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High frequency magnetic excitations in solids, such as ferromagnetic
resonance (FMR) and spin waves, are of importance to physicists and
engineers for a variety of reasons. For physicists, magnetism remains
a vast, still fully unexplored field where quantum, statistical, and
classical mechanics play as large a role as Maxwell's equations. High
frequency magnetic excitations are particularly well suited for the study of
nonlinear phenomena including chaos and solitons. Recent
advances in magnetic multilayers and superlattices, and the discoveries of
giant magnetoresistance (GMR) and colossal magnetoresistance (CMR) indicate
that much new physics probably lies ahead as well. An excellent introduction
to many of these magnetic phenomena can be found in the
April 1995 issue of
Physics Today.
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.
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.
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.
Next stop: The Spin Waves Page
Last updated: April 21 1997
Section 1: Introduction (or, What's so Exciting About Magnetic
Excitations)
How to use this applet: