05MagnetostaticModes.pdf

5 Magnetostatic Modes We saw in Chapter 4 that the equations of magneto-quasi-statics are useful for describing waves when the wavelength in the medium is very different from that of an ordinary electromagnetic wave at the same frequency. We will now elaborate on this idea and show how the magneto-quasi-static approximation can be used to analyze modes in a variety of geometries.1 5.1 Walker’s Equation The equations of magneto-quasi-statics were shown in Section 4.10 to be (cf. Eqs. (4.139), (4.140), and (4.141)) ∇ × h = 0, (5.1) ∇ · b = 0, (5.2) ∇ × e = iωb. (5.3) To uniquely determine the field quantities, we must also specify the constitu- tive relations. For a magnetized ferrite, we have (cf. (4.21) and (4.23)) b = μ · h, (5.4) where2 μ = μ0 (I + χ). (5.5) The permeability tensor in the absence of exchange and anisotropy is (cf. (4.104)) 1 Additional general references on these topics include Lax and Button [1], Soohoo [2], and Sodha and Srivastava [3]. 2 The subscript m on the magnetic susceptibility tensor will be omitted when there is no possibility of confusion between the electric and magnetic susceptibilities. D.D. Stancil, A. Prabhakar, Spin Waves, DOI 10.1007/978-0-387-77865-5 5 139 c Springer Science+Business Media, LLC 2009 140 5 Magnetostatic Modes ⎡ ⎤ 1 + χ −iκ 0 μ = μ0 ⎣ iκ 1 + χ 0⎦ , (5.6)