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A generalization of Snoek's law to ferromagnetic films and composites

Olivier Acher
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  • PersonId : 843060
Sébastien Dubourg
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  • PersonId : 842618


The integral of the imaginary permeability times frequency associated to magnetic materials has very remarkable properties. A generalization of Snoek's law is that this quantity is bounded by the square of saturation magnetization times a constant. While previous results have been obtained in the case of non conductive materials, this work is a generalization to ferromagnetic materials and ferromagnetic-based composites with significant skin effect. The effect of truncating the summation to finite upper frequencies is investigated, and estimates associated to the finite summation are given. It is established that in practice, the integral does not dependent of the damping model under consideration. Numerical experiments are performed in the exactly solvable case of ferromagnetic thin films with uniform magnetization. The validity of our derivations is confirmed with a good precision. Microwave permeability measurements on soft amorphous films are reported. The relation between and is verified experimentally. The integral is useful to quantify the magnitude of the magnetization normal to the microwave measurement field. It provides an unprecedented "see-through" ability to investigate the orientation of the magnetization in materials with complex magnetization configuration. It may also be used to demonstrate the accuracy of microwave measurements systems. For some applications, such as electromagnetic compatibility or radar absorbing materials, the relations established here provide useful indications for the design of efficient materials, and simple figure of merits to compare the properties measured on different materials.
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Dates and versions

cea-00175996 , version 1 (02-10-2007)
cea-00175996 , version 2 (28-11-2007)



Olivier Acher, Sébastien Dubourg. A generalization of Snoek's law to ferromagnetic films and composites. 2007. ⟨cea-00175996v1⟩
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