Microwave Propagation in Ferrimagnetics

Abstract

Chapters 1 to 3 present the basic concepts of electromagnetic and magnetoelastic wave propagation in biased ferrif!Iagnetics. The response of a ferrimagnetic to external electromagnetic and elastic fields is discussed in Chapter 1. The permeability tensor has been obtained for magnetically saturated ferrimagnetic, considering the various interactions present in a real ferrimagnetic. The coupled magnetoelastic equations have also been developed. Chapter 2 discusses electromagnetic and magnetoelastic plane wave propagation in ferrimagnetics. Chapter 3 presents an analysis of electromagnetic and magnetoelastic wave propagation across plane interfaces; these studies provide a physical insight into the relevant phenomena and serve as a background for the appreciation of more complex wave propagation phenomena in ferrimagnetics (which is of practical importance). In Chapter 4 we discuss the propagation oi magnetostatic waves in layered planar structures; the analysis and experimental results pertaining to a number of practical configurations are presented. The applications to delay lines, filters, convolvers, and magnetostatic wave amplifiers are also discussed. Chapter 5 considers magnetoelastic guided wave propagation in layered planar structures and its applications. Gaussian units have been used throughout the book.We wish to thank our colleague Prof. A.K. Ghatak for providing the inspiration to write this book. We are also grateful to Dr. I. Rattan for a critical review of the manuscript, to Mr. S. S. Gupta and Mr. S. N. Bajpai for helpful discussions, and to Mr. T. N. Gupta for his kind and ungrudging assistance in the preparation of the manuscript. The financial support of NSF (USA) for the original work reported in this book is gratefully acknowledged.

Biased Magnetic Materials in Ram Applications

“…It can be shown [6,7,24,27] that the dynamics of the magnetization in a domain, when interacting with a magnetic eld is given by is the gyromagnetic ratio for the material, m e and e represent the mass and charge of the electron and the g-factor (spectroscopic splitting factor) is ∼ = 2 for most ferro- …”

“…Hence, equation frequency equal to the precession frequency of the magnetization is superimposed on H 0 , then it can be shown [27] that, in a small signal approximation regime, the amplitude of the magnetization tends to grow and energy is transferred from the magnetic eld to the material in an e cient way, i.e. we have a resonance condition.…”

“…This equation is often referred to as the Landau-Lifshitz-Gilbert equation(LLG). The damping factor can be found from the resonance line halfwidth measurements [7,24,27] and it seems that its largest value is of the order α ≈ 0.1, although some values as large as 0.4 or even 0.92 can be found in the literature [29,31] . …”

“…In order to incorporate these interactions, the magnetic eld, H, is replaced by an e ective magnetic eld, H e , that includes other torque-producing contributions besides the external magnetic eld. The e ective magnetic eld can be modeled in the following way [3,8,27] H e = H + H an + H ex + H me (3.9) where the di erent terms are: 1) the classical magnetic eld, H, appearing in Maxwell's equations 2) the crystal anisotropy eld H an = −N c · M due to magnetocrystalline anisotropy of a ferro-or ferrimagnetic material, 3) the exchange eld H ex = λ ex ∇ 2 M due to non-uniform exchange interaction of the precessing spins 4) the magnetoelastic eld H me due to interaction between the magnetization and the mechanical strain of the lattice. The anisotropy tensor N c is assumed to be known, as well as the exchange constant λ ex .…”

Modal Expansions and Orthogonal Complements in the Theory of Complex Media Waveguide Excitation by External Sources for Isotropic, Anisotropic, and Bianisotropic Media

“…Later the similar idea to apply waves in solids for signal processing gave rise to new lines of solid-state electronics. They are due to applying the surface acoustic waves (SAW) in elastic piezo-dielectrics [15][16][17], the magnetostatic spin waves (MSW) in magnetized ferrites [18][19][20][21][22][23], and the space charge waves (SCW) in semiconductors with negative differential mobility of electrons [10,24,25]. These waves refer to the quasistatic part of the electromagnetic spectrum of waveguiding structures for which a relevant potential field (electric for SAW and SCW or magnetic for MSW) dominates over its curl counterpart.…”