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Modulational Instability and Quantum Local Modes in Easy-Axis Ferromagnetic Chains with the Dzyaloshinskii-Moriya Interaction

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Abstract

A theoretical work on modulational instability and quantum local breather modes in a one-dimensional easy-axis Heisenberg ferromagnetic spin lattice with the Dzyaloshinskii-Moriya interaction is completed in the Hartree approximation. By means of the discrete modulational instability analysis, we discuss the influence of the Dzyaloshinskii-Moriya interaction on modulational instability regions and predict the presence condition for the bright stationary localized solution. We find that that the region of the modulational instability moves to the left of the Brillouin zone because of the introduction of the Dzyaloshinskii-Moriya interaction, which is a new finding. Moreover, we get the analytical bright stationary localized solution and analyze the influence of the on-site easy-axis anisotropy and the Dzyaloshinskii-Moriya interaction on their appearance conditions. By the use of such bright stationary localized single-boson wave functions, we construct the quantum breather state that has obvious quantum properties. In addition, the role of the easy-axis anisotropy and the Dzyaloshinskii-Moriya interaction on quantum breather modes is discussed.

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Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grant No. 11604121, the Scientific Research Fund of Hunan Provincial Education Department under Grant No. 16B210, and the Natural Science Fund Project of Hunan Province under Grant No. 2017JJ3255.

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  1. College of Physics, Mechanical and Electrical Engineering, Jishou University, Jishou, 416000, Hunan, China

    Bing Tang

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Tang, B. Modulational Instability and Quantum Local Modes in Easy-Axis Ferromagnetic Chains with the Dzyaloshinskii-Moriya Interaction. Int J Theor Phys 56, 2310–2324 (2017). https://doi.org/10.1007/s10773-017-3384-9

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  • DOI: https://doi.org/10.1007/s10773-017-3384-9

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