Quasi-one-dimensional S = 1/2 Heisenberg system Rb2Cu2Mo3O12 described by the J1 - J2 model with the nearest-neighbor ferromagnetic and next-nearest-neighbor antiferromagnetic exchange interactions have been investigated by 87/85Rb-NMR under extended field range up to 18 T. From the thermal-activation-type temperature dependence of l/T1, opening of the spin excitation gap was confirmed under the low field below 2 T. With increasing the field, the system becomes gapless, and the gap opens again in the high field saturation region, where the field dependence of the gap size showed the coherent excitation of the neighbouring two spins.
Quasi-one-dimensional S = 1/2 Heisenberg system Rb2Cu2Mo3O12 described by the J1 - J2 model with the nearest-neighbor ferromagnetic and next-nearest-neighbor antiferromagnetic exchange interactions have been investigated by 87/85Rb-NMR under extended field range up to 18 T. From the thermal-activation-type temperature dependence of l/T1, opening of the spin excitation gap was confirmed under the low field below 2 T. With increasing the field, the system becomes gapless, and the gap opens again in the high field saturation region, where the field dependence of the gap size showed the coherent excitation of the neighbouring two spins.
A Rb-NMR study has been performed on the quasi-one-dimensional competing spin chain Rb2Cu2Mo3O12 with ferromagnetic and antiferromagnetic exchange interactions on nearest-neighboring and next-nearest neighboring spins, respectively. The system changes from a gapped ground state at zero field to a gapless state at ${H}_{\mathrm{C}}\ensuremath{\simeq}2\phantom{\rule{0.16em}{0ex}}\mathrm{T}$, where the existence of magnetic order below 1 K was demonstrated by a broadening of the NMR spectrum, associated with a critical divergence of 1/T1. In the higher-temperature region, ${T}_{1}^{\ensuremath{-}1}$ showed a power-law-type temperature dependence, from which the field dependence of the Luttinger parameter K was obtained and compared with theoretical calculations based on the spin nematic Tomonaga-Luttinger liquid (TLL) state.
Various forms of antiferromagnetic exchange interaction among quantized spins in one-dimensional and quasi-one-dimensional lattices are examined. Primary results are reported in two real compounds, the sodium vanadate NaV2O5 and the copper germanate CuGeO3, and in a class of compounds of real materials modeled as dimerized antiferromagnetically coupled spin-1/2 chains susceptible to spin-1 impurity doping and that include such examples as the strontium cuprate Sr14Cu24O41 and vanadium pyrophosphate (VO)2P2O7. Sodium vanadate, NaV2O5, a quarter-filled two-leg ladder compound that was originally thought to be composed of magnetic legs and nonmagnetic legs was subsequently shown to be a charge ordered system below room temperature. Initial models of the material as isolated antiferromagnetically coupled spin-1/2 chains can be mapped to the subsequently resolved magnetic system of the charge ordered state with the spins on molecular orbitals of V-O-V rungs antiferromagentically coupled between neighboring rungs either on the same ladder or on neighboring ladders. Comparing the model's dynamic structure factor to inelastic neutron scattering data could distinguish between the proposed spin coupling schemes and consequently reveal the details of the interaction between the lattice and the "zig-zag" charge density as well as the magnetic stabilization of the low temperature phase. Copper germanate, the first and only known inorganic spin-Peierls compound, exhibits a strong temperature dependent exchange coupling pattern among the spin-1/2 Cu2+ chains. Above the spin-Peierls transition temperature an unmodulated antiferromagnetic nearest neighbor exchange interaction J1 competes with an antiferromagnetic next nearest neighbor interaction J2. The next nearest neighbor exchange represents an effective coupling equivalent to the net effect of all longer range exchange interactions. This frustration to the nearest neighbor spin exchange produces a distinctive magnetic susceptibility χ (T) much different from the Bonner-Fisher susceptibility of the spin-1/2 Heisenberg chain with nearest neighbor antiferromagnetic exchange only. The ratio of the second to first nearest neighbor couplings α = J2/J1 ≈ 0.36 is sufficient to open a spontaneous gap in the spin-wave excitation spectrum at low temperatures. Below TSP = 14K, the dynamical structure factor is used to fit the dimerization δ and the exchange interactions J1 and J2 to the inelastic neutron scattering data of CuGeO3 at T = 10K. It is found that both δ and α increase significantly at lower temperatures, relative to the values obtained in the high temperature phase and at the onset of dimeration at 14 K. Static structure factor calculations how Scattering inconsistent with the δâJ1âJ2 model and can be attributed primarily to the phonon degrees of freedom but possibly also to the couplings between chains in the b and a directions of the crystal lattice. Structurally dimerized compounds of antiferromagnetic spin-1/2 chains possess dynamic structure factor and magnetic susceptibility features that are very sensitive to doping with magnetic and nonmagnetic impurities. It is shown that the effects of spin-1 impurities are very similar to those of nonmagnetic (S = 0) impurities if the coupling between impurity and native spin is about the same magnitude as or larger than between native S = 1/2 spins. The microscopic origins of the similarity can be appreciated with the consideration that neighboring spins to the impurity find it more energetically favorable to couple to the impurity than the other spins of the lattice. Thus the spin-1 impurity and its neighboring S = 1/2 spins decouple from the lattice, creating a nonmagnetic break in the chain. The spins that now observe a nonmagnetic cluster on one side can couple to the S = 1/2 spins on the other side with a higher AF correlation than in the pure compound since they do not have to have a ï¬uctuating dimer resonating between two neighbors. Such enhancements to the local correlations can stabilize the global AF order in one dimensional compounds as shown in theoretical and experimental studies of CuGeO3. ED calculations of the dynamic structure factor show that S(q, ω) developes states with ω = 0 in the gap at q = π. Magnetic susceptibilites in the presense of spin-1 impurities were obtained for 80 site chains by QMC simulations and for 16 site chains by ED calculations. An impurity concentration-dependent second peak in the low temperature region reveals an increasing second maximum with T as observed in doped copper germanates and suggests that the results of the study are applicable even to phonon mediated dimerization. This is not immediately apparent because spin-phonon coupling could distort the dimerization patterns. However, experimental and theoretical results show that elastic coupling between chains can stabilize the dimerization pattern due to the impurities and the results will still apply.
