Like almost everything in life, you can lump magnets into two broad classes:
local moment magnets and itinerant (sometimes called band) magnets. The
difference between the two is where the electrons that carry the magnetism live.
In local moment magnets, the magnetic electrons live near the ions that make up
the solid. In itinerant magnets the magnetic electrons live in what is called
the conduction band. Itinerant magnets are conductors, but local moment magnets
can be insulators.
There are four elements that are magnetic at room temperature: cobalt (Co),
iron (Fe), nickel (Ni), and gadolinium (Gd). (Technically chromium (Cr) is also
magnetic, but in that element the ionic moments align pointing in opposite
directions. This is called antiferromagnetism. For a brief discussion of
magnetic order go here.) Nickel is considered to be one
of the prototypical
itinerant magnets. Iron is closer to a local moment and cobalt is somewhere in
between. Gadolinium is local moment. In gado (as it is known in the trade) the
magnetic electrons are buried beneath other electrons. So when a lot of gado
ions get together and form a crystal the magnetic electrons stay very close to
their own ion.
These ideas of local moment vs. itinerant are based on how certain data fit the
different theories, and on what are called band
structure calculations. It comes down to a matter of interpretation of
results. To
date, there has been no unambiguous measurement to discern the two.
We feel the TDR supplies just such a measurement. Data on the local moment
systems we have show a sharp peak in susceptibility in the immediate vicinity of
the transition temperature. This peak is suppressed with applied magnetic
fields. Further, the maximum is shifted to higher temperatures. Data on the
one itinerant system (ZrZn2) we have collected show an increase in
susceptibility at the transition temperature (TC) that evolves into a
broad maximum at about 80% of TC. The amplitude of the maximum
decreases and shifts to lower temperatures in applied magnetic fields.
The local moment behavior is reasonably well understood in terms of the relevant
energy sources in the system. These energy sources are the exchange energy
tending to align the localized moments with one another, the field energy
tending to align the localized moments with the field, and thermal energy
tending to randomize the individual moment directions. In zero field, when the
exchange energy exceeds the thermal energy, the material orders. Applied fields
help the exchange energy work against thermal energy, therefore the change from
non-magnetized to magnetized state happens at higher temperatures.
What we do not understand is what causes the itinerant response in applied
fields. Generally, one thinks of applied fields as adding energy to combat
thermal fluctuations. In this case the field seems to assist thermal energy.
One possibility is that there is a fundamental difference between the magnetic
domains (to be explained later) in local moment systems and itinerant systems.
Another possibility is that in itinerant systems the conduction electrons remain
highly polarizable deep into the ordered state. We know that this extreme
polarizability exists above TC, however it is somewhat less clear
what should happen below. A third possibility is the very low anisotropy
inherent in itinerant systems permits the susceptibility to remain large to low
temperatures. (Anisotropy is a measure of how different the sample "looks" in
different directions. A new pencil is a very anisotropic object because it is
very long in one direction and very narrow in the perpendicular direction. An
unchewed gumball is very isotropic. It looks pretty much the same in all
directions.)
It is unlikely we have established some sort of resonance condition. For one
thing, the frequency we operate at supplies about 1/1000 of the energy needed to
make the electrons change levels. For another thing, it is known that electron
spin resonance experiments require much larger magnetