Characterization and modeling of magnetic domain wall dynamics using reconstituted hysteresis loops from Barkhausen noise

•Barkhausen noise energy versus excitation field hysteresis cycles MBNenergy(H).•Difference in the dynamics of the induction field B and of the MBNenergy.•Dynamic behavior of MBNenergy(H) cycles is first-order.•Dynamic behavior of B(H) cycles is non-entire order. By means of a post-processing technique, we succeeded in plotting magnetic Barkhausen noise energy hysteresis cycles MBNenergy(H). These cycles were compared to the usual hysteresis cycles, displaying the evolution of the magnetic induction field B versus the magnetic excitation H. The divergence between these comparisons as the excitation frequency was increased gave rise to the conclusion that there was a difference in the dynamics of the induction field and of the MBNenergy related to the domain wall movements. Indeed, for the MBNenergy hysteresis cycle, merely the domain wall movements were involved. On the other hand, for the usual B(H) cycle, two dynamic contributions were observed: domain wall movements and diffusion of the magnetic field excitation. From a simulation point of view, it was demonstrated that over a large frequency bandwidth a correct dynamic behavior of the domain wall movement MBNenergy(H) cycle could be taken into account using first-order derivation whereas fractional orders were required for the B(H) cycles. The present article also gives a detailed description of how to use the developed process to obtain the MBNenergy(H) hysteresis cycle as well as its evolution as the frequency increases. Moreover, this article provides an interesting explanation of the separation of magnetic loss contributions through a magnetic sample: a wall movement contribution varying according to first-order dynamics and a diffusion contribution which in a lump model can be taken into account using fractional order dynamics.