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Progress of Theoretical Physics

Effect of the Magnetic Field on the des Cloizeaux-Pearson Spin-Wave Spectrum

Norikazu Ishimura, Hiroyuki Shiba

Published Jun 1, 1977• 63 citations
Publisher

Abstract

The des Cloizeaux and Pearson's exact solution for the spin-wave spectrum of the S=1/2 antiferromagnetic Heisenberg chain is extended to the case of finite external field. It reproduces naturally the des Cloizeaux-Pearson spectrum in the zero-field limit as well as the spin-wave spectrum in the ferromagnetic state for fields larger than the critical field. The results are discuessed by comparing them with predictions of other approximate theories.

DOI
10.1143/ptp.57.1862

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Physical review. B, Solid state•Jul 1, 1974•174 citations
The des Cloizeaux and Pearson's exact solution for the spin-wave spectrum of the S=1/2 antiferromagnetic Heisenberg chain is extended to the case of finite external field. It reproduces naturally the des Cloizeaux-Pearson spectrum in the zero-field limit as well as the spin-wave spectrum in the ferromagnetic state for fields larger than the critical field. The results are discuessed by comparing them with predictions of other approximate theories.
The magnetic-field effect on the transverse and longitudinal spin fluctuation spectra is studied for one-dimensional spin 1/2 isotropic Heisenberg antiferromagnet. We perform an exact calculation of dynamical correlation functions for finite-spin chains. The result shows that a large portion of the intensity is concentrated on the des Cloizeaux-Pearson spectrum, which was studied previously for finite-magnetic-field case by the authors (Prog. Theor. Phys. 57 (1977), 1862). This observation is combined with general considerations on dynamical correlation functions. We compare the present theory with Heilmann et al.'s neutron experiment on CuCl2·2NC5D5. A study is made also on the magnetic-field dependence of the static correlation functions. The longitudinal static correlation function in particular shows interesting wave-vector dependence, which is worth investigating experimentally.
The one-dimensional Heisenberg antiferromagnet with 8=1/2 is treated with the use of the Fermi operators and an additional condition that the long-range order is absent.Our spin wave spectrum of a one-dimensional Heisenberg antiferromagnet without longrange order is expressed by andThis is in good agreement with the exact spin wave spectrum role =1!'/2lsin kl which is obtained by des Cloizeaux and Pearson at T=O.Correlation functions <S1S2> and <SlSs> are in good agreement with the exact value at T=O, also.Thermodynamic properties of this system agree with those of Bulaevskii and those of Katsura and Inawashiro. § I. IntroductionThe one-dimensional Heisenberg antiferromagnet has been investigated by many authors.Most of previous theories have been for either zero or infinite temperatures.Recently various experiment on (CD3) 4NMnCl 3 (TMMC)ll requires further theoretical work of a Heisenberg linear-chain magnet for finite temperatures.The experimental results of linear antiferromagnet show that at low temperatures there are long-lived spin waves in spite of the absence of long-range order.At T= 0, the spin wave spectrum, wqoc I sin ql, is gained approximately by Anderson 2 l and exactly by des Cloizeaux and Pearson.8 l Recently Richards, 4 l Scales and Gersh, 5 l Kondo and Yamaji 6 l obtained the spin wave spectrum of linear antiferromagnet at finite temperatures with the use of the second-order Green's function theory.The spin wave spectrum, however, does not show exactly wqoc I sin ql at finite temperatures.
Spectral properties of the spin-1/2 antiferromagnetic Heisenberg chain in a magnetic field are investigated by using exact Bethe-ansatz solutions. We argue that not only quasiparticles called psinon and antipsinon but also a quasiparticle representing a 2-string in the Bethe ansatz plays an important role for dynamical properties in a magnetic field. Combined with psinon and antipsinon, the quasiparticle for a 2-string forms a continuum in the high-energy regime for transverse dynamical structure factor S +− ( κ,ω ). In the zero-field limit, the continuum is located on the mode of the lowest excited states in zero field called the des Cloizeaux-Pearson mode. In a magnetic field, the continuum separates from other low-energy continua, and reduces to the mode of bound states of overturned spins from the fully polarized state near the saturation field. We confirm the relevance through comparisons with available experimental results on the quasi-one-dimensional antiferromagnet CuCl 2 ·2N(C 5 D 5 ).
Exact sum rules are obtained for the nearest-neighbor Heisenberg antiferromagnet and XYX YXY ferromagnet in one dimension. In the Heisenberg case the sum rules may be used to show that most of the spectral weight of the spin correlation function at small kkk and T=0T=0T=0 is concentrated near the frequency of the "des Cloizeaux-Pearson" states. In the XYX YXY case, the corresponding "Schultz-Lieb-Mattis" states only carry a negligible portion of the weight at small kkk.