Antiferromagnetic Barkhausen noise induced by weak random-field disorder

TL;DR

The paper addresses field-driven magnetisation reversal in a three-dimensional antiferromagnetic Ising system with weak quenched random fields, analyzed at low temperature. Using zero-temperature, adiabatically driven dynamics on a $3$D lattice with Gaussian random fields of width $f$ and parallel updates, the authors characterize the resulting AF-BHN and associated avalanches through multifractal and cyclical-trend analyses. They report six hysteresis plateaus and seven peaks per branch linked to local clusters of spins with specific flipped-neighbour counts, with avalanches displaying a two-slope, SOC-like size distribution and a disorder-dependent scaling collapse; the dominant avalanche exponent is $\tau_s \approx 1$. The findings reveal a geometry-driven, self-organised criticality in weakly disordered antiferromagnets that is markedly different from ferromagnetic RFIM behavior and bears relevance to experiments on disordered ferrimagnets and quantum Barkhausen noise, highlighting active geometric regions as the key to universal dynamics.

Abstract

This study numerically investigates magnetisation reversal processes driven by an external magnetic field in three-dimensional antiferromagnetic spin models with weak random field disorder. Considering an extremely weak disorder and low temperature, we observe a step-wise hysteresis loop and the appearance of short magnetisation bursts of a characteristic triangular shape; the number of bursts increases with disorder, indicative of Barkhausen-type noise. These phenomena are attributed to the simultaneous reversal at a given external field of segments composed of spins with identical neighbourhoods. A local random field orients one or more spin neighbours, resulting in small, ferromagnetic-like clusters distributed throughout the system. As disorder increases, these clusters may merge to form a labyrinthine structure within the antiferromagnetic background, facilitating brief avalanche propagation. The results demonstrate that, compared with familiar random-field ferromagnets, the observed antiferromagnetic Barkhausen noise and the related avalanche sequence have a profoundly different structure, organised into peaks associated with the transition between magnetisation plateaus. They exhibit prominent cyclical trends and disorder-dependent multifractal fluctuations, with the singularity spectrum quantifying the degree of disorder. The activity avalanches exhibit scale invariance resembling that recently found in experiments with disordered ferr\textit{i}magnets and martensites, as well as in quantum Barkhausen noise, which are associated with active geometric regions rather than individual-spin dynamics. The observed scaling behaviour is interpreted in terms of self-organised critical dynamics.

Figures (4)

• Figure 1: (a) The hysteresis loop $M$ vs $H$ for the antiferromagnetic system with a weak random-field disorder $f=0.01$, showing the magnetisation plateaus and the changing transition regions between them for slightly increased disorder $f=0.1$. (b) The appearance of magnetisation bursts $n_t$ for very low disorder $f=0.01$, and the magnetisation evolution along the descending and ascending hysteresis branches $M_t$ (normalised to fit the scale). (c) The hysteresis loops for different disorder $f$, indicated in the legend, and fixed probability $p=0.95$. The inset (d) shows how the hysteresis loop for fixed disorder $f=0.3$ changes when $p$ is varied from 0.995 (inner line), to 0.9 (middle line) and 0.8 (outer line).
• Figure 2: The Barkhausen noise signal $n_t$ vs time $t$ recorded during the whole hysteresis loop for varied disorder $f=$ 0.04, 0.3, and 0.5 (bottom to top panel), exhibiting seven peaks along each branch, but with different scales and durations. From left to right, seven peaks correspond to the reversal of the system's segments comprising of spins with $k=0,1,2,\cdots 6$ reversed nearest neighbour spins, leading to the magnetisation steps along the ascending branch at the external field $H_t^{ca}$ indicated in the Table \ref{['tab:fmclusters']}. Similarly, the following seven peaks are observed at these fields in the reversed order along the descending branch.
• Figure 3: (a) The main panel shows the AF-BHN signal for $f=0.1$ exhibiting characteristic groups of different sizes registered at the descending branch of the hysteresis loop; inset shows a close-up view of the signal between the second and third peak and its trend, indicated by dashed line. (b) The fluctuation function $F_q(n)$ vs. time interval $n$ of the whole loop signal's trend; each line corresponds to a different $q\in[-4.5,4.5]$, every second line is shown for better vision; the thick straight lines indicate the scaling region where the generalised Hurst exponent is determined. The inset shows the corresponding singularity spectrum $\Psi(\alpha )$ vs $\alpha$. (c) The main panel shows the sequence of avalanche sizes for $f=0.3$ (black line) and its cyclical trend (red line). Inset: the singularity spectrum $\Psi(\alpha)$ vs $\alpha$ of the avalanche-sequence trend for three values of the random-field disorder indicated in the legend.
• Figure 4: (a) Main panel shows the differential distributions $P(s)$ of the avalanche sizes $S$ obtained from magnetisation bursts along the entire hysteresis loop for different disorder strength $f$, indicated in the legend; each line is fitted by the function (\ref{['eq:gx']}) with appropriate parameters. Inset: the scaling collapse of these distributions according to the expression (\ref{['eq:scaling']}), with the corresponding average value $<S>$ of the avalanche size. Fit line by the expression (\ref{['eq:gx']}) with parameters $a_1=12,a_2=10, h=0.2,d=0.9, c=1.8, \kappa=0.65,\sigma=1.3$. (b) Sample-averaged cumulative distribution of the avalanche size (longer lines) and duration (shorter lines with the same symbol) collected along the ascending hysteresis branch for varied disorder $f$, indicated in the legend. The whole curve fit, shown by thick full line for $P(S)$ at weak disorder, gives the exponent $\tau_s-1=0.09$ and approximately the same slopes indicated by dashed lines apply for the straight segments of the curves at larger disorder, but their cut-offs are no longer exponential. Similarly, for the duration distribution we have $\tau_T-1=0.15$. Inset: average avalanche size of a given duration $<S>_T$ vs duration $T$ for all recorded avalanches; the scaling with the exponent $\gamma_{sT}\approx 1.9$ applies only in the intermediate durations.