By exploiting density-matrix renormalization group techniques, we investigate the dynamical spin structure factor of a spin-1/2 Heisenberg chain with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor exchange interactions in an applied magnetic field. In a field-induced spin nematic regime, we find gapless longitudinal and gapped transverse spin excitation spectra, in accordance with quasi-long-ranged longitudinal and short-ranged transverse spin correlations, respectively. The gapless point coincides with the dominant longitudinal spin correlation, whereas the gap position exhibits a characteristic field dependence contradicting the dominant transverse spin correlation.
We study the dependence of the magnetization M with magnetic field B at zero temperature in the spin-1/2 XXZ chain with nearest-neighbor (NN) J1 and next-NN J2 exchange interactions, with anisotropies ${\ensuremath{\Delta}}_{1}$ and ${\ensuremath{\Delta}}_{2},$ respectively. The region of parameters for which a jump in M(B) exists is studied using numerical diagonalization, and analytical results for two magnons on a ferromagnetic background in the thermodynamic limit. We find a line in the parameter space ${(J}_{2}{/J}_{1},{\ensuremath{\Delta}}_{1}{/J}_{1},{\ensuremath{\Delta}}_{2}{/J}_{1})$ (determined by two simple equations) at which the ground state is highly degenerate. M(B) has a jump near this line, and at or near the isotropic case with ferromagnetic J1 and antiferromagnetic J2, with $|{J}_{2}{/J}_{1}|\ensuremath{\sim}1/4.$ These results are relevant for some systems containing CuO chains with edge-sharing CuO4 units.
We study Heisenberg spin-1/2 and spin-1 chains with alternating ferromagnetic (J1F) and antiferromagnetic (J1A) nearest-neighbor interactions and ferromagnetic next-nearest-neighbor interaction (J2F). In this model frustration is induced by the non-zero J2F and the effect of dimerization is realized by changing the strength of J1A for a fixed value of J1F. The model with site spin s behaves like a Haldane spin chain with site spin 2s in the limit of vanishing J2F and large J1F/J1A. We show that the exact ground state of the model can be found along a line in the parameter space. The phase diagram in the space of J1A−J2F is determined using numerical techniques complemented by some analytical calculations. A number of quantities, including the ground state spin, energy gap, structure factor, entanglement entropy, and zero temperature magnetization, are studied to understand the complete phase diagram. An interesting and application-wise important feature of this model is that it exhibits a macroscopic magnetization jump in the presence of a magnetic field; we study this using an effective Hamiltonian.
Results of systematic structural, magnetic, electron-spin resonance, and specific-heat investigations of the S=1/2 quantum antiferromagnet compound LiCu2O2 are presented. A spin-singlet ground state is revealed at temperatures above $T\ensuremath{\sim}23\mathrm{K}.$ In this temperature region LiCu2O2 may be regarded as a quantum S=1/2 chain with competing nearest- and next-nearest-neighbor interactions in the intermediate range of the J2/J1 ratio $({\ensuremath{\alpha}}_{c1}<{J}_{2}{/J}_{1}<{\ensuremath{\alpha}}_{c2}).$ The size of the energy gap between the spin-singlet ground state and the first excited triplet, \ensuremath{\Delta}, is found to be \ensuremath{\sim}72 K. The study confirms a magnetic phase transition in LiCu2O2, which results in the collapse of the spin-singlet ground state at a temperature below 23 K. In addition, a second low-temperature transition was found at $T\ensuremath{\sim}9\mathrm{K}.$ Peculiarities of the magnetic excitation spectrum in the dimer phase of LiCu2O2 and its magnetic structure are discussed.