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Dynamical Spin Structure Factors of Anisotropic Spin Ladder in a Longitudinal Magnetic Field

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Abstract

We have addressed the magnetic excitations of quasi-one-dimensional two-leg anisotropic antiferromagnetic spin ladder under the influence of longitudinal magnetic field. Such excitations can be obtained via the study of frequency behavior of dynamical spin structure factors. The original spin model hamiltonian can be transformed to a hard core bosonic gas using a generalized bond operator formalism. We have used the linear response theory within Green’s function approach to obtain the frequency behavior of both longitudinal and transverse dynamical spin structure factor in the gapful regime. The results show energy gap vanishes at critical magnetic field which depends on anisotropic parameters. We have also found the longitudinal spin structure factor shows a sharp single peak at a particular frequency. The position of this peak moves to lower frequencies with increase of both intersite and local anisotropy parameters. However, the effect of intersite anisotropy on the position of peak in the longitudinal structure factor is more remarkable compared to another one. Also the change of magnetic field shows no considerable effect on the behavior of longitudinal spin structure factor. Furthermore, we have studied the dependence of the transverse structure factor on frequency for different magnetic field and anisotropy parameters. Unlike longitudinal case, two separate peaks appears in the transverse spin structure. The enhancement of magnetic field causes that the peaks in the transverse structure factor become far away from each other. Also, the influences of both anisotropies on the spin excitation spectrum of transverse spin components have been discussed.

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Authors and Affiliations

  1. Physics Department, Razi Univerity, Kermanshah, Iran

    H. Rezania

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  1. H. Rezania
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Correspondence to H. Rezania.

Appendix: Excitation Spectrum, Quasiparticle Weight, and Bogoliuobov Coefficients

Appendix: Excitation Spectrum, Quasiparticle Weight, and Bogoliuobov Coefficients

In this appendix, we present the final results for excitation spectrums and residue of quasiparticle excitation and Bogoliubov coefficients as

$$\begin{array}{@{}rcl@{}} {\Omega}(k)&=&\sqrt{(\frac{h}{2})^{2}+Z_{+}(k)Z_{-}(k)[(A_{k}+{\Sigma}_{n,+}(k,0)+g\mu_{B}B)(A_{k}+{\Sigma}_{n,-}(k,0)-g\mu_{B}B)-{B_{k}^{2}}]},\\ {\Omega}_{+(-)}(k)&=&+(-)\frac{h}{2}+{\Omega}(k), \\ h&\equiv&{\Sigma}_{n,+}(k,0)Z_{+}(k)-{\Sigma}_{n,-}(k,0)Z_{-}(k)-A_{k}(Z_{-}(k)-Z_{+}(k))\\&+&g\mu_{B}B(Z_{-}(k)+Z_{+}(k)), \\ {\Omega}_{k,z}&=&Z_{k,z}\sqrt{[A_{k,z}+{\Sigma}_{n,z}(k,0)]^{2}-[B_{k,z}]^{2}},\\ Z_{k,z}^{-1}&=&1-(\frac{\partial {\Sigma}(k,\omega)_{n,z}}{\partial \omega})_{\omega=0},\\ Z_{k,+(-)}^{-1}&=&1-(\frac{\partial {\Sigma}(k,\omega)_{+(-)}}{\partial \omega})_{\omega=0},\\ U_{k,z}^{2} (V_{k,z}^{2})&=&(-)\frac{1}{2}+\frac{Z_{k,z}[A_{k,z}+{\Sigma}_{n,z}(k,0)]}{2{\Omega}_{k,z}},\\U_{k,+(-)}^{2} &=&\frac{Z_{-(+)}(k,0)\left(A_{k}+{\Sigma}_{n,-(+)}(k,0)-(+)g\mu_{B}B\right)+(-)\frac{h}{2}+{\Omega}_{k}}{2{\Omega}_{k}}\\ V_{k,+(-)}^{2}&=&\frac{Z_{-(+)}(k,0)\left(A_{k}+{\Sigma}_{n,-(+)}(k,0)-(+)g\mu_{B}B\right)+(-)\frac{h}{2}-{\Omega}_{k}}{2{\Omega}_{k}} \end{array} $$
(B1)

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Rezania, H. Dynamical Spin Structure Factors of Anisotropic Spin Ladder in a Longitudinal Magnetic Field. J Supercond Nov Magn 29, 2127–2139 (2016). https://doi.org/10.1007/s10948-016-3525-z

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  • DOI: https://doi.org/10.1007/s10948-016-3525-z

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