Theoretical and experimental developments in quantum spin liquid in geometrically frustrated magnets: a review

The exotic substances have exotic properties. One class of such substances is geometrically frustrated magnets, where correlated spins reside in the sites of triangular or kagome lattice. In some cases, such magnet would not have long-range magnetic order. Rather, its spins tend to form kind of pairs, called valence bonds. At $$T \rightarrow 0$$ these highly entangled quantum objects condense in the form of a liquid, called quantum spin liquid (QSL). The observation of a gapless QSL in actual materials is of fundamental significance both theoretically and technologically, as it could open a path to creation of topologically protected states for quantum information processing and computation. In the present review, we consider QSL formed by spinons that are chargeless fermionic quasiparticles with spin 1/2, filling the Fermi sphere up to the Fermi momentum $$p_{\rm F}$$. We expose a state of the art in the theoretical and experimental investigations of the thermodynamic, relaxation, transport, optical and scaling properties of geometrically frustrated magnets with QSL. We show how different theoretical approaches and that based on so-called fermion condensation concept among them, permit to describe the multitude of experimental results regarding the thermodynamic and transport properties of QSL in geometrically frustrated magnets like herbertsmithite $$\hbox {ZnCu}_3(\hbox {OH})_6\hbox {Cl}_2$$, the organic insulators $$\hbox {EtMe}_3\hbox {Sb}[\hbox {Pd(dmit)}_2]_2$$ and $$\kappa {\text {-}}(\hbox {BEDT-TTF})_2\hbox {Cu}_2(\hbox {CN})_3$$, quasi-one-dimensional spin liquid in the $$\hbox {Cu}(\hbox {C}_4\hbox {H}_4\hbox {N}_2)(\hbox {NO}_3)_2$$ insulator and QSL formed in two-dimensional $$^3\hbox {He}$$. Our theoretical results are in good agreement with experimental facts, while predictions, elucidating the existence of gapless QSL in magnets, still await their experimental confirmation.