Note: This site is still being developed. I am working on some Java applets that will help illustrate some of the basic (and not-so-basic) concepts of high-frequency magnetic excitations in ferromagnetic materials. Much of this work is taken from my Ph.D. dissertation, "Two Magnon Scattering and Relaxation in Thin Magnetic Films," completed at Colorado State University in 1996.

## Introduction to High Frequency Magnetic Excitations in Ferromagnets

### Section 1: Introduction (or, What's so Exciting About Magnetic Excitations)

For engineers, magnetic materials provide unique possibilities to be exploited in device design. Besides the well known applications in recording, ferrites are employed in the processing of electromagnetic signals at microwave frequencies. Device applications include phase shifters, delay lines, tunable oscillators, filters, signal-to-noise enhancers, isolators, circulators, power limiters, and more. Microwave applications such as radar, communications, and electronic warfare systems often utilize devices constructed from ferrite materials.

In order to explore the rich variety of magnetic excitations and the many technological applications of ferrites, one must first understand the basic behavior of a magnetic moment in the presence of a magnetic field. In this tutorial, we will consider the behavior of the magnetization vector of a magnetic sample. You may recall that the magnetization is defined to be the volume average of the magnetic dipole moment.

Consider the magnetization vector M of a ferromagnetic sample saturated by an external magnetic field H. At static equilibrium, M lies parallel to H. Once distrurbed from this orientation, however, the magnetization will undergo precession, as a result of the torque exerted on the magnetization by the external magnetic field (analagous to the familiar motion of a spinning top in a gravitational field). The frequency is more or less proportional to the magnetic field strength, but sample shape and crystalline anisotropy influence the frequency as well.

##### How to use this applet:

Below is a simple Java applet which demonstrates the damped precessional motion of the magnetization vector M, drawn in red. The blue vector represents the externally applied static magnetic field, H. Click and drag on the M vector to move it out of equilibrium, and then release it to see the precession. The buttons allow you to change the dynamics of the precession by changing the strength of H and the amount of damping. Pressing Finish will stop the applet execution.

The Java applet should have appeared here. Since it has not, this means (a) your browser is not capable of viewing Java applets (In which case you should consider downloading a new browser from Netscape or Microsoft) or (b) you need to check your browser settings to enable Java.

There are several important observations about the motion which are worth noting. First, the magnetization always precesses in the same direction (counter-clockwise when viewed from above). This "handedness" is the basis of many of the novel device applications of magnetic excitations. Suppose a magnetically saturated sample was subject to microwave radiation with a circular polarization. If the polarization rotated in the same direction as the precessing magnetization, there would be a strong interaction between the microwaves and the magnet. On the other hand, if the radiation was polarized in the opposite sense, there would be no interaction at all. This concept is exploited by a microwave device called a resonance isolator, which allows microwaves to pass in one direction, while attenuating microwaves which travel in the opposite direction. Its a bit like a diode for microwaves.

Second, notice that the motion is more complicated than just simple precession about the equilibrium direction. The magnetization vector actually spirals in to the equilibrium position parallel to the magnetic field, as a result of dissipation, or damping in the system. This is analogous to the effect of friction on mechanical motion. The causes for this damping are in general very complicated, and will be explored in detail later in this this tutorial. For now, you can adjust the parameters in the applet and see how the motion changes.

The motion demonstrated above may remind you of other, more familiar physical systems, such as a damped mass on a spring. The equations of motion, with a few subtleties aside, are the same.

The simple precessional motion is the basis for a rich variety of excitations in ferromagnetic materials, inclding ferromagnetic resonance (FMR) and spin waves. FMR occurs when the magnetized ferrite is subject to microwave radiation with a frequency near the natural precessional frequency of the magnetization. Spin waves, which as the name implies, involve propagating magnetic excitations, will be discussed in the next section. Spin waves play a key role in the process of damping the motion of the magnetization vector.

Last updated: March 1998