History-induced critical behavior in disordered systems

Barkhausen noise as found in magnets is studied both with and without long-range (LR) demagnetizing fields using the nonequilibrium, zero-temperature random-field Ising model. Two distinct subloop behaviors arise and are shown to qualitatively agree with experiments on thin film magnets and soft ferromagnets. With LR fields present subloops resemble a self-organized critical system, while their absence results in subloops that reflect the critical point seen in the saturation loop as the system disorder is changed. In the former case, power law distributions of noise appear in subloops, while in the latter case history-induced critical scaling is studied in avalanche size distributions and their second moments as well as spin-flip correlation functions.

Figure 1

Hysteresis loops with concentric inner subloops for (a) RFIM with ${240}^3$ spins, $J_{\mathrm{LR}}=0.25$, and $R=1.8$, (b) RFIM with ${240}^3$ spins, $J_{\mathrm{LR}}=0$, and $R=2.7$, (c) a $\mathrm{Co}∕\mathrm{Pt}$ multilayer thin film measured in a MOKE setup, and (d) a CoPtCrB alloy thin film measured using an AGM.

Figure 2

Experimental avalanche size distributions for subloops of a soft ferromagnet. The three subloops analyzed are shown in the inset, with the largest corresponding to the saturation loop. The distributions were extracted from a window of width $\Delta H\approx 20\mathrm{A}∕\mathrm{m}$ which started near $H=0\mathrm{A}∕\mathrm{m}$. A power law of $-1.75$ is shown by the offset, dash-dot line.

Figure 3

Integrated spin-flip correlation functions for ${480}^3$ systems at $R=2.198$ and averaged over 20 random seeds. The inset contains a collapse of the three respective distributions, yielding $d+{\beta }_l∕{\nu }_l=3.0\pm 0.2$ and $1∕{\nu }_f=1.28\pm 0.40$ with $H_{{\mathit{max}}_c}=1.427$.