Abstract
In our review, we focus on the quantum spin liquid (QSL), defining the thermodynamic, transport, and relaxation properties of geometrically frustrated magnet (insulators) represented by herbertsmithite ZnCu 3 ( OH ) 6 Cl 2 . The review mostly deals with an historical perspective of our theoretical contributions on this subject, based on the theory of fermion condensation closely related to the emergence (due to geometrical frustration) of dispersionless parts in the fermionic quasiparticle spectrum, so-called flat bands. QSL is a quantum state of matter having neither magnetic order nor gapped excitations even at zero temperature. QSL along with heavy fermion metals can form a new state of matter induced by the topological fermion condensation quantum phase transition. The observation of QSL in actual materials such as herbertsmithite is of fundamental significance both theoretically and technologically, as it could open a path to the creation of topologically protected states for quantum information processing and quantum computation. It is therefore of great importance to establish the presence of a gapless QSL state in one of the most prospective materials, herbertsmithite. In this respect, the interpretation of current theoretical and experimental studies of herbertsmithite are controversial in their implications. Based on published experimental data augmented by our theoretical analysis, we present evidence for the the existence of a QSL in the geometrically frustrated insulator herbertsmithite ZnCu 3 ( OH ) 6 Cl 2 , providing a strategy for unambiguous identification of such a state in other materials. To clarify the nature of QSL in herbertsmithite, we recommend measurements of heat transport, low-energy inelastic neutron scattering, and optical conductivity σ ¯ in ZnCu 3 ( OH ) 6 Cl 2 crystals subject to an external magnetic field at low temperatures. Our analysis of the behavior of σ ¯ in herbertsmithite justifies this set of measurements, which can provide a conclusive experimental demonstration of the nature of its spinon-composed quantum spin liquid. Theoretical study of the optical conductivity of herbertsmithite allows us to expose the physical mechanisms responsible for its temperature and magnetic field dependence. We also suggest that artificially or spontaneously introducing inhomogeneity at nanoscale into ZnCu 3 ( OH ) 6 Cl 2 can both stabilize its QSL and simplify its chemical preparation, and can provide for tests that elucidate the role of impurities. We make predictions of the results of specified measurements related to the dynamical, thermodynamic, and transport properties in the case of a gapless QSL.
Highlights
The frustrated magnet herbertsmithite ZnCu3(OH)6Cl2 is one of the best candidates for identification as a material that hosts a quantum spin liquid (QSL), thereby determining the nature of its thermodynamic, relaxation, and transport properties
We show that QSL is situated near fermion condensation quantum phase transition (FCQPT), which stems from the dependence of σ on the external magnetic field
Since the contribution coming from phonons does not depend on the magnetic field, we propose that measurements of the variation δσ, i.e., δσ = σ(ω, B) − σ(ω, B = 0), can reveal both the physics of strongly correlated quantum spin liquid (SCQSL) and the ground state of ZnCu3(OH)6Cl2, as well as the ground state of other materials hosting a QSL
Summary
The frustrated magnet (insulator) herbertsmithite ZnCu3(OH)6Cl2 is one of the best candidates for identification as a material that hosts a quantum spin liquid (QSL), thereby determining the nature of its thermodynamic, relaxation, and transport properties. Herbertsmithite is the best candidate among quantum magnets to contain QSL described above [3,4,5,6,7,8] These assessments are supported by model calculations indicating that an antiferromagnet on a kagome lattice has a gapless spin liquid ground state [16,17,18,19,20,21,22,23]. The main aim of the present review is to expose QSL as a new state of matter, formed by heavy fermion (HF) metals, and to attract attention to experimental studies of ZnCu3(OH)6Cl2 that have the potential to reveal both the underlying physics of QSL and the presence or absence of a gap in spinon excitations that form the thermodynamic, transport, and relaxation properties. The observed gap [24] related to the kagome planes may not be a real one as it is not a physical mechanism for the observed thermodynamic, relaxation, and conductivity properties of ZnCu3(OH)6Cl2
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