Dynamical implications of sample shape for avalanches in 2-dimensional random-field Ising model with saw-tooth domain wall

Abstract

We study dynamics of a built-in domain wall (DW) in 2-dimensional disordered ferromagnets with different sample shapes using random-field Ising model on a square lattice rotated by 45 degrees. The saw-tooth DW of the length L x is created along one side and swept through the sample by slow ramping of the external field until the complete magnetisation reversal and the wall annihilation at the open top boundary at a distance L y . By fixing the number of spins N = L x × L y = 10 6 and the random-field distribution at a value above the critical disorder, we vary the ratio of the DW length to the annihilation distance in the range L x /L y ∈ [1/16, 16]. The periodic boundary conditions are applied in the y-direction so that these ratios comprise different samples, i.e., surfaces of cylinders with the changing perimeter L x and height L y . We analyse the avalanches of the DW slips between following field updates, and the multifractal structure of the magnetisation fluctuation time series. Our main findings are that the domain-wall lengths materialised in different sample shapes have an impact on the dynamics at all scales. Moreover, the domain-wall motion at the beginning of the hysteresis loop (HLB) probes the disorder effects resulting in the fluctuations that are significantly different from the large avalanches in the central part of the loop (HLC), where the strong fields dominate. Specifically, the fluctuations in HLB exhibit a wide multi-fractal spectrum, which shifts towards higher values of the exponents when the DW length is reduced. The distributions of the avalanches in this segments of the loops obey power-law decay and the exponential cutoffs with the exponents firmly in the mean-field universality class for long DW. In contrast, the avalanches in the HLC obey Tsallis density distribution with the power-law tails which indicate the new categories of the scale invariant behaviour for different ratios L x /L y . The large fluctuations in the HLC, on the other hand, have a rather narrow spectrum which is less sensitive to the length of the wall. These findings shed light to the dynamical criticality of the random-field Ising model at its lower critical dimension; they can be relevant to applications of the dynamics of injected domain walls in two-dimensional nanowires and ferromagnetic films.

Barkhausen Noise from Precessional Domain Wall Motion

“…close to the values expected for the quenched Edwards Wilkinson (qEW) equation, ∂h(x, t)/∂t = ν∇ 2 h(x, t) + η(x, h) + F ext , describing a short-range elastic string h(x, t) driven by an external force F ext in a quenched random medium η [29]. The value of the τ S exponent is also close to that found very recently for "creep avalanches" [30], and to that describing avalanches in the central hysteresis loop in a 2D RFIM with a built-in DW [31]. The cutoff avalanche size and duration depend on the imposed threshold level, but appear to saturate to a value set by the "demagnetizing factor" k in the limit of a low threshold.…”

The critical Barkhausen avalanches in thin random-field ferromagnets with an open boundary

“…The signals exhibit long-range temporal correlations with the power spectrum over an extended range of frequencies f . The previous studies of the multifractal features of the BHN in 2D and bulk samples in a strong disorder regime 19,36 , suggest that the signal shape differs in different segments of the hysteresis loop. Here, we demonstrate how the size and temporal correlations of the signal change along the hysteresis loop in the 3D sample at the critical disorder, see Fig.…”

“…Hence, there is an increased interest in the experimental investigations of the Barkhausen noise (BHN) accompanying the magnetisation reversal along the hysteresis loop in nanowires [6], thin films [7][8][9][10][11][12][13][14], and systems with a finite thickness [15,16]. On the other hand, theoretical and numerical investigations of the impact of the specific sample shape on the magnetisation reversal processes are still in their infancy [17][18][19][20]. The domain structure in these materials is primarily related to the intrinsic disorder that contributes to the enhanced stochasticity of the DW motion [21][22][23][24][25], but this remains poorly understood.…”

“…In contrast, much less is known about the structure of such states in finite geometry samples or in the two-dimensional limit, which appears to be the lower critical dimensionality of the field-theory model. Recent numerical investigations [18][19][20]32] indicate a rich dynamical critical behaviour, prone to the impact of geometry and disorder. Therefore, we adopt an adiabatic driving mode, where the field increments adjust to the current minimal local field (see Methods) and focus on the nature of fluctuations in the central part of the hysteresis loop.…”

Self-Organised Critical Dynamics as a Key to Fundamental Features of Complexity in Physical, Biological, and Social Networks

“…They depend on the fractal energy landscape; for example, in the bistable spin systems under the slowly increasing external fields, the spanning avalanches in different dimensions obey different scaling properties [35]. Besides the physical geometry of the sample [36,37], the implicated portion of the phase space plays the role. Thus, the avalanches originating in the centre of the hysteresis loop, when the system is away from the two global minima, have different scaling properties compared to the ones observed at both ends of the loop [36].…”