Quantum kagome frustrated antiferromagnets: One route to quantum spin liquids

After introducing the field of Highly Frustrated Magnetism through the quest for a quantum spin liquid in dimension higher than one, we focus on the emblematic case of the kagome network. From a theoretical point of view, the simple Heisenberg case for an antiferromagnetic kagome lattice decorated with quantum spins has been a long-standing problem, not solved yet. Experimental realizations have remained scarce for long until the discovery of herbertsmithite ZnCu3(OH)(6)Cl-2 in 2005. This is one of the very few quantum kagome spin liquid candidates that triggered a burst of activity both on theory and experiment sides. We give a survey of theory outcomes on the kagome problem, review the experimental properties of that model candidate and shortly discuss them with respect to recent theoretical results. (C) 2015 Published by Elsevier Masson SAS on behalf of Academie des sciences.