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Intrinsic Localized Modes in Quantum Ferromagnetic XXZ Chains in an Oblique Magnetic Field

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Abstract

A semiclassical study of intrinsic localized spin-wave modes in a one-dimensional quantum ferromagnetic XXZ chain in an oblique magnetic field is presented in this paper. We quantize the model Hamiltonian by introducing the Dyson-Maleev transformation, and adopt the coherent state representation as the basic representation of the system. By means of the method of multiple scales combined with a quasidiscreteness approximation, the equation of motion for the coherent-state amplitude can be reduced to the standard nonlinear Schrödinger equation. It is found that, at the center of the Brillouin zone, when θ < θ c a bright intrinsic localized spin-wave mode appears below the bottom of the magnon frequency band and when θ > θ c a dark intrinsic localized spin-wave resonance mode can occur above the bottom of the magnon frequency band. In other words, the switch between the bright and dark intrinsic localized spin-wave modes can be controlled via varying the angle of the magnetic field. This result has potential applications in quantum information storage. In addition, we find that, at the boundary of the Brillouin zone, the system can only produce a dark intrinsic localized spin-wave mode, whose eigenfrequency is above the upper of the magnon frequency band.

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References

  1. Q., Loh, K.P.: Graphene mode locked, wavelengthtunable, dissipative soliton fiber laser. Appl. Phys. Lett. 96, 111112 (2010)

    Article  ADS  Google Scholar 

  2. Zhao, C., Zou, Y., Chen, Y., Wang, Z., Lu, S., Zhang, H., Wen, S., Tang, D.: Wavelength-tunable picosecond soliton fiber laser with topological insulator: Bi2Se3 as a mode locker. Opt. Express 20, 27888–27895 (2012)

    Article  ADS  Google Scholar 

  3. Lü, X., Tian, B.: Novel behavior and properties for the nonlinear pulse propagation in optical fibers. Europhys. Lett. 97, 10005 (2012)

    Article  Google Scholar 

  4. Lü, X., Peng, M.: Systematic construction of infinitely many conservation laws for certain nonlinear evolution equations in mathematical physics. Commun. Nonlinear Sci. Numer. Simul. 18, 2304–2312 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  5. Lü, X., Peng, M.: Nonautonomous motion study on accelerated and decelerated solitons for the variablecoefficient Lenells-Fokas model. CHAOS 23, 013122 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  6. Lü, X., Peng, M.: Painlevé-integrability and explicit solutions of the general two-coupled nonlinear Schrödinger system in the optical fiber communications. Nonlinear Dyn. 73, 405 (2013)

    Article  MATH  Google Scholar 

  7. Liu, W.J., Tian, B., Zhen, H.L., Jiang, Y.: Analytic study on solitons in gas-filled hollow-core photonic crystal fibers. Europhys. Lett. 100, 64003 (2012)

    Article  ADS  Google Scholar 

  8. Liu, W.J., Tian, B., Zhang, H.Q., Xu, T., Li, H.: Solitary wave pulses in optical fibers with normal dispersion and higher-order effects. Phys. Rev. A 79, 063810 (2009)

    Article  ADS  Google Scholar 

  9. Flach, S., Gorbach, A.V.: Discrete breathers – advances in theory and applications. Phys. Rep. 467, 1–116 (2008)

    Article  ADS  MATH  Google Scholar 

  10. Sievers, A.J., Takeno, S.: Intrinsic localized modes in anharmonic crystals. Phys. Rev. Lett. 61, 970–973 (1988)

    Article  ADS  Google Scholar 

  11. Takeno, S., Kisoda, K., Sievers, A. J.: Intrinsic localized vibrational modes in anharmonic crystals. Prog. Theo. Phys. Supp. 94, 242–269 (1988)

    Article  ADS  Google Scholar 

  12. Page, J. B.: Asymptotic solutions for localized vibrational modes in strongly anharmonic periodic systems. Phys. Rev. B 41, 7835–7838 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  13. Sandusky, K.W., Page, J.B.: Schmidt K E. Stability and motion of intrinsic localized modes in nonlinear periodic lattices. Phys. Rev. B 46, 6161–6168 (1990)

    Article  ADS  Google Scholar 

  14. Flytzanis, N., Malomed, B.A., Neuper, A.: Odd and even intrinsic modes in diatomic nonlinear lattices. Physcia D 113, 191–195 (1998)

    Article  ADS  Google Scholar 

  15. Bickham, S.R., Sievers, A.J.: Intrinsic localized modes in a monatomic lattice with weakly anharmonic nearest-neighbor force constants. Phys. Rev. B 43, 2339–2346 (1991)

    Article  ADS  Google Scholar 

  16. Yoshimura, K., Watanbe, S.: Envelope soliton as an intrinsic localized mode in a one-dimensional nonlinear lattice. J. Phys. Soc. Jpn. 60, 82–87 (1991)

    Article  ADS  Google Scholar 

  17. Huang, G.X., Shi, Z.P., Xu, Z.X.: Asymmetric intrinsic localized modes in a homogeneous lattice with cubic and quartic anharmonictity. Phys. Rev. B 47, 14561–14564 (1993)

