Barkhausen Noise from Precessional Domain Wall Motion

The jerky dynamics of domain walls driven by applied magnetic fields in disordered ferromagnets—the Barkhausen effect—is a paradigmatic example of crackling noise. We study Barkhausen noise in disordered $\mathrm{Pt}/\mathrm{Co}/\mathrm{Pt}$ thin films due to precessional motion of domain walls using full micromagnetic simulations, allowing for a detailed description of the domain wall internal structure. In this regime the domain walls contain topological defects known as Bloch lines which repeatedly nucleate, propagate, and annihilate within the domain wall during the Barkhausen jumps. In addition to bursts of domain wall propagation, the in-plane Bloch line dynamics within the domain wall exhibits crackling noise and constitutes the majority of the overall spin rotation activity.

Figure 1

$v_{\mathrm{DW}}$ as a function of $B_{\text{ext}}$ in a perfect strip and in a disordered system where the disorder strength $r$ has been tuned to roughly match the $v_{\mathrm{DW}}(B_{\text{ext}})$ curve with the experimental one of Ref. [19]; the disorder-induced depinning field exceeds the Walker field of the perfect strip. Inset: Example snapshot of a rough DW containing BLs in the disordered system with $B_{\text{ext}}=17\mathrm{mT}$.

Figure 2

(a) An example of a sequence of DW magnetization configurations in between successive avalanches (as defined by thresholding the $v_{\mathrm{DW}}$ signal); the DW is moving to the $+x$ direction. The corresponding crackling noise signals, with (b) the DW velocity $v_{\mathrm{DW}}(t)$, (c) the in-plane activity $A_{xy}(t)$, and (d) the out-of-plane activity $-A_z(t)$.

Figure 3

Distribution of the in-plane magnetization angle ${\varphi }_{\text{initial}}$ of the DW segments where avalanches are initiated versus the corresponding distribution of ${\varphi }_{\mathrm{DW}}$ for all DW segments. The two distributions look almost identical, suggesting that the presence or absence of BLs within the DW is not important for the avalanche triggering process.

Figure 4

Distributions of the avalanche sizes obtained by thresholding (a) the $A_z(t)$ signal and (b) the $A_{xy}(t)$ signal. The corresponding avalanche duration distributions are shown in (c) and (d), respectively. Different threshold values ($A_z^{\mathrm{th}}$ and $A_{xy}^{\mathrm{th}}$, respectively) considered are indicated in the legends. The insets in (a) and (c) show the corresponding avalanche size and duration distributions computed from the $v_{\mathrm{DW}}(t)$ signal using $v_{\mathrm{DW}}^{\mathrm{th}}=0.1\mathrm{m}/\mathrm{s}$. Solid lines correspond to fits of power laws terminated by a large-avalanche cutoff (see text), while the dashed lines show the fitted power-law exponent in each case.

Figure 5

Scaling of the average avalanche size as a function of duration for different threshold values: (a) $⟨S_v(T)⟩$, (b) $⟨S_{A_z}(T)⟩$, and (c) $⟨S_{A_{xy}}(T)⟩$. The insets in (a) and (c) illustrate the threshold-dependent nature of the exponent $\gamma$ characterizing the size versus duration scaling.