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Physical review. B, Condensed matter

Numerical analysis of electron-spin resonance in the spin- 12 XY model

Yoshitaka Maeda, Masaki Oshikawa

Published Jun 19, 2003• 14 citations
Publisher

Abstract

This paper presents numerical results of the ESR absorption spectrum for $S=\frac{1}{2}$ $\mathrm{XY}$ model in one dimension. We obtain detailed numerical results for a wide range of temperature and magnetic field for a large system of 400 sites, using the method developed by Derzhko et al. In the high-temperature regime, a similar behavior is observed for both the ferromagnet and the antiferromagnet; these line shapes have only one peak. On the other hand, in the low-temperature regime, line shapes show very different behaviors depending on the sign of the exchange coupling. While the line shape for the ferromagnet has only one peak as in the high-temperature regime, the line shape for antiferromagnet has two peaks and shows very strong magnetic-field dependence. We also discuss the physical meaning by comparing our numerical results with several theoretical results: the exact result in the high-temperature limit, Kubo-Tomita theory, field theory, mean-field theory, and elementary excitations.

DOI
10.1103/physrevb.67.224424

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This paper presents numerical results of the ESR absorption spectrum for S=12S=\frac{1}{2}S=21​ XY\mathrm{XY}XY model in one dimension. We obtain detailed numerical results for a wide range of temperature and magnetic field for a large system of 400 sites, using the method developed by Derzhko et al. In the high-temperature regime, a similar behavior is observed for both the ferromagnet and the antiferromagnet; these line shapes have only one peak. On the other hand, in the low-temperature regime, line shapes show very different behaviors depending on the sign of the exchange coupling. While the line shape for the ferromagnet has only one peak as in the high-temperature regime, the line shape for antiferromagnet has two peaks and shows very strong magnetic-field dependence. We also discuss the physical meaning by comparing our numerical results with several theoretical results: the exact result in the high-temperature limit, Kubo-Tomita theory, field theory, mean-field theory, and elementary excitations.
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.
The electron spin resonance spectrum of the XXZ\mathit{XXZ}XXZ spin chain with finite length shows a double-peak structure at high temperatures around the electron paramagnetic resonance (EPR) frequency. This fact has been pointed out by direct numerical methods [S. El Shawish, O. C\'epas, and S. Miyashita, Phys. Rev. B 81, 224421 (2010); H. Ikeuchi, H. De Raedt, S. Bertaina, and S. Miyashita, Phys. Rev. B 92, 214431 (2015)]. The question of whether the double-peak structure survives in the thermodynamics is of particular interest. We study the size dependence of the line shape, including the even-odd effect. It is found that the peaks forming the double-peak structure are assigned to individual resonances, each of which is specified by the magnetizations of the resonating states $(M,M\ensuremath{-}1)$. To understand dependences, we decompose the spectrum into contributions from transitions specified by the magnetization, and we characterize the structure of the spectrum by individual contributions. We analyze the size dependence of each contribution individually by extending the moment method introduced by M. Brockman et al. to each component, and we find that the mean of each peak approaches the paramagnetic resonance point with 1/N1/N1/N (where NNN is the length of the chain), which indicates that the separation of the peaks of the double-peak structure also vanishes inversely with the system size. We also study the temperature dependence of the structure. At low temperatures, the spectrum has a single peak with a finite width at a position with a finite shift from the frequency of EPR, as pointed out by the analysis of field-theoretical works [M. Oshikawa and I. Affleck, Phys. Rev. Lett. 82, 5136 (1999)]. The study of the temperature dependence of the spectrum shows how the high-temperature spectrum changes to the low-temperature one with a drastic broadening of the spectrum.
We analyze the absorption of microwaves by the Heisenberg-Ising chain combining exact calculations, based on the integrability of the model, with numerical calculations. Within linear response theory, the absorbed intensity is determined by the imaginary part of the dynamical susceptibility. The moments of the normalized intensity can be used to define the shift of the resonance frequency induced by the interactions and the linewidth independently of the shape of the spectral line. These moments can be calculated exactly as functions of temperature and strength of an external magnetic field, as long as the field is directed along the symmetry axis of the chain. This allows us to discuss the linewidth and the resonance shift for a given magnetic field in the full range of possible anisotropy parameters. For the interpretation of these data, we need a qualitative knowledge of the line shape, which we obtain from fully numerical calculations for finite chains. Exact analytical results on the line shape are out of reach of current theories. From our numerical work, we could extract, however, an empirical parameter-free model of the line shape at high temperatures, which is extremely accurate over a wide range of anisotropy parameters, and is exact at the free-fermion and isotropic points. Another prediction of the line shape can be made in the zero-temperature and zero magnetic field limits, where the sufficiently anisotropic model shows strong absorption. For anisotropy parameters in the massive phase, we derive the exact two-spinon contribution to the spectral line. From the intensity sum rule, it can be estimated that this contribution accounts for more than 80% of the spectral weight if the anisotropy parameter is moderately above its value at the isotropic point.
The field and temperature dependence of the line shape of ESR for strongly interacting quantum spin systems would provide various important informations for the magnetic interaction. We have introduced a method of direct numerical estimation of the dynamical susceptibility with the Kubo formula and applied it to spin systems of various lattice structures. There the ESR line shape shows significant dependence on the strength of the field, and also on the geometrical situation among the directions of the fields and lattice axes.
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.