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We study effects of nonmagnetic impurities in a spin-1/2 frustrated triangular antiferromagnet with the aim of understanding the observed broadening of $^{13}$C NMR lines in the organic spin liquid material $kappa$-(ET)$_2$Cu$_2$(CN)$_3$. For high temperatures down to $J/3$, we calculate local susceptibility near a nonmagnetic impurity and near a grain boundary for the nearest neighbor Heisenberg model in high temperature series expansion. We find that the local susceptibility decays to the uniform one in few lattice spacings, and for a low density of impurities we would not be able to explain the line broadening present in the experiments already at elevated temperatures. At low temperatures, we assume a gapless spin liquid with a Fermi surface of spinons. We calculate the local susceptibility in the mean field and also go beyond the mean field by Gutzwiller projection. The zero temperature local susceptibility decays as a power law and oscillates at $2 k_F$. As in the high temperature analysis we find that a low density of impurities is not able to explain the observed broadening of the lines. We are thus led to conclude that there is more disorder in the system. We find that a large density of point-like disorder gives broadening that is consistent with the experiment down to about 5K, but that below this temperature additional mechanism is likely needed.
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A layered triangular lattice with spin-1/2 ions is an ideal platform to explore highly entangled exotic states like quantum spin liquid (QSL). Here, we report a systematic in-field neutron scattering study on a perfect two-dimensional triangular-lattice antiferromagnet, CsYbSe$_2$, a member of the large QSL candidate family rare-earth chalcogenides. The elastic neutron scattering measured down to 70 mK shows that there is a short-range 120$^{circ}$ magnetic order at zero field. In the field-induced ordered states, the spin-spin correlation lengths along the $c$ axis are relatively short, although the heat capacity results indicate long-range magnetic orders at 3 T $-$ 5 T. The inelastic neutron scattering spectra evolve from highly damped continuum-like excitations at zero field to relatively sharp spin wave modes at the plateau phase. Our extensive large-cluster density-matrix renormalization group calculations with a Heisenberg triangular-lattice nearest-neighbor antiferromagnetic model reproduce the essential features of the experimental spectra, including continuum-like excitations at zero field, series of sharp magnons at the plateau phase as well as two-magnon excitations at high energy. This work presents comprehensive experimental and theoretical overview of the unconventional field-induced spin dynamics in triangular-lattice Heisenberg antiferromagnet and thus provides valuable insight into quantum many-body phenomena.
The perovskite Ba8CoNb6O24 comprises equilateral effective spin-1/2 Co2+ triangular layers separated by six non-magnetic layers. Susceptibility, specific heat and neutron scattering measurements combined with high-temperature series expansions and spin-wave calculations confirm that Ba8CoNb6O24 is basically a twodimensional (2D) magnet with no detectable spin anisotropy and no long-range magnetic ordering down to 0.06 K. In other words, Ba8CoNb6O24 is very close to be a realization of the paradigmatic spin-1/2 triangular Heisenberg model, which is not expected to exhibit symmetry breaking at finite temperature according to the Mermin and Wagner theorem.
We report on high-field electron spin resonance (ESR) studies of magnetic excitations in the spin-1/2 triangular-lattice antiferromagnet Cs$_2$CuBr$_4$. Frequency-field diagrams of ESR excitations are measured for different orientations of magnetic fields up to 25 T. We show that the substantial zero-field energy gap, $Deltaapprox9.5$ K, observed in the low-temperature excitation spectrum of Cs$_2$CuBr$_4$ [Zvyagin $et~al.$, Phys. Rev. Lett. 112, 077206 (2014)], is present well above $T_N$. Noticeably, the transition into the long-range magnetically ordered phase does not significantly affect the size of the gap, suggesting that even below $T_N$ the high-energy spin dynamics in Cs$_2$CuBr$_4$ is determined by short-range-order spin correlations. The experimental data are compared with results of model spin-wave-theory calculations for spin-1/2 triangle-lattice antiferromagnet.
We study the spin liquid candidate of the spin-$1/2$ $J_1$-$J_2$ Heisenberg antiferromagnet on the triangular lattice by means of density matrix renormalization group (DMRG) simulations. By applying an external Aharonov-Bohm flux insertion in an infinitely long cylinder, we find unambiguous evidence for gapless $U(1)$ Dirac spin liquid behavior. The flux insertion overcomes the finite size restriction for energy gaps and clearly shows gapless behavior at the expected wave-vectors. Using the DMRG transfer matrix, the low-lying excitation spectrum can be extracted, which shows characteristic Dirac cone structures of both spinon-bilinear and monopole excitations. Finally, we confirm that the entanglement entropy follows the predicted universal response under the flux insertion.
We study the spin-$1/2$ Heisenberg model on the triangular lattice with the nearest-neighbor $J_1 > 0$, the next-nearest-neighobr $J_2 > 0$ Heisenberg interactions, and the additional scalar chiral interaction $J_{chi}(vec{S}_i times vec{S}_j) cdot vec{S}_k$ for the three spins in all the triangles using large-scale density matrix renormalization group calculation on cylinder geometry. With increasing $J_2$ ($J_2/J_1 leq 0.3$) and $J_{chi}$ ($J_{chi}/J_1 leq 1.0$) interactions, we establish a quantum phase diagram with the magnetically ordered $120^{circ}$ phase, stripe phase, and non-coplanar tetrahedral phase. In between these magnetic order phases, we find a chiral spin liquid (CSL) phase, which is identified as a $ u = 1/2$ bosonic fractional quantum Hall state with possible spontaneous rotational symmetry breaking. By switching on the chiral interaction, we find that the previously identified spin liquid in the $J_1 - J_2$ triangular model ($0.08 lesssim J_2/J_1 lesssim 0.15$) shows a phase transition to the CSL phase at very small $J_{chi}$. We also compute spin triplet gap in both spin liquid phases, and our finite-size results suggest large gap in the odd topological sector but small or vanishing gap in the even sector. We discuss the implications of our results to the nature of the spin liquid phases.
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