The study of critical phenomena and universal power laws has been one of the central advances in statistical mechanics during the second half of the past century, explaining traditional thermodynamic critical points 1 , avalanche behaviour near depinning transitions 2,3 and a wide variety of other phenomena 4 . Scaling, universality and the renormalization group claim to predict all behaviour at long length and timescales asymptotically close to critical points. In most cases, the comparison between theory and experiments has been limited to the evaluation of the critical exponents of the power-law distributions predicted at criticality. An excellent area for investigating scaling phenomena is provided by systems exhibiting crackling noise, such as the Barkhausen effect in ferromagnetic materials 5 . Here we go beyond powerlaw scaling and focus on the average functional form of the noise emitted by avalanches-the average temporal avalanche shape 4 . By analysing thin permalloy films and improving the data analysis methods, our experiments become quantitatively consistent with our calculation for the multivariable scaling function in the presence of a demagnetizing field and finite field-ramp rate.The average temporal avalanche shape has been measured for earthquakes 6 and for dislocation avalanches in plastically deformed metals 7,8 , but the primary experimental and theoretical focus has always been Barkhausen avalanches in magnetic systems 5,6,[9][10][11] . Theory and experiment agreed well for avalanche sizes and durations, but the strikingly asymmetric shapes found experimentally in ribbons 11 disagreed sharply with the theoretical predictions, for which the asymmetry in the scaling shapes under time reversal was at most very small 4,6 . (We note that the relevant models are not microscopically time-reversal invariant; temporal symmetry is thus emergent.) Doubts about universality 4 were resolved when eddy currents were shown to be responsible for the asymmetry, at least on short timescales 12 , but the exact form of the asymptotic universal scaling function of the Barkhausen avalanche shape still remained elusive.Here, we report an experimental study of Barkhausen noise in permalloy thin films, where a careful study of the average avalanche shapes leads to symmetric shapes, undistorted by eddy currents (which are suppressed by the sample geometry). We provide a quantitative explanation of the experimental results by solving exactly the mean-field theories for two general models of magnetic reversal: a domain-wall dynamics model 13 Time-series data (jagged line) are traditionally separated into avalanches using a threshold V th set above the instrumental noise (dotted blue line)-here breaking one avalanche into a few pieces. We instead do an optimal Wiener deconvolution (smoothed red curve, see text), allowing the use of a zero threshold (solid black line), which avoids distortions of the average shape and also gives more decades of size and duration scaling. Averaging over all avalanches with this duratio...

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The magnetoimpedance (MI) effect of amorphous Co70.4Fe4.6Si15B10 ribbons, subjected to different annealing conditions with and without an external field, has been measured up to a frequency of 100 kHz. We show that the large MI effect is the result of transverse magnetic anisotropy, which is present in the as-cast and the suitably field-annealed samples.

Magneto-impedance effects have been observed in thin films of amorphous Fe73.5Cu1Nb3Si13.5B9. Large magneto-impedance values have been obtained in field-annealed samples, but not in as-deposited samples. Transverse magneto-impedance effects with magnitudes comparable to the longitudinal case have been observed. These results are discussed in terms of appropriate magnetic permeability.

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