Ferromagnetic Resonance On Metallic Glass Ribbons
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Ferromagnetic Resonance On Metallic Glass Ribbons M. Chipara, M. Toacsen1, M. Sorescu2 Department of Physics and Astronomy, University of Nebraska, Lincoln, NE 68588-0111. 1 Institute for Physics and Technology of Materials, Bucharest, PO BOX MG-7, Romania. 2 Physics Department, Duquesne University, Pittsburgh, Pennsylvania 15282-0321, USA. ABSTRACT Ferromagnetic resonance data on metallic glasses, at room temperature, in X band, are discussed. The spectra were decomposed into two Lorentzian lines and the angular dependence of their main parameters (line width and position) is fully analyzed. It is proved that the usual approaches are not able to describe accurately the experimental data. This behavior is ascribed to the misalignment of the magnetization with respect to the external magnetic field, and successfully tested by using a “relaxed” resonance condition that allows a small misalignment of the magnetization relative to the external magnetic field.
INTRODUCTION Metallic glasses are available as ribbons produced by rapid quenching from the melt. They exhibit both metallic and soft magnetic features and present high mechanical strength and hardness. Striped domain morphology is obtained [1] by annealing the metallic glass in external magnetic fields, confined within the plane of the ribbon. Magnetostrictive transducers are produced from metallic glasses, as the magnetomechanical coupling is usually large. Under the effect of the external magnetic field, the domain wall motion has a negligible contribution to the reorientation of the magnetization in an external magnetic field [1]. The free energy of a magnetic material, of unit volume, is [2]: r r
F = − MH + K1 (α12α 22 + α12α 32 + α 22α 32 ) + K 2 (α12α 22α 32 ) + α12 K1U + α14 K 2U + + ( N X M X2 + N Y M Y2 + N z M Z2 ) + E ’(λ , σ , NM 2 )
(1)
The terms occurring in this equation are associated with (in the order of appearance) are: The Zeeman energy, the first and second order cubic magnetocrystalline anisotropy, the first and second order uniaxial anisotropy, the demagnetizing effects, the magnetostriction and higher order contributions. M is the magnetization, H the intensity of the applied magnetic field, K1 and K2 the cubic magnetocrystalline anisotropy constants, K1U and K2U the uniaxial magnetocrystalline anisotropy constants, and αi (i =1,2,3) the direction cosines of the magnetization with respect to the coordinate axes. In the derivation of (1), only the diagonal components of the demagnetizing tensor N (Njj = Nj where j = X, Y, Z) were considered. The last term, E', depends on the magnetostriction constants λ, stresses σ demagnetizing factor N and on the direction of the magnetization, M. It was introduced to take into consideration stress and magnetostriction effects. The position of the ferromagnetic resonance line is given by [2, 3]:
U1.4.1
2 2 1/ 2 1 + ε 2 ) ∂ 2 F ∂ 2 F ∂ 2 F ( ω 2 = H eff = 2 2 2 2 − M sin θ 0 ∂θ ∂ϕ ∂θ∂ϕ γ
∂F ϕ =ϕ0 = 0 ∂ϕ
∂F θ =θ = 0 ∂θ
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