Strongly correlated quantum spin liquid

Strongly correlated quantum spin liquid (SCQSL) is a specific realization of a possible quantum spin liquid (QSL) representing a new type of strongly correlated electrical insulator (SCI) that possesses properties of heavy fermion metals with one exception: it resists the flow of electric charge. At low temperatures T the specific heat of this type of insulator is proportional to Tⁿ with n less or equal 1 rather than n=3, as it should be in the case of a conventional insulator when the heat capacity is proportional to T³. When a magnetic field B is applied to SCI the specific heat depends strongly on B, contrary to conventional insulators. There are a few candidates of SCI; the most promising among them is Herbertsmithite that is a mineral with chemical structure ZnCu₃(OH)₆Cl₂.

Specific properties

File:Herb4.png

Fig. 1: T-dependence of the electronic specific heat C/T of YbRh₂Si₂ at different magnetic fields as shown in the legend. The values of (C/T)_max and T_max at B=8 Tesla are shown. The maximum (C/T)_max decreases with growing magnetic field B, while T_max shifts to higher T reaching 14 K at B=18 Tesla. Observing that C/T~χ~M*, one concludes that SCQSL in ZnCu₃(OH)₆Cl₂ shown in Fig. 2 exhibits the similar behavior as heavy fermions in YbRh₂Si₂.

File:Magnetic susceptibility of a function of temperature vs magnetic field - Herbertsmithite.png

Fig.2: T-dependence of the magnetic susceptibility χ at different magnetic fields for ZnCu₃(OH)₆Cl₂. The values of χ_max and T_max at B=7 Tesla are shown. T-dependence T^(-2/3) at B=0 is depicted by the solid curve. The maximum χ_max(T) decreases as magnetic field B grows, while T_max(B) shifts to higher T reaching 15 K at B=14 Tesla. Observing that χ~C/T~M*, one concludes that the specific heat of YbRh₂Si₂ shown in Fig. 1 exhibits the similar behavior as χ does. Thus, SCQSL in ZnCu₃(OH)₆Cl₂ behaves as heavy fermions in YbRh₂Si₂.

Exotic SCQSL’s are formed with such hypothetical particles as fermionic spinons carrying spin 1/2 and no charge. The experimental studies of Herbertsmithite ZnCu₃(OH)₆Cl₂ single crystal have found no evidence of long range magnetic order or spin freezing indicating that Herbertsmithite is the promising system to investigate SCQSL. The planes of the Cu²⁺ ions can be considered as two-dimensional layers with negligible magnetic interactions along the third dimension. Experiments have found neither long range magnetic order nor glassy spin freezing down to temperature 50 mK making Herbertsmithite the best candidate for QSL realization. Frustration of a simple kagome lattice leads to dispersionless topologically protected flat bands. In that case fermion condensation quantum phase transition (FCQPT) can be considered as quantum critical point (QCP) of Herbertsmithite. FCQPT creates SCQSL composed of chargeless fermions with spin=1/2 occupying the corresponding Fermi sphere with a finite Fermi momentum. Herbertsmithite's thermodynamic and relaxation properties are similar to those of heavy fermion metals and two-dimensional ³He. The key features of the findings are the presence in Herbertsmithite of spin–charge separation and SCQSL formed with itinerant spinons. Herbertsmithite represents a fascinating example of SCI where particles-spinons, non-existing as free, replace the initial particles appearing in the Hamiltonian and define the thermodynamic and relaxation properties at low temperatures. Because of the spin-charge separation, heat transport, thermodynamic and relaxation properties at low temperatures of the SCI Herbertsmithite are similar to those of heavy-fermion metals rather than of insulators.

Fermion condensation quantum phase transition

The experimental facts collected on heavy fermion (HF) metals and two dimensional ³He demonstrate that the quasiparticle effective mass M* is very large, or even diverges. Fermion condensation quantum phase transition (FCQPT) preserves quasiparticles and is directly related to the unlimited growth of the effective mass M*. Near FCQPT, M* starts to depend on temperature T, density x, magnetic field B and other external parameters such as pressure P etc. In contrast to the Landau paradigm based on the assumption that the effective mass is constant, in the FCQPT theory the effective mass of new quasiparticles strongly depends on T, x, B etc. Therefore, to agree/explain with the numerous experimental facts, extended quasiparticles paradigm based on FCQPT has to be introduced. The main point here is that the well-defined quasiparticles determine the thermodynamic, relaxation, scaling and transport properties of strongly correlated Fermi-systems and M* becomes a function of T, x, B, P etc. The data collected for very different strongly correlated Fermi systems demonstrate universal scaling behavior; in other words distinct materials with strongly correlated fermions unexpectedly turn out to be uniform.

Identification in Experiments

Quantum spin liquid - the new state of matter - is realized in Herbertsmithite, ZnCu₃(OD)₆Cl₂. Magnetic response of this material displays scaling relation in both the bulk ac susceptibility and the low energy dynamic susceptibility, with the low temperature heat capacity strongly depending on magnetic field. This scaling is seen in certain quantum antiferromagnets and heavy-fermion metals as a signature of proximity to a quantum critical point. The low-temperature specific heat follows the linear temperature dependence. These results suggest that a SCQSL state with essentially gapless excitations is realized in Herbertsmithite.