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arXiv:cond-mat/0101423 · Physical review. B, Condensed matter

Magnetic properties of the one-dimensional multicomponent spin-gap system

Akira Kawaguchi, Tatsuya Fujii, Norio Kawakami

Published Mar 19, 2001• 4 citations
arXivHTMLPDF

Abstract

Magnetic properties of a one-dimensional multicomponent quantum-spin system with an excitation gap are studied based on the integrable spin model introduced by Bariev et al. [Z. Phys. B 96, 395 (1995)]. By exactly computing the magnetization, we show how a characteristic structure with plateaus and cusps appears in the magnetization process. To study the low-energy dynamics of the system, we apply a finite-size scaling analysis to the excitation spectrum, and thereby evaluate the power-law exponent as well as the enhancement factor for the low-temperature NMR relaxation rate ${1/T}_{1}.$ We discuss the critical properties of ${1/T}_{1}$ around plateaus and cusps in the magnetization curve.

DOI
10.1103/physrevb.63.144413

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Magnetic properties of a one-dimensional multicomponent quantum-spin system with an excitation gap are studied based on the integrable spin model introduced by Bariev et al. [Z. Phys. B 96, 395 (1995)]. By exactly computing the magnetization, we show how a characteristic structure with plateaus and cusps appears in the magnetization process. To study the low-energy dynamics of the system, we apply a finite-size scaling analysis to the excitation spectrum, and thereby evaluate the power-law exponent as well as the enhancement factor for the low-temperature NMR relaxation rate 1/T1.{1/T}_{1}.1/T1​. We discuss the critical properties of 1/T1{1/T}_{1}1/T1​ around plateaus and cusps in the magnetization curve.
The NMR relaxation rate 1/T11/T_{1}1/T1​ is studied for one-dimensional multicomponent spin-orbital systems. By combining the bosonization techniques and the exact solution of the SU(nnn) model, we evaluate the power-law exponent and the enhancement factor for 1/T11/T_11/T1​ at low temperatures. We discuss how the band splitting affects the relaxation rate, and find that 1/T11/T_{1}1/T1​ may be enhanced around the critical value of the band splitting. The crossover behavior in 1/T11/T_11/T1​ around the critical point is discussed in terms of the low-frequency dynamical spin susceptibility. The effect of the hole-doping is also addressed.
By means of nuclear spin-lattice relaxation rate ${T}_{1}^{\ensuremath{-}1}$, we follow the spin dynamics as a function of the applied magnetic field in two gapped quasi-one-dimensional quantum antiferromagnets: the anisotropic spin-chain system ${\mathrm{NiCl}}_{2}\mathrm{\text{\ensuremath{-}}}4\mathrm{SC}({\mathrm{NH}}_{2}{)}_{2}$ and the spin-ladder system (C5H12N)2CuBr4({\mathrm{C}}_{5}{\mathrm{H}}_{12}\mathrm{N}{)}_{2}\mathrm{Cu}{\mathrm{Br}}_{4}(C5​H12​N)2​CuBr4​. In both systems, spin excitations are confirmed to evolve from magnons in the gapped state to spinons in the gapless Tomonaga-Luttinger-liquid state. In between, ${T}_{1}^{\ensuremath{-}1}$ exhibits a pronounced, continuous variation, which is shown to scale in accordance with quantum criticality. We extract the critical exponent for ${T}_{1}^{\ensuremath{-}1}$, compare it to the theory, and show that this behavior is identical in both studied systems, thus demonstrating the universality of quantum-critical behavior.
An interesting feature of spin- chains with a gap is that they undergo a commensurate-incommensurate transition in the presence of an external magnetic field H. The system is in a gapless incommensurate regime for all values of the magnetic field between the lower critical field Hc1{\mathrm{H}}_{\mathrm{c}1}Hc1​ and an upper critical field Hc2{\mathrm{H}}_{\mathrm{c}2}Hc2​, where it is gapless and has power-law correlations. We calculate the critical exponents for such a generic gapped system in the incommensurate regime at the critical field Hc1{\mathrm{H}}_{\mathrm{c}1}Hc1​ and in its vicinity. Our analysis also applies to the spin- ladder. We compute the full dynamical susceptibilities at finite temperature. We use the same to discuss the thermal broadening of various modes and obtain the low-temperature behavior of the nuclear spin relaxation rate ${\mathrm{T}}_{1}^{\mathrm{\ensuremath{-}}1}$. We discuss the results obtained here for the special cases of the dimerized chain, frustrated chain, and the spin- ladder.
The energy spectra and low-temperature magnetic properties of two one-dimensional Heisenberg mixed spin (s = 1, 1/2) systems, namely decorated two-leg mixed spin ladders with the lattice topology of polyacene, are studied. The gapless character of the exact excitation energy spectra for both ladder models has been determined. We found numerically that the model with macroscopic ground state spin S0 has gapped excitations with the spin S > S0. This leads to the appearance of an intermediate plateau in field dependence of magnetization at low temperatures. We have shown that the ladder with equal coupling in legs has the maximal size of this plateau at the same coupling in rungs. For a mixed spin ladder model with Ising interactions in legs, the appearance of two intermediate magnetization plateaus at low temperatures and some values of coupling parameters was shown.
In the framework of the exactly solvable model, using nonperturbative methods, the temperature and magnetic field behavior of the NMR relaxation rate (and low-energy dynamical structure factor) for the antiferromagnetic Heisenberg spin-1/2 chain with magnetic impurities is calculated. For a single magnetic impurity, totally screened at low temperatures by spinons of the chain, the critical exponents, which determine the low-temperature and magnetic field behavior, get renormalized. For the finite concentration of impurities with the random distribution of the impurity-chain coupling the weak disorder in the distribution does not produce essential changes to the dynamical structure factor. Contrary, the strong disorder yields drastically different behavior of the low-energy dynamical characteristics, comparing to the homogeneous chain. Our results are generic, and they qualitatively agree in limiting cases with the results of perturbative calculations for disordered spin chains and with the data of experiments on quasi-one-dimensional spin compounds.
The excitation spectrum of the one-dimensional spin-orbital model in a magnetic field is studied, using a recently developed dynamical density-matrix renormalization-group technique. The method is applied to chains with up to 80 sites, and examined for test cases such as the one-dimensional spin-1/2 Heisenberg antiferromagnet whose excitation spectrum is known exactly from the Bethe ansatz. In the spin-orbital chain, the characteristic dynamical response depends strongly on the model parameters and the applied magnetic field. The coupling between the spin and orbital degrees of freedom is found to influence the incommensuration at finite magnetizations. In the regions of the phase diagram with only massive spin and orbital excitations, a finite field is required to overcome the spin gap. An orbital mode is found to become massless in this partially spin-polarized regime, indicating a strong coupling between the two degrees of freedom. In the critical region with three elementary gapless excitations, a prominent particle-hole excitation is observed at higher energies, promoted by the biquadratic term in the model Hamiltonian of the spin-orbital chain.