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Spin-reorientation critical dynamics in the two-dimensional XY model with a domain wall

X. W. Lei, N. J. Zhou, Y. Y. He, and B. Zheng
Phys. Rev. E 99, 022129 – Published 19 February 2019
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  • INTRODUCTION
  • MODEL AND SCALING ANALYSIS
  • MONTE CARLO SIMULATION
  • THEORETICAL ANALYSIS
  • CONCLUSION
  • ACKNOWLEDGMENTS
    • References

    Abstract

    In recent years, static and dynamic properties of non-180∘ domain walls in magnetic materials have attracted a great deal of interest. In this paper, spin-reorientation critical dynamics in the two-dimensional XY model is investigated with Monte Carlo simulations and theoretical analyses based on the Langevin equation. At the Kosterlitz-Thouless phase transition, the dynamic scaling behaviors of the magnetization and the two-time correlation function are carefully analyzed, and critical exponents are accurately determined. When the initial value of the angle between adjacent domains is slightly lower than π, a critical exponent is introduced to characterize the abnormal power-law increase of the magnetization in the horizontal direction inside the domain interface, which is measured to be ψ=0.0568(8). In addition, the relation ψ=η/2z is analytically deduced from the Langevin dynamics in the long-wavelength approximation, well consistent with numerical results.

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    • Received 22 November 2018

    DOI:https://doi.org/10.1103/PhysRevE.99.022129

    ©2019 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Critical phenomenaNonequilibrium statistical mechanics
    1. Techniques
    Langevin equationMonte Carlo methodsXY model
    Statistical Physics & Thermodynamics

    Authors & Affiliations

    X. W. Lei1, N. J. Zhou2,*, Y. Y. He3, and B. Zheng3,4,†

    • 1Institute of Electronic Information and Automation, Aba Teachers University, Wenchuan 623002, People's Republic of China
    • 2Department of Physics, Hangzhou Normal University, Hangzhou 311121, People's Republic of China
    • 3Department of Physics, Zhejiang University, Hangzhou 310027, People's Republic of China
    • 4Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, People's Republic of China

    • *zhounengji@hznu.edu.cn
    • †zhengbo@zju.edu.cn

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    Issue

    Vol. 99, Iss. 2 — February 2019

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    Images

    • Figure 1
      Figure 1

      The initial spin configuration of a semiordered state is shown for the two-dimensional XY model. Spins of both sides form an angle of 2ϕ∈[0,π]. The vertical and horizontal components of the spins, shown in the enlargement of two arrows on the right, are denoted by S⊥ and S∥, respectively.

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    • Figure 2
      Figure 2

      Time evolution of magnetization (M∥,M⊥) starting from the semiordered state with the angle 2ϕ=0.988π on a double-log scale. Dashed lines show the power-law fits. The circles represent a power-law correction M∥∼tψ(1+c/t) to scaling, with ψ=0.0568 as a result.

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    • Figure 3
      Figure 3

      The horizontal component of magnetization M∥(t,x) is plotted as a function of the time t on a double-log scale for the initial states with the angle 2ϕ=0.8π in (a) and 0.5π in (b). The dashed lines show the power-law fits.

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    • Figure 4
      Figure 4

      The scaling functions M∥(t,x)ξ(t)−ψz with respect to x/ξ(t) in (a) and C(t′,t,x)ξ(t′)η with a fixed s′=ξ(t′)/x as a function of ξ(t)/ξ(t′) in (b) on a double-log scale. The initial states with the angle 2ϕ=0.998π are prepared, and data collapse for different x and t′ is observed when the correction to the scaling defined in Eq. (12) is considered for the correlation length ξ(t). Dashed lines show the power-law fits.

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    • Figure 5
      Figure 5

      Theoretical results of the horizontal magnetization M∥(t,x) from analytical calculations based on the Langevin dynamics, as shown in Eqs. (34) and (43), are plotted at the angles 2ϕ=0.50π in (a) and 0.988π in (b), respectively, for various values of x as a function of the time t on a log-log scale. The dashed lines represent the power-law fits.

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