Numerical study of magnetic Raman scattering spectra in ladder antiferromagnets

Abstract

Recently, the experiment of Raman scattering in Sr(14-x)Ca(x)Cu24O41 which has an antiferromagnetic ladder with two legs has been reported. In this study, the exchange scattering spectra expressed in terms of continued fractions were calculated for a Heisenberg ladder with antiferromagnetic exchange couplings J(sub r) for the rung and J(sub c) for the leg. The exchange scattering spectra were obtained for the coupling ratio, J(sub c)/J(sub r) = 4/5, 1, and 5/4. The spectra have peaks around 1.2J(sub r) and 2.5J(sub r) and are consistent with the experimental results of Raman spectra. Here the peak position 1.2J(sub r (hereafter called '2-Delta peak') and 2.5J(sub r) (called '5-Delta peak') corresponds to the twice and five times the spin gap Delta. In order to investigate the characteristic behavior of these peaks and Reyleigh scattering in detail, the coupling ratio dependence of scattering intensities was studied for two polarization configurations (zz), and (xx) for the direction along the legs and the rungs, respectively. Here (uv) means the cases that u is the polarization vector of incident lights and v is that of scattered lights. The intensity of 2-Delta peak becomes strong for both cases of J(sub c) much less than J(sub r) and J(sub r) much less than J(sub c), while the intensity of 5-Delta peak has a large value for J(sub r) approximately equal to J(sub c). The reason of the strong intensity of 5-Delta peak in comparison with that of 2-Delta peak is under investigation.

最近、2脚の反強磁性ラダーを持つSr(14-x)Ca(x)Cu24O41についてのラマン散乱の実験が報告された。本研究では、ラングに対しJ(sub r)、レッグに対しJ(sub c)の反強磁性交換結合を持つハイゼンベルグラダーについて、連分数で表された交換散乱スペクトルを数値計算した。結合定数比、J(sub c)/J(sub r)=4/5、1、5/4、に対し交換散乱スペクトルを得た。スペクトルは、1.2J(sub r)と2.5J(sub r)にピークを持ち、ラマンスペクトルの実験結果と一致した。ここで、1.2J(sub r)(以降2-Δピークと呼ぶ)と2.5J(sub r)(5-Δピークと呼ぶ)のピークは、それぞれスピンギャップΔの2倍、5倍に対応する。さらに、これらのピークの振る舞いとレイリー散乱を詳しく調べるために、散乱強度の結合定数比依存性を2種の偏光配位(zz)、(xx)に関して調べた。ここで、(uv)は、uが入射光の、vが散乱光の偏光ベクトルの場合である。どちらの偏光配位に対しても、2Δピークの強度は、J(sub c)<<J(sub r)あるいはJ(sub r)<<J(sub c)で強くなるのに対し、5Δピークの強度は、J(sub c)〜J(sub r)において強くなる結果を得た。5Δのピーク強度は、2Δに比べ強く、理由は、今後の研究課題とした。