Thermodynamic properties of the kagome lattice in herbertsmithite

Abstract

Strongly correlated Fermi systems are among the most intriguing and fundamental systems in physics, whose realization in some compounds is still to be discovered. We show that herbertsmithite ZnCu3(OH)6Cl2 can be viewed as a strongly correlated Fermi system whose low temperature thermodynamic in magnetic fields is defined by a quantum critical spin liquid. Our calculations of its thermodynamic properties are in good agreement with recent experimental facts and allow us to reveal their scaling behavior which strongly resembles that observed in HF metals and 2D 3 He. An explanation of the rich behavior of strongly correlated Fermi systems still continues to be among the main problems of the condensed matter physics. One of the most interesting and puzzling issues in the research of strongly correlated Fermi systems is the non-Fermi liquid (NFL) behavior detected in their thermodynamic properties. Under the application of external fields, e.g. magnetic field B, the system can be driven to a Landau Fermi liquid behavior (LFL). Such a behavior was observed in quite different objects such as heavy-fermion (HF) metals [1, 2] and two-dimensional 3 He [2-5] Recently the herbertsmithite ZnCu 3 (OH) 6 Cl 2 has been exposed as a S = 1/2 kagome antiferromagnet [6] and new experimental investigations have revealed its unusual behavior [7][8][9]. Because of the electrostatic environment, Cu 2+ is expected to occupy the distorted octahedral kagome sites. Magnetic kagome planes Cu 2+ S = 1/2 are separated by nonmagnetic Zn 2+ layers. Observations have found no evidence of long range magnetic order or spin freezing down to temperature of 50 mK, indicating that ZnCu 3 (OH) 6 Cl 2 is the best model found of quantum kagome lattice [7][8][9][10]. The specific heat C, arising from the Cu spin system, at T < 1 K appears to be governed by a power law with an exponent which is less than or equal to 1. At the lowest explored temperature, namely over the temperature range 106 < T < 400 mK, C follows a linear law temperature dependence, C ∝ T , and for temperatures of a few Kelvin and higher, the specific heat becomes C(T ) ∝ T 3 and is dominated by the lattice contribution [7][8][9]. At low temperatures T ≤ 1, the strong magnetic field dependence of the specific heat C suggests that C is predominately magnetic in origin [7][8][9]. There are a number of papers suggesting that the S = 1/2 model on the kagome lattice can be viewed as the gapless critical spin liquid [7][8][9][13][14][15][16]. These facts allow us to test both the NFL and LFL behavior of ZnCu 3 (OH) 6 Cl 2 and to show that a Fermi quantum spin liquid formed in the herbertsmithite determines its low temperature thermodynamic properties.Contrary to the C ∝ T behavior [7,8], the observed spin liquids contribute a T 2 specific heat which in the model is not sensitive to an applied magnetic field [15,16]. Moreover the magnetic susceptibility χ(T ) of ZnCu 3 (OH) 6 Cl 2 shown in Fig.

Heat transport in magnetic fields by quantum spin liquid in the organic insulators EtMe 3 Sb[Pd(dmit) 2 ] 2 and κ -(BEDT - TTF) 2 Cu 2 (CN) 3

“…Then, FCQPT can be considered as quantum critical point of SC-QSL, composed of chargeless heavy spinons with S = 1/2 and the effective mass M * mag , occupying the corresponding Fermi sphere with the Fermi momentum p F . Therefore, the properties of insulating compounds coincide with those of heavy-fermion metals with one exception: it resists the flow of electric charge [7,9,10]. As we are dealing with compounds confining non-ideal triangular and kagome lattices, we have to bear in mind that the real magnetic interactions and possible distortion of the lattices can shift the SCQSL from the exact FCQPT, positioning it somewhere near FCQPT.…”

“…Representing a special case of QSL, SCQSL is a quantum state of matter composed of spinons -chargeless fermionic spinons with spin 1/2 [7,9,10]. In insulating compounds, SCQSL can emerge when interactions among the magnetic components are incompatible with the underlying crystal geometry, leading to a geometric frustration generated by the triangular and kagome lattices of magnetic moments, as it is in the case of ZnCu 3 (OH) 6 Cl 2 , see e.g.…”

“…We employ a model of strongly correlated quantum spin liquid (SCQSL) located near the fermion condensation phase transition (FCQPT) to analyze the B-dependence of κ [7][8][9][10]. Our analysis allows us to detect a scaling behavior of κ(B, T ), and relate it to the scaling behavior of the spin-lattice relaxation rate (1/T 1 T ) measured on both the herbertsmithite ZnCu 3 (OH) 6 Cl 2 and the heavy-fermion (HF) metal YbCu 5−x Au x , and the magnetoresistivity measured on the HF metal YbRh 2 Si 2 .…”

Fermion condensate generates a new state of matter by making flat bands

“…10. The striking feature of the specific heat behavior is the strong dependence on the magnetic field seen from the Figure. It is seen that both C mag /T and C/T exhibit the same qualitative behavior that allows us to view the herbertsmithite as insulator with QSL, and QSL itself as SCQSL [43][44][45]. The specific heat Cmag/T of QSL is extracted from measurements of the specific heat on ZnCu3(OH)6Cl2 at different magnetic fields shown in the legend [41,42].…”

Heavy fermion spin liquid in herbertsmithite

“…A number of QSLs with various types of ground states are proposed [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] but the lack of real materials possessing them obscure the underlying physical mechanism. On the other hand, one needs a real theory that plays important role in the understanding and interpreting accessible experimental facts [19][20][21][22]. Measurements on magnetic insulators with geometrical frustration produce important experimental data shedding light on the nature of spinon composing QSL.…”