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Physical Review B

Theory of the electron spin resonance in quantum spin chains with nearest, next-nearest neighbor, and alternating interactions

Andrei A. Zvyagin

Published Feb 27, 2009• 9 citations
Publisher

Abstract

The dynamical mean-field-like theory of the electron spin resonance (ESR) in spin-1/2 chains with nearest and next-nearest neighbor interactions (or zigzag spin ladders) and alternation is developed. It is explained that either the magnetic anisotropy of spin-spin couplings or the Dzyaloshinskii-Moriya interaction causes shifts of the resonance position in spin chains, comparing to only magnetically isotropic interactions. The power of the ac ESR field, absorbed by the spin chain, is calculated. It is shown that the temperature dependence of the shift of the resonance position is related to the temperature dependence of the ESR absorption. Depending on the strength of next-nearest neighbor interactions, the shift of the ESR position can become either exponentially small or can be increased near quantum critical points. The absorbed by the alternating spin chain power of the ac magnetic field is calculated, manifesting two resonances. The influence of mentioned spin-spin interactions on the linewidth of the ESR is analyzed.

DOI
10.1103/physrevb.79.064422

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The dynamical mean-field-like theory of the electron spin resonance (ESR) in spin-1/2 chains with nearest and next-nearest neighbor interactions (or zigzag spin ladders) and alternation is developed. It is explained that either the magnetic anisotropy of spin-spin couplings or the Dzyaloshinskii-Moriya interaction causes shifts of the resonance position in spin chains, comparing to only magnetically isotropic interactions. The power of the ac ESR field, absorbed by the spin chain, is calculated. It is shown that the temperature dependence of the shift of the resonance position is related to the temperature dependence of the ESR absorption. Depending on the strength of next-nearest neighbor interactions, the shift of the ESR position can become either exponentially small or can be increased near quantum critical points. The absorbed by the alternating spin chain power of the ac magnetic field is calculated, manifesting two resonances. The influence of mentioned spin-spin interactions on the linewidth of the ESR is analyzed.
A systematic field-theory approach to electron spin resonance (ESR) in the S=1/2S=1/2S=1/2 quantum antiferromagnetic chain at low temperature T (compared to the exchange coupling J) is developed. In particular, effects of a transverse staggered field h and an exchange anisotropy (including a dipolar interaction) \ensuremath{\delta} on the ESR line shape are discussed. In the lowest order perturbation theory, the linewidth is given as $\ensuremath{\propto}{\mathrm{Jh}}^{2}{/T}^{2}$ and $\ensuremath{\propto}(\ensuremath{\delta}{/J)}^{2}T,$ respectively. In the case of a transverse staggered field, the perturbative expansion diverges at lower temperature; nonperturbative effects at very low temperature are discussed using exact results on the sine-Gordon field theory. We also compare our field-theory results with the predictions of Kubo-Tomita theory for the high-temperature regime, and discuss the crossover between the two regimes. It is argued that a naive application of the standard Kubo-Tomita theory to the Dzyaloshinskii-Moriya interaction gives an incorrect result. A rigorous and exact identity on the polarization dependence is derived for certain class of anisotropy, and compared with the field-theory results.
A one-dimensional spin-1∕2 model in which the alternation of the exchange interactions between neighboring spins is accompanied by the next-nearest-neighbor (NNN) spin exchange (zig-zag spin ladder with alternation) is studied. The thermodynamic characteristics of the model quantum spin chain are obtained in the mean-field-like approximation. Depending on the strength of the NNN interactions, the model manifests either the spin-gapped behavior of low-lying excitations at low magnetic fields, or ferrimagnetic ordering in the ground state with gapless low-lying excitations. The system undergoes second-order or first-order quantum phase transitions, governed by the external magnetic field, NNN coupling strength, and the degree of the alternation. Hence, NNN spin–spin interactions in a dimerized quantum spin chain can produce a spontaneous magnetization. On the other hand, for quantum spin chains with a spontaneous magnetization, caused by NNN spin–spin couplings, the alternation of nearest-neighbor (NN) exchange interactions can cause destruction of that magnetization and the onset of a spin gap for low-lying excitations. Alternating NN interactions produce a spin gap between two branches of low-energy excitations, and the NNN interactions yield asymmetry of the dispersion laws of those excitations, with possible minima corresponding to incommensurate structures in the spin chain.
Electron spin resonance (ESR) is an important experimental technique. A comprehensive theory of ESR has been di cult to establish, and as such several di erent approximations are used to predict and explain experimental results. This thesis applies the bond-mean- eld theory to the problem of ESR frequency shift for the one-dimensional antiferromagnetic Heisenberg spin chain with uniaxial exchange anisotropy. We use this theory to calculate the ESR resonance frequency shift as a function of temperature and magnetic eld. We perform numerical calculations using the expression obtained. These results are compared to existing results in the literature; they are in broad agreement with theoretical results such as those of Oshikawa and A eck obtained via bosonisation, but they show discrepancies with experimental results. We agree with the theoretical authors that the discrepancy is due to our use of the simplest-case interaction model.
The dynamical structure factor of the S=1/2 bond-alternating spin chain with a next-nearest-neighbor interaction in magnetic field is investigated using the continued fraction method based on the Lanczos algorithm. When the plateau exists on the magnetization curve, the longitudinal dynamical structure factor shows a large intensity with a periodic dispersion relation, while the transverse one shows a large intensity with an almost dispersionless mode. The periodicity and the amplitude of the dispersion relation in the longitudinal dynamical structure factor are sensitive to the coupling constants. The dynamical structure factor of the S=1/2 two-leg ladder in magnetic field is also calculated in the strong interchain-coupling regime. The dynamical structure factor shows gapless or gapful behavior depending on the wave vector along the rung.
We analyze the effects of different coupling anisotropies in a spin-1/2 ladder on the electron spin resonance (ESR) shift. Combining a perturbative expression in the anisotropies with density matrix renormalization group computation of the short range correlations at finite temperature, we provide the full temperature and magnetic field evolution of the ESR paramagnetic shift. We show that for well chosen parameters the ESR shift can be in principle used to extract quantitatively the anisotropies and, as an example, discuss the material BPCB.
We study magnetic excitations for anisotropic spin dimer systems. We present a theory that describes not only the lowest-lying excitation mode but also higher-lying modes of the spin dimers, where the latter modes are important for quantum phase transitions driven by magnetic field and pressure in spin-gapped systems. As the most intriguing application, we calculate electron spin resonance (ESR) intensity in the presence of Dzyaloshinskii–Moriya (DM) interaction, which couples the local triplet with the singlet states of the dimer. The ESR intensities under various configurations of the DM interactions are reported in both disordered and field-induced ordered phases, which are very useful for the analysis of high-field ESR data.