VP18-01 Modelling of loss in amorphous ribbons with longitudinal-induced anisotropy: theory and experiments
Creators: O. de la Barrière
C. Ragusa
E. Ferrara
A. Magni
F. Mazaleyrat
F. Fiorillo
Publisher: name: IEEE
Year: 2025

The amorphous (AM) and nanocrystalline (NC) ribbons are endowed with thickness in the 10–20um range, relatively high resistivity, and weak dependence of properties on temperature, and appear as excellent alternatives to soft ferrites in power electronic applications. Their high saturation polarization allows for a significant volume reduction, while the loss remains generally lower at all frequencies [1]. Among different annealing treatments, transverse-induced anisotropy (TA) samples have received considerable interest [2][3], because, due to the predominance of magnetization rotations, the permeability cutoff can be shifted towards the MHz range, with the loss figure strongly reduced with respect to zero-field or longitudinal field-annealed (LA) samples [1]. The magnetisation process in TA ribbons is linked to spin rotations at high frequencies and, therefore, can be addressed via the Landau–Lifshitz–Gilbert equation [1]. LA, however, exhibit higher permeability than their TA counterpart at frequencies and induction values useful for a number of applications, e.g. in transformers and power electronics [4][5]. There is, however, limited understanding of the broadband frequency dependence of the magnetic loss in AM/NC LA ribbons, which compounds with the lack of direct observations of the related domain wall (dw) dynamics. In this communication, we discuss loss measurements carried out in 17 - 22 µm thick LA Co-based AM and NC ribbons, tested either as single strip samples or tapewound rings up to a few MHz, in parallel with stroboscopic Kerr effect imaging [6] of the evolving longitudinal domain pattern up to about 1 MHz. Under conditions of constant domain wall spacing (much larger than the ribbon thickness), less-than-linear increase of the dynamic energy loss Wdyn(f) with frequency is observed beyond a few kHz. Both deterministic and statistical models are worked out, to connect the observed dw dynamics to the broadband W(f) behavior. The former is based, in particular, on a numerical model, dwelling on the concept of dw bowing [7] applied to small and fast oscillations of domain walls. An example of calculated Wdyn(f) is shown, compared with the experimental data, in Fig. 1.References: [1] C. Beatrice, et al., «Broadband magnetic losses of nanocrystalline ribbons and powder cores,» JMMM, vol. 420, pp. 317-323, 2016. [2] A. Magni, et al., «Domain wall processes, rotations, and high-frequency losses in thin laminations,» IEEE Trans. Magn., vol. 48, n°111, pp. 3796-3799, 2012. [3] A. Magni, et al., «Spin precession by pulsed inductive magnetometry in thin amorphous plates,» JAP, vol. 115, n°117, p. 14A338, 2014. [4] H. Cui, B. Dong, Y. Xing, L. Wang et S. Zhou, Journal of Materials Science: Materials in Electronics, vol. 35, n°1393, 2024. [5] R. Hasegawa, «Applications of amorphous magnetic alloys,» Materials Science and Engineering: A, vol. 375, pp. 90-97, 2004. [6] A. Magni, International Journal of Applied Electromagnetics and Mechanics, vol. 48, n°12-3, pp. 295-300, 2015. [7] J. E. L. Bishop, «Modelling domain wall motion in soft magnetic alloys,» JMMM, vol. 41, n°11-3, pp. 261-271, 1984.
The amorphous (AM) and nanocrystalline (NC) ribbons are endowed with thickness in the 10–20um range, relatively high resistivity, and weak dependence of properties on temperature, and appear as excellent alternatives to soft ferrites in power electronic applications. Their high saturation polarization allows for a significant volume reduction, while the loss remains generally lower at all frequencies [1]. Among different annealing treatments, transverse-induced anisotropy (TA) samples have received considerable interest [2][3], because, due to the predominance of magnetization rotations, the permeability cutoff can be shifted towards the MHz range, with the loss figure strongly reduced with respect to zero-field or longitudinal field-annealed (LA) samples [1]. The magnetisation process in TA ribbons is linked to spin rotations at high frequencies and, therefore, can be addressed via the Landau–Lifshitz–Gilbert equation [1]. LA, however, exhibit higher permeability than their TA counterpart at frequencies and induction values useful for a number of applications, e.g. in transformers and power electronics [4][5]. There is, however, limited understanding of the broadband frequency dependence of the magnetic loss in AM/NC LA ribbons, which compounds with the lack of direct observations of the related domain wall (dw) dynamics. In this communication, we discuss loss measurements carried out in 17 - 22 µm thick LA Co-based AM and NC ribbons, tested either as single strip samples or tapewound rings up to a few MHz, in parallel with stroboscopic Kerr effect imaging [6] of the evolving longitudinal domain pattern up to about 1 MHz. Under conditions of constant domain wall spacing (much larger than the ribbon thickness), less-than-linear increase of the dynamic energy loss Wdyn(f) with frequency is observed beyond a few kHz. Both deterministic and statistical models are worked out, to connect the observed dw dynamics to the broadband W(f) behavior. The former is based, in particular, on a numerical model, dwelling on the concept of dw bowing [7] applied to small and fast oscillations of domain walls. An example of calculated Wdyn(f) is shown, compared with the experimental data, in Fig. 1.References: [1] C. Beatrice, et al., «Broadband magnetic losses of nanocrystalline ribbons and powder cores,» JMMM, vol. 420, pp. 317-323, 2016. [2] A. Magni, et al., «Domain wall processes, rotations, and high-frequency losses in thin laminations,» IEEE Trans. Magn., vol. 48, n°111, pp. 3796-3799, 2012. [3] A. Magni, et al., «Spin precession by pulsed inductive magnetometry in thin amorphous plates,» JAP, vol. 115, n°117, p. 14A338, 2014. [4] H. Cui, B. Dong, Y. Xing, L. Wang et S. Zhou, Journal of Materials Science: Materials in Electronics, vol. 35, n°1393, 2024. [5] R. Hasegawa, «Applications of amorphous magnetic alloys,» Materials Science and Engineering: A, vol. 375, pp. 90-97, 2004. [6] A. Magni, International Journal of Applied Electromagnetics and Mechanics, vol. 48, n°12-3, pp. 295-300, 2015. [7] J. E. L. Bishop, «Modelling domain wall motion in soft magnetic alloys,» JMMM, vol. 41, n°11-3, pp. 261-271, 1984.