    Article  ADS  Google Scholar 

  18. Mackay, R.S., Aubry, S.: Proof of existence of breathers for time-reversible or Hamiltonian networks of weakly coupled oscillators. Nonlineaity 7, 1623–1643 (1994)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  19. Sepulchre, J.A., MacKay, R.S.: Localized oscillations in conservative or dissipative networks of weakly coupled autonomous oscillators. Nonlinearity 10, 679–713 (1997)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  20. Yoshimura, K.: Existence and stability of discrete breathers in diatomic Fermi–Pasta–Ulam type lattices. Nonlinearity 24, 293–317 (2011)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  21. Flach, S.: Existence of localized excitations in nonlinear Hamiltonian lattices. Phys. Rev. E 51, 1503–1507 (1995)

    Article  ADS  Google Scholar 

  22. Bose, S.: Quantum communication through an unmodulated spin chain. Phys. Rev. Lett. 91, 207901 (2003)

    Article  ADS  Google Scholar 

  23. Zippilli, S., Grajcar, M., Il’ichev, E., Il’ichev, F.: Simulating long-distance entanglement in quantum spin chains by superconducting flux qubits. Phys. Rev. A 91, 022315 (2015)

    Article  ADS  Google Scholar 

  24. Christandl, M., Datta, N., Ekert, A., Landahl, A.J.: Perfect state transfer in quantum spin networks. Rev. Phys. Lett. 92, 187902 (2004)

    Article  Google Scholar 

  25. Lai, R., Kiselev, S.A., Sievers, A.J.: Intrinsic localized spin-wave resonances in ferromagnetic chains with nearest- and next-nearest-neighbor exchange interactions. Phys. Rev. B 56, 5345–5354 (1997)

    Article  ADS  Google Scholar 

  26. Wallis, R.F., Mills, D.L., Boardman, A.D.: Intrinsic localized spin modes in ferromagnetic chains with on-site anisotropy. Phys. Rev. B 52, R3828—R3831 (1995)

    Article  ADS  Google Scholar 

  27. Khalack, J.M., Zolotaryuk, Y., Christiansen, P.L.: Discrete breathers in classical ferromagnetic lattices with easy-plane anisotropy. CHAOS 13, 683–692 (2003)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  28. Rakhmanova, S.V., Shchegrov, A.V.: Intrinsic localized modes of bright and dark types in ferromagnetic Heisenberg chains. Phys. Rev. B 57, R14012—R14015 (1998)

    Article  ADS  Google Scholar 

  29. Kim, S.W., Kim, S.: Internal localized eigenmodes on spin discrete breathers in antiferromagnetic chains with on-site easy-axis anisotropy. Phys. Rev. B 66, 212408 (2002)

    Article  ADS  Google Scholar 

  30. Lai, R., Kiselev, S.A., Sievers, A.J.: Intrinsic localized spin-wave modes in antiferromagnetic chains with single-ion easy-axis anisotropy. Phys. Rev. B 54, R12665—R12668 (1996)

    Article  ADS  Google Scholar 

  31. Takeno, S., Kawasaki, K.: Intrinsic self-localized magnons in one-dimensional antiferromagnets. Phys. Rev. B 45, 5083–5086 (1992)

    Article  ADS  Google Scholar 

  32. Huang, G., Xu, Z., Xu, W.: Magnetic gap solitons as the intrinsic self-localized magnons in Heisenbergantiferromagnetic chain. J. Phys. Soc. Jpn. 62, 3231–3238 (1993)

    Article  ADS  Google Scholar 

  33. Tang, B., Li, D. J., Hu, K., Tang, Y.: Intrinsic localized modes in quantum ferromagnetic Ising-Heisenberg chains with single-ion uniaxial anisotropy. Int. J. Mod. Phys. B 27, 1350139 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  34. Lu, J., Zhou, L., Kuang, L. M., Sun, C.P.: Controlling soliton excitations in Heisenberg spin chains through the magic angle. Phys. Rev. E 79, 016606 (2009)

    Article  ADS  Google Scholar 

  35. Dyson, F.J.: General theory of spin-wave interactions. Phys. Rev. 102, 1217–1230 (1956)

    Article  ADS  MathSciNet  Google Scholar 

  36. Dyson, F.J.: Thermodynamic behavior of an ideal ferromagnet. Phys. Rev. 102, 1230–1244 (1956)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  37. Glauber, R.J.: Coherent and incoherent states of the radiation field. Phys. Rev. 131, 2766–2788 (1963)

    Article  ADS  MathSciNet  Google Scholar 

  38. Smith, H.: Introduction to quantum mechanics. Singapore, Proceedings World Scientific, p. 108 (1991)

  39. Yoshimura, K., Watanabe, S.: Envelope soliton as an intrinsic localized mode in a one-dimensional nonlinear lattice. J. Phys. S.c. Spn. 60, 82–87 (1991)

    ADS  Google Scholar 

  40. Remoissenet, M.: Waves called solitons. Concepts and experiments, 2nd edn., pp. 238–239. Springer (1996)

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Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grant No. 11264012.

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

    De-Jun Li

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  1. De-Jun Li
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Li, DJ. Intrinsic Localized Modes in Quantum Ferromagnetic XXZ Chains in an Oblique Magnetic Field. Int J Theor Phys 55, 1201–1210 (2016). https://doi.org/10.1007/s10773-015-2761-5

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  • DOI: https://doi.org/10.1007/s10773-015-2761-5

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