Quantum Spin-Liquid Behavior in the Spin-1/2 Random-Bond Heisenberg Antiferromagnet on the Kagome Lattice

Abstract

The effect of the quenched bond-randomness on the ordering of the S = 1/2 antiferromagnetic Heisenberg model on the kagome lattice is investigated by means of an exact-diagonalization method. When the randomness exceeds a critical value, the ground state of the model exhibits a transition within the non-magnetic state into the randomness-relevant gapless spin-liquid state. Implications to the S = 1/2 kagome-lattice antiferromagnet herbertsmithite is discussed.Since the proposal by P.W. Anderson of the resonating valence bond state [1], the quantum spin-liquid (QSL) state possibly realized in certain S = 1/2 frustrated magnets has attracted interest of researchers [2]. After a long experimental quest, several candidate materials were recently reported in geometrically frustrated magnets, including both the triangular-lattice and the kagome-lattice antiferromagnets (AFs).Examples of the triangular-lattice AF might be S = 1/2 organic salts such as κ-(ET) 2 Cu 2 (CN) 3 [3][4][5][6] and [7][8][9][10], which exhibit no magnetic ordering, neither regular nor random, down to a very low temperature. The QSL state of these compounds exhibits gapless behaviors characterized by, e.g., the lowtemperature specific heat [4,9] or the thermal conductivity [5,8] linear in the absolute temperature T . An example of the second category, the kagome-lattice AF, might be herbertsmithite CuZn 3 (OH) 6 Cl 2 [11][12][13][14][15][16][17]. No magnetic order is observed down to 20mK in spite of the exchange coupling of 180K, while gapless behaviors are observed in various physical quantities.The origin of the QSL behavior observed in these triangular-lattice organic salts and the kagome-lattice herbertsmithite has attracted tremendous interest, and various theoretical proposals have been made. The simplest possible reference model might be the S = 1/2 AF Heisenberg model with the nearest-neighbor (n.n.) bilinear coupling. In the triangular case, the ground state of such n.n. model is known to be the standard AF longrange order (LRO), the 120-degrees structure [18,19]. Hence, to explain the QSL behavior observed in these organic salts, some ingredient not taken into account in the simplest Heisenberg model is required. In the kagome case, by contrast, the ground state of the n.n. model is believed to be some sort of QSL state without the magnetic LRO, although its nature is still under hot debate. Various scenarios, including the Z 2 spin liquid [20][21][22][23][24], the algebraic U(1) spin liquid [25][26][27][28], the chiral spin liquid [29] and the valence bond crystal (VBC) [30][31][32] etc. have been proposed. It is not entirely clear at the present stage, however, which of these, or any of these, applies to the experimentally observed QSL state of herbertsmithite.Most of the recent theories pre-assumes that the system is clean enough that the quenched randomness plays a negligible role. Meanwhile, it was recently suggested in ref. [33] that the QSL of the triangular-lattice organic salts might be the randomness-induced one, the randomsi...

Static and dynamical spin correlations of theS=12random-bond antiferromagnetic Heisenberg model on the triangular and kagome lattices

“…These AF orders are not realized in the random model, either 67 . Yet, the temperature and the size dependence ofm s is expected to provide us useful information about the associated AF short-range order.…”

“…66 and 67 , the random-singlet ground state is realized when the randomness is stronger than a critical value ∆ c . In the triangular model, ∆ c is estimated to be ≃ 0.6 where ∆ c separates the AF phase and the random-singlet phase 66 , while in the kagome model it is estimated to be ∆ c ≃ 0.4 where ∆ c separates the the randomness-irrelevant QSL phase (e.g., the Z 2 spin-liquid phase) and the randomness-relevant randomsinglet phase 67 . In the present paper, we employ the exact diagonalization (ED) method in computing various physical quantities.…”

“…The origin, or even the existence of the quenched randomness in triangualr organic salts and kagome herbersmithite is a non-trivial matter, especially in view of the fact that the theory requires a considerable amount of randomness, not an infinitesimal one, to realize the QSLlike behavior 66,67 . In the case of the triangular organic salts, it was suggested that the randomness for the spin degrees of freedom was self-generated at low temperatures via the random freezing of the electric-polarization degrees of freedom inherent to these organic salts consisting of molecular dimers 66 .…”

“…In the case of kagome herbertsmithite, the quenched randomness comes from the random substitution of nonmagnetic Zn 2+ by magnetic Cu 2+ , located on the triangular layer adjacent to the kagome layer 63,67 octahedra, leading to the random modification of the exchange path, and subsequently the exchange strength, connecting the Cu 2+ on the kagome layer 74 . Indeed, the numerical results on a simplified random S = 1/2 AF Heisenberg model on the triangular and the kagome lattices appear to reproduce many of experimentally observed features 66,67 of various thermodynamic quantities, including the T -lienar low-temperature specific heat 35,47,59 , the gapless magnetic susceptibility occasionally accompanying a Curie-like tail 62 , and the gapless temperature dependence of the NMR relaxation rate 1/T 1 33,45 . In view of this apparent success of the random model in reproducing the experimentally observed QSL-like behaviors, it would be desirable to further investigate the nature of the static and the dynamical spin correlations of the randomness-induced QSL state, the random singlet state.…”

Quantum phase transition between disordered and ordered states in the spin-12kagome lattice antiferromagnet(Rb1−xCsx<

“…ically, and the valence-bond-glass (VBG) phase was argued to be the ground state. [49][50][51][52] The VBG phase has finite susceptibility but no long-range ordering. The VBG phase is similar to the Bose glass phase, which emerges in an interacting boson system with random potential 53,54 and/or in a disordered dimer magnet in a magnetic field.…”