Creep motion of a domain wall in the two-dimensional random-field Ising model with a driving field

Dong, Rui; Zheng, Bo; Zhou, N. J.

doi:10.1209/0295-5075/98/36002

Cited by 12 publications

(11 citation statements)

References 50 publications

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“…Here φ xy (t) denotes the field at site (x, y). We may also map φ xy to a Ising spin, i.e., S xy = Sgn(φ xy ), and then define the height function as in the DRFIM model [15,18]. Our simulations show that after a microscopic time scale t mic , these two definitions yield the same results.…”

Section: P-1mentioning

confidence: 91%

“…To understand the domain-wall motion at a microscopic level, one may build lattice models based on microscopic structures and interactions. Very recently, with Monte Carlo simulations, the depinning transition and relaxation-to-creep transition have been carefully examined in the two-dimensional (2D) random-field Ising model with a driving field (DRFIM) [15][16][17][18]. The results indicate that the QEW equation and DRFIM model are not in a same universality class, mainly due to the presence of overhangs and islands in the DR-FIM model.…”

mentioning

confidence: 99%

“…In fact, ω 2 b (t) quickly stabilizes to a constant. Thus, for a sufficiently large lattice, the pure roughness function should scale as [15,18,31,32] Dω…”

mentioning

confidence: 99%

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Hamiltonian equation of motion and depinning phase transition in two-dimensional magnets

Dong

Zheng

Zhou

2012

EPL

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Based on the Hamiltonian equation of motion of the φ 4 theory with quenched disorder, we investigate the depinning phase transition of the domain-wall motion in two-dimensional magnets. With the short-time dynamic approach, we numerically determine the transition field, and the static and dynamic critical exponents. The results show that the fundamental Hamiltonian equation of motion belongs to a universality class very different from those effective equations of motion.

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Section: P-1mentioning

confidence: 91%

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confidence: 99%

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Hamiltonian equation of motion and depinning phase transition in two-dimensional magnets

Dong

Zheng

Zhou

2012

EPL

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“…Thus with the application of sufficiently small amount of field, the motion of domain wall can reach a nonzero mean velocity, which is known as creep motion [10,11,12]. Very recently, the creep motion of domain wall in the two dimensional RFIM was studied (by Monte Carlo simulations) with a driving field [13] and observed field-velocity relationship and estimated the creep exponent.…”

Section: Introductionmentioning

confidence: 99%

Random field Ising model swept by propagating magnetic field wave: Athermal nonequilibrium phasediagram

Acharyya

2013

Journal of Magnetism and Magnetic Materials

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The dynamical steady state behaviour of the random field Ising ferromagnet swept by a propagating magnetic field wave is studied at zero temperature by Monte Carlo simulation in two dimensions. The distribution of the random field is bimodal type. For a fixed set of values of the frequency, wavelength and amplitude of propagating magnetic field wave and the strength of the random field, four distinct dynamical steady states or nonequilibrium phases were identified. These four nonequilibrium phases are characterised by different values of structure factors. State or phase of first kind, where all spins are parallel (up). This phase is a frozen or pinned where the propagating field has no effect. The second one is, the propagating type, where the sharp strips formed by parallel spins are found to move coherently. The third one is also propagating type, where the boundary of the strips of spins is not very sharp. The fourth kind, shows no propagation of strips of magnetic spins, forming a homogeneous distribution of up and down spins. This is disordered phase. The existence of these four dynamical phases or modes depends on the value of the amplitude of propagating magnetic field wave and the strength of random (static) field. A phase diagram has also been drawn, in the plane formed by the amplitude of propagating field and the strength of random field. It is also checked that, the existence of these dynamical phases is neither a finite size effect nor a transient phenomenon. The behaviour of Ising ferromagnet with randomly quenched magnetic field is an active field of modern research. The zero temperature ferro-para transition [1] by the random field, made it more interesting. A simple model was proposed to understand the hysteresis incorporating the return point memory [2] and Barkhausen noise [3]. Later, the statistics [4] and the dynamic critical behaviour [5] of Barkhausen avalanches were studied in random field Ising model (RFIM). The hysteresis loop was exactly determined in one dimensional RFIM [6]. The RFIM was also studied [7] in the Bethe lattice.The dynamics of the domain wall in RFIM is another area of interest in modern research of statistical physics. The motion of domain wall shows very interesting depinning transition at zero temperature. Due to the energy barriers created by disorder (random field), the domain wall is pinned and the motion of the domain wall remains stopped upto a critical field [8,9]. However, at any finite temperature the depinning transition is softened and the thermal fluctuation assists to overcome the energy barrier. Thus with the application of sufficiently small amount of field, the motion of domain wall can reach a nonzero mean velocity, which is known as creep motion [10,11,12]. Very recently, the creep motion of domain wall in the two dimensional RFIM was studied (by Monte Carlo simulations) with a driving field[13] and observed field-velocity relationship and estimated the creep exponent.All the above mentioned studies are done with constant and uniform magnetic field ...

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“…In the DRFIM model, overhangs and islands are created in the dynamic evolution, and the domain wall is not single-valued. Very recently it has been demonstrated that the DRFIM model does not belong to the universality class of the QEW equation, due to the dynamic effect of overhangs and islands [10][11][12], and its results are closer to experiments [13][14][15][16]. The DRFIM model does not suffer from the theoretical self-inconsistence as in the QEW equation, and may go beyond the QEW equation, for example, to describe the relaxation-to-creep transition [16,17].…”

Section: Introductionmentioning

confidence: 99%

Depinning phase transition in the two-dimensional clock model with quenched randomness

2012

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With Monte Carlo simulations, we systematically investigate the depinning phase transition in the two-dimensional driven random-field clock model. Based on the short-time dynamic approach, we determine the transition field and critical exponents. The results show that the critical exponents vary with the form of the random-field distribution and the strength of the random fields, and the roughening dynamics of the domain interface belongs to the new subclass with ζ≠ζ(loc)≠ζ(s) and ζ(loc)≠1. More importantly, we find that the transition field and critical exponents change with the initial orientations of the magnetization of the two ordered domains.

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Creep motion of a domain wall in the two-dimensional random-field Ising model with a driving field

Cited by 12 publications

References 50 publications

Hamiltonian equation of motion and depinning phase transition in two-dimensional magnets

Hamiltonian equation of motion and depinning phase transition in two-dimensional magnets

Random field Ising model swept by propagating magnetic field wave: Athermal nonequilibrium phasediagram

Depinning phase transition in the two-dimensional clock model with quenched randomness

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