Excitations in a Four-Leg Antiferromagnetic Heisenberg Spin Tube

Abstract

Inelastic neutron scattering is used to investigate magnetic excitations in the quasi-one-dimensional quantum spin-liquid system Cu 2 Cl 4 D 8 C 4 SO 2 . Contrary to previously conjectured models that relied on bond-alternating nearest-neighbor interactions in the spin chains, the dominant interactions are actually next-nearest-neighbor in-chain antiferromagnetic couplings. The appropriate Heisenberg Hamiltonian is equivalent to that of a S 1=2 4-leg spin-tube with almost perfect one dimensionality and no bond alternation. A partial geometric frustration of rung interactions induces a small incommensurability of short-range spin correlations.

Series expansion analysis of a frustrated four-spin tube

“…Spin-1/2 moments are located on the solid circles and all couplings, j 0 , j 1 and j 2 are antiferro- magnetic (we set j 0 = 1 hereafter). This FFST is simpler than the one proposed for Cu 2 Cl 4 ·D 8 C 4 SO 2 , where only part of the surface squares experience diagonal exchange, and the leg-couplings seem to be in-equivalent 8 . Apart its relation to existing materials, the FFST is of interest as a 1D variant of the anisotropic triangular lattice on the torus with four site circumference, i.e.…”

“…For N = 3, magnetic frustration surfaces as an additional ingredient, already for tubes with only nearest neighbor exchange, leading to a rich variety of phenomena not present in two-leg ladders [11][12][13][14][15] . Experimentally, the four-spin tube Cu 2 Cl 4 ·D 8 C 4 SO 2 has been suggested to display frustrating antiferromagnetic next-nearest neighbor exchange 8 . Theoretically, unfrustrated four-spin tubes have been considered in two seminal papers 16,17 , in the weak and the strong rung-coupling limit, and in the context of a broader study of magnetization plateaux in ladders with an arbitrary number of legs.…”

Low-energy effective theory and two distinct critical phases in a spin-12frustrated three-leg spin tube

“…As the model preserves the SU(2) symmetry, the transition from the dimer phase to the gapless phase with c= 3 2 might be in the SU(2) k=2 Wess-ZuminoWitten-Novikov (WZWN) universality class 23 . In combination with the bosonization analysis, it is observed that for J 3 ≫J 2 the RG flows of H twist go to the strong coupling regime faster than H JJ that leads to a dimerized phase 17,24 , and one may judge that such a gapless phase with nontrivial central charge c= 3 2 in the frustrated three-leg Heisenberg spin tube is probably induced by the twist term H twist .…”

“…6, in the gapless phase with large J 2 (for instance J 2 =2.0, J 3 =0.1), both results for S l are fitted quite well with c=1, which indicates that this gapless phase belongs to the same universality class as the spin-1 2 Heisenberg AF chain. In the gapless phase with large J 3 like J 2 =0.2, J 3 =7.0, the central charge is identified as c= 3 2 . Therefore, we can label the different phases with its central charge in Fig.…”

“…With the discovery of several spin tube materials, such as [(CuCl 2 tachH) 3 Cl]Cl 2 1 , Na 2 V 3 O 7 2 and Cu 2 Cl 4 · D 8 C 4 SO 2 3 , etc., much effort has been made to investigate the low-lying excitations [4][5][6][7][8][9] , long range order 10,11 , phase transitions 5,12 , magnetization plateau [13][14][15] and other ground state properties of spin tubes due to the inter-chain frustrated couplings. A spin tube, geometrically, can be seen as a multi-leg spin ladder with periodic condition along the rung direction (See Fig.…”