Domain wall dynamics and Barkhausen jumps in thin-film permalloy microstructures

Domain wall jump-amplitude and velocity distributions associated with Barkhausen jumps in a 300-{}-thick thin-film permalloy and a 200×2000.3em0ex(μm)²×220--thick permalloy sample microstructrue are measured using a high-speed magneto-optic Kerr effect polarimeter. The jump-amplitude and velocity distributions are obtained for applied-field sweep rates from 0.90.3em0exOe∕s to 6.3×10⁴0.3em0exOe∕s. The velocity distributions exhibit statistical properties consistent with the stochastic description of field-driven domain wall motion developed by ABBM [B. Alessandro, C. Beatrice, G. Bertotti, and A. Montorsi, J. Appl. Phys. 68, 2901 (1990)]. Averaged velocity distributions exhibit the expected increase of dynamic coercivity as the sweep rate is increased, and the maximum domain wall velocity measured as a function of the applied field at the stochastic depinning threshold is shown to be governed by the mobility limit imposed by local spin damping. The averaged velocity ⟨ν(H-H₀)⟩ obtained from the distributions is observed to depart from the commonly accepted linear-dependence model, especially at higher drive-field sweep rates. This departure is interpreted as an indication of a sweep-rate-dependent mobility. Sweep-rate-dependent jump-amplitude distributions P(ΔM) versus ΔM are obtained from the Barkhausen effect data. These distributions exhibit power-law behavior with a sharp cutoff at large values of ΔM. Attempts to reconcile the measured jump-amplitude distributions and sweep-rate-dependent exponents with various models of universal scaling are described. Power-law fits to P(ΔM) distributions measured to optimize temporal resolution (required for the velocity-distribution studies) yield a sweep-rate-dependent exponent that varies from β=1.45±0.05 to β=1.0 as $dH∕dt$ is varied from 250.3em0exOe∕s to 6.3×10⁴0.3em0exOe∕s. This range of sweep-rate-dependent β agrees with the ABBM model and is consistent with the sweep-rate dependence exponent rule that predicts linear sweep-rate scaling for the adiabatic value β=3∕2 [R. A. White and K. A. Dahmen, Phys. Rev. Lett. 91, 085702 (2003)]. Additional experiments on both 300-{}-thick continuous films and the same microstructures optimized for ΔM sensitivity yield a more accurate value of β0.3em0ex(β=1.33±0.01), which corresponds to a CZDS model (β=4∕3) [C. Cizeau, S. Zapperi, G. Durin, and H. E. Stanley, Phys. Rev. Lett. 79, 4669 (1997); Phys. Rev. B 58, 6353 (1998)]. Adiabatic limit values of β determined from all of the experiments are definitively outside the range β~1.0 for self-organized criticality in a two-dimensional system [P. Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987)], and also appear to be inconsistent with experimental results for 900 {} Fe films on MgO in which β=1.1 was obtained from rescaled P(ΔM) distributions [E. Puppin, Phys. Rev. Lett. 84, 5415 (2000)]. The sweep-rate dependence of β determined in a system that manifests an adiabatic limit of β that is not equal to $3∕2$ also violates the model of White and Dahman that prohibits sweep-rate-dependent scaling for β=4∕3.