Quantum Spin Liquid in Geometrically Frustrated Magnets and the New State of Matter

Abstract

In this Chapter, we consider QSL formed by spinons that are chargeless fermionic quasiparticles with spin 1/2, filling up the Fermi sphere up to the Fermi momentum \(p_F\). The excitations of QSL are spinons, which are chargeless fermionic quasiparticles with spin 1/2. We expose a state of the art in the investigations of physical properties of geometrically frustrated magnets with QSL. As the QSL excitations are fermions, the most appropriate description of observed phenomena should be based on some fermionic formalism rather than on different forms of standard spin-wave approaches. So, one more purpose of this chapter centers on a theory employed, demonstrating its range of applicability to a novel expression of magnetic behavior. We elucidate the nature of the used QSL in terms of both experimental facts and the theory of fermion condensation (FC). Our analysis, based on the FC theory, permits to describe the multitude of experimental results regarding the thermodynamic and transport properties of QSL in geometrically frustrated magnets like herbertsmithite \(\mathrm{ZnCu}_3(\mathrm{OH})_6\mathrm{Cl}_2\) , the organic insulators \(\mathrm{EtMe}_3\mathrm{Sb}[\mathrm{Pd}(\mathrm{dmit})_2]_2\) and \(\kappa -(\mathrm{BEDT-TTF})_2\mathrm{Cu}_2(\mathrm{CN})_3\) , quasi-one-dimensional spin liquid in the \(\mathrm{Cu}(\mathrm{C}_4\mathrm{H}_4\mathrm{N}_2)(\mathrm{NO}_3)_2\) insulator, and QSL formed in two-dimensional \(^3\mathrm{He}\). Transport properties of the compounds shed light on the nature of quantum spin liquid. Analysis of the heat conductivity detects its scaling behavior resembling those of both the spin-lattice relaxation rate and the magnetoresistivity. It reveals a strong magnetic field dependence of the spinons effective mass. As a result, the strongly correlated electrical insulator gains also a new magnetic feature of the matter, for the spins represented by the deconfined QSL get mobility. Based on the experimental facts and the theory, we show that the considered magnets exhibit the universal scaling behavior resembling that of heavy-fermion metals, including T/B scaling with T being temperature and B magnetic field. We also show that QSL as a member of strongly correlated Fermi systems represents the new state of matter.