### Section 3: Ferromagnetic Resonance (FMR)

On the previous pages of the tutorial, we saw how a single magnetization vector, or a collection of spins, underwent precessional motion when disturbed from equilibrium. The next natural question is: how does one disturb the magnetic moment(s)? In the applet, we just click and drag with the mouse, but in reality, we need a different method.

A good way to move the magnetization vector is to apply another, smaller magnetic field, perpendicular to the static H field. The precession can then be driven by varying the strength of this small field over time. Historically, this field has been called the "pump field." For typical materials and operating conditions, the pump field is readily supplied by the magnetic component of microwave radiation.

The situation is analogous to a damped, driven, simple harmonic oscillator. Again, think of a mass-on-a-spring, but this time, suppose it is driven by a harmonically-varying force. If the frequency of the driving force is varied, one will find that the amplitude of the responding motion changes. At resonance, the amplitude is maximum.

Ferromagnetic resonance (FMR) is similar. If a magnetization vector is subject to a static field and a perpendicularly applied pump field, resonance will occur at a frequency more or less proportional to the strength of the static field. The microwave power absorbed by the magnetic sample as a function of frequency will typically be a lorentzian centered at resonance.

In practice, however, it is difficult to vary the frequency of the microwave field during the experiment. It is much easier to keep the frequency fixed and instead vary the strength of the static field very slowly.

##### How to use this applet:

The applet below gives a simple demonstration of both a frequency-swept and a field-swept FMR experiment. The plot shows the microwave power absorbed as a function of either frequency or field. The power is proportional to the square of the amplitude of the precession. Try both ways, and then try changing the damping to see the effect on the absorption spectra. 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.

Last updated: April 21 1997