layers for Cu$_3$Zn(OH)$_6$FBr are thus derived by removing the contributions from the residual interlayer Cu$^{2+}$ magnetic impurities. Accordingly, the kagome spin system exhibits spin continuum with momentum-dependent spin gap and a large magnetic entropy at low temperature that is insensitive to magnetic field, which can be understood as the evidences of spinons and visons in this kagome quantum spin liquid candidate. Our results suggest the existence of the Z2 anyons in the material, and therefore provide a comprehensive set of evidences for the Z2 topological order in kagome quantum spin liquid and bring their choreographed entanglement dances to the stage of real materials.