Spin Waves

The previous chapters concentrated on the origins of magnetic moments in individual ions or atoms and collective excitations of spin systems coupled by the exchange interaction. In this chapter, we will discuss the magnetic properties of macroscopic media composed of very large numbers of individual moments and the dependence of these properties on the magnetic field. Specifically, we are interested in the net magnetization (magnetic dipole moment per unit volume) that exists either spontaneously or in response to an applied magnetic field.

In Chapter 5, we solved for the magnetostatic modes in a variety of geometries. These geometries were characterized by simple boundary shapes, uniform bias fields, and uniform materials. In some cases, however, material and field non-uniformities may be needed to control the dispersion or to guide and localize the magnetostatic mode energy. In other cases, the effects of undesired inhomogeneities need to be assessed. Such problems are not easily attacked by the classical boundary value techniques used in Chapter 5. Consequently, this chapter is devoted to a variational approach capable of treating arbitrary inhomogeneities in a relatively simple and elegant way.

Gedanken (or thought) experiments are often followed by practical demonstrations of underlying physics. Once laboratory experiments establish the physics, we could witness the emergence of a new technology. In parallel, as existing technologies mature, there is a rebirth of established ideas with the possibility of new applications. This chapter attempts to describe a few areas of current research in spin-waves, where the fate of novel physics and emerging technology are closely intertwined. For example, the advent of submicron lithographic techniques has given rise to nano-contact spin-wave generation structures using current-driven spin-transfer torques. Also, an improved understanding of spin-wave excitations helps describe noise in patterned nano-structures, and new techniques such as the Magneto-Optic Kerr Effect (MOKE) make it possible to probe the modes of patterned structures. Finally, the properties of backward spin-waves make it possible to observe the long-predicted inverse Doppler effect. Since these are all “hot topics,” we cannot do full justice to them or cover all the frontier areas of research. However, in this chapter, we shall attempt to provide self-contained descriptions of a few topics while referring the reader to recently published literature for a more complete account of the theoretical and technological nuances.