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

Abstract

Inspired by the recent theoretical suggestion that the random-bond S = 1/2 antiferromagnetic Heisenberg model on the triangular and the kagome lattices might exhibit a randomness-induced quantum spin liquid (QSL) behavior when the strength of the randomness exceeds a critical value, and that this "random-singlet state" might be relevant to the QSL behaviors experimentally observed in triangular organic salts κ−(ET)2Cu2(CN)3and EtMe3Sb[Pd(dmit)2]2 and in kagome herbertsmithite ZnCu3(OH)6Cl2, we further investigate the nature of the static and the dynamical spin correlations of these models. We compute the static and the dynamical spin structure factors, S(q) and S(q, ω), by means of an exact diagonalization method. In both triangular and kagome models, the computed S(q, ω) in the random-singlet state depends on the wavevector q only weakly, robustly exhibiting gapless behaviors accompnied by the broad distribution extending to higher energy ω. Especially in the strongly random kagome model, S(q, ω) hardly depends on q, and exhibits an almost flat distribution for a wide range of ω, together with a ω = 0 peak. These features agree semi-quantitatively with the recent neutron-scattering data on a single-crystal herbertsmithite. Furthermore, the computed magnetization curve agrees almost quantitatively with the experimental one recently measured on a single-crystal herbertsmithite. These results suggest that the QSL state observed in herbersmithite might indeed be the randomness-induced QSL state, i.e., the random-singlet state.

Anisotropy: Spin order and magnetization of single-crystallineCu4(OH)6FBrbarlowite

“…The small excess magnetization, 16% of the value permitted for stoichiometric composition, is another indication of a small J ′ . In applied fields, the impurity magnetization of herbertsmithite is approximately twice that permitted for the interlayer spins 25 , which likely polarize the kagome lattice through superexchange and thus induce intra-kagome disorder 26 . The interlayer spins affect about half of the kagome lattice 25 and efforts to chemically minimize their concentration have been unsuccessful.…”

“…This suggests that, in applied fields, the interlayer moments cannot be separated from the kagome spins in a trivial manner. When establishing a complete phase diagram connecting the zero-field ground state and its in-field variations, this conundrum complicates the interpretation of herbertsmithite's properties 26 . By contrast, in barlowite, the excess magnetization is 16% of the value permitted for stoichiometric composition.…”

Sc2Ga2CuO7: A possible quantum spin liquid near the percolation threshold

“…There is also recent work [19] that proposes disorder driven spin-orbital liquid in such systems. Another possibility is disorder induced bond randomness, which can give rise to a random singlet QSL as has been suggested in herbertsmithite [34]. Further low-T magnetization and local probe investigations such as μSR would be useful to explore the properties of SGCO in greater details.…”

“…However, there could be other explanations. Recently, randomness-induced QSL (also called random singlet) has been suggested for organic triangular salts [33] as also for inorganic ones such as herbertsmithite [34] with the kagome structure. In herbertsmithite, a Zn/Cu disorder might cause a random Jahn-Teller distortion of the [Cu(OH) 6 ] 4− giving rise to a random modification of the exchange coupling in the kagome layer.…”

Gapless spin excitations in the S=1/2 Kagome- and triangular-lattice Heisenberg antiferromagnets

“…Such behaviors were also examined in various frustrated magnets [32,33,34,35,36]. A randomness effect in these systems was additionally examined [37,38]. Under such circumstances, the present study tackles a fundamental issue concerning properties of systems without effects owing to significantly large fields and randomness are investigated.…”