Multi-layered Fe Films for Microwave Applications

Abstract

The microwave permeability of multi-layered Fe fllms is under study. The multi- layer fllms are found to possess more rigid magnetic structure and larger damping factor of ferro- magnetic resonance compared to those of single-layer fllms. Bulk materials with high microwave permeability may be produced as laminated structures of these multi-layer ferromagnetic fllms. In the paper, experimental data are presented on the microwave permeability of such laminated regular structures based on Fe fllms. Possible technical applications of the materials under study include thin wideband radar absorbers and miniaturized patch antennas. For many microwave applications, materials with high microwave permeability values are needed. The frequency dependence of microwave permeability is typically due to the ferromagnetic reso- nance. In many magnetic materials, the permeability varies slightly with frequency until an abrupt drop appears at the ferromagnetic resonance frequency. Above the resonance, the permeability takes values that are close to unity. Hence, an estimate of microwave permeability of a magnetic material may be made from its static permeability s and resonance frequency fr. The static per- meability characterizes the magnetic performance in the operating frequency band. The resonance frequency is an estimate for the cutofi frequency, above which the material is no more permeable enough and magnetic loss increases greatly. For high microwave permeability be attained, both fr and s must be as high as possible. These values often reveal a complex dependence on the material composition, magnetic and crystalline structure, features of manufacturing and processing, etc. However, s and fr are related closely to each other by well known Snoek's law: an increase of one leads to a decrease of another, with the product of these being dependent only on the saturation magnetization Ms of the material. The anisotropy fleld or other structure-dependent values are not involved in Snoek's law. For thin fllms with in-plane magnetization, s is reciprocal to squared fr in difierence to con- ventional Snoek's law (1): (s i 1)f 2 r = (∞4…Ms) 2 (1) where ∞ … 3GHz/kOe is the gyromagnetic ratio. Eq. (1), which is referred to as Acher's law in the literature, also has the right-side part depending on the saturation magnetization only. Therefore, Eq. (1) provides a constraint for the microwave permeability of magnetic fllms that is determined by the composition and is independent of structure, the same as Snoek's law does for bulk materials. When fr < ∞4…Ms, which is several GHz or several dozens GHz for typical high-permeability fllms, Eq. (1) produces far higher values of s and, therefore, higher microwave permeability compared to Snoek's law. Therefore, thin ferromagnetic fllms are promising materials for microwave applications. However, most applications require bulk samples. With the increase of fllm thickness, the microwave permeability of the fllm degrades because of the efiect of eddy currents and out-of-plane magnetization. For these efiects to be avoided, laminates of thin ferromagnetic layers are useful. Since the thickness of substrate is large compared to that of ferromagnetic fllm, multi-layer fllms may be used to obtain high volume fractions of ferromagnetic material in the laminate. Therefore, this study presents experimental data on the microwave performance of both multi-layer thin Fe fllms and laminates made of such fllms. 2. EXPERIMENT