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...

We provide the first quantitative comparison between Barkhausen noise experiments and recent predictions from the theory of avalanches for pinned interfaces, both in and beyond mean field. We study different classes of soft magnetic materials, including polycrystals and amorphous samples-which are characterized by long-range and short-range elasticity, respectively-both for thick and thin samples, i.e., with and without eddy currents. The temporal avalanche shape at fixed size as well as observables related to the joint distribution of sizes and durations are analyzed in detail. Both long-range and short-range samples with no eddy currents are fitted extremely well by the theoretical predictions. In particular, the short-range samples provide the first reliable test of the theory beyond mean field. The thick samples show systematic deviations from the scaling theory, providing unambiguous signatures for the presence of eddy currents.

The magnetoimpedance (MI) effect was investigated in NiFe/Ag multilayered (ML) and ML/SiO 2 /Ag/SiO 2 /ML structured multilayered (SD) ferromagnetic films grown by magnetron sputtering. The MI measurements were performed with an impedance analyzer over a wide frequency range, from 10 MHz to 1.8 GHz. Sample geometries are mainly responsible for the different MI behaviours and by considering the entire frequency range, distinct mechanisms responsible for MI changes were associated. For the ML sample, a maximum value of 80%, associated with the appearance of ferromagnetic resonance (FMR), was reached at around 1 GHz. For the SD sample, the striking feature is the existence of two distinct frequency ranges with high MI% values of 80% at around 100 MHz, related to the skin and magnetoinductive effects, and of 120% at around 1 GHz, associated with the strong skin and FMR effect.

We investigate the magnetization dynamics through the magnetoimpedance effect in ferromagnetic NiFe/Cu/Co films. We observe that the magnetoimpedance response is dependent on the thickness of the non-magnetic Cu spacer material, a fact associated to the kind of the magnetic interaction between the ferromagnetic layers. Thus, we present an experimental study on asymmetric magnetoimpedance in ferromagnetic films with biphase magnetic behavior and explore the possibility of tuning the linear region of the magnetoimpedance curves around zero magnetic field by varying the thickness of the non-magnetic spacer material, and probe current frequency. We discuss the experimental magnetoimpedance results in terms of the different mechanisms governing the magnetization dynamics at distinct frequency ranges, quasi-static magnetic properties, thickness of the non-magnetic spacer material, and the kind of the magnetic interaction between the ferromagnetic layers. The results place ferromagnetic films with biphase magnetic behavior exhibiting asymmetric magnetoimpedance effect as a very attractive candidate for application as probe element in the development of auto-biased linear magnetic field sensors.