By M. S. Sodha, N. C. Srivastava
During the final 3 a long time, curiosity within the box of interplay of microwaves with ferrimagnetics has gradually elevated. Investigations in tlris box have ended in the improvement of a couple of units used for quite a few functions. The preliminary emphasis of the investigators used to be at the microwave habit of ferrimagnetics positioned in cavities and steel waveguides and linked units. This paintings has been offered in quite a few books, monographs, and stories written throughout the sixties. lately, curiosity in microwave propagation in ferrimagnetics has shifted from loaded waveguides to quite new components, e. g. , magnetostatic and magnetoelastic waves in layered buildings, microwave propagation in ferrimagnetic strip strains and microstrips, and so forth. Such investigations are very important from the perspective of units corresponding to hold up traces, filters, convolvers, guided wave amplifiers, striplines, and microstrip section shif ters, circulators, facet guided mode isolators, and so on. As such, we feit the necessity for a textual content (meant for graduate scholars beginning paintings in those parts as weil as training electric engineers and utilized physicists) which offers a coherent account of a number of the facets of propagation of microwaves (electromagnetic as weil as magnetoelastic) in biased ferrimagnetics and discusses the particularly fresh advancements within the conception and operation of the aforementioned units, and this e-book is the end result. A biased ferrimagnetic is, within the mathematical experience, a classy medium, electromagnetically as weil as elastically.
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Additional info for Microwave Propagation in Ferrimagnetics
Sec. 45). 46) is widely applicable. 45). 42) may be valid. 14) so as to make the latter applicable in Situations where magnetization is spatially nonuniform (spin wave). The explicit effect of exchange interaction on a permeability tensor can be examined by studying the variation of the oscillating part of the magnetization m as exp j ( wt - k · r ), where k = ßn. 25). The only modification on account of the exchange term is that, in the expressions for p. 38 X 10- 16 erg/deg K. Since Tc, the critical temperature, is about l000°K for a typical ferrimagnetic material, we have Hw = 107 Oe.
Consequently, each spin experiences a torque which tends to orient it parallel to the neighboring spins. We will now derive§ an expression for this torque, called exchange torque. • A simple derivation has been given by Feynman (1972). ' Incidently, even when the overlap integral is small, the magnetic order occurs at sufficiently Iow temperatures, where the thermal agitation does not dominate over the magnetic order. arge. ' The exchange interaction is a short-range interaction. • The present derivation is by no means rigorous; it has been carried out only to bring out the essential features of the exchange term.
Moreover, only even powers of a, should be involved in the expansion because the opposite ends of any crystal axis are equivalent. 50) Since a is a unit vector, we have L; a i = 1. Since the addition or subtraction of a constant to U. 51) • Magnetocrystalline anisotropy should be distinguished from an isotropy associated with wave propagation. A magnetized ferrite (with no magnetocrystalline anisotropy) exhibits anisotropic wave propagation; the wave velocity is different for propagation in different directions relative to the biasing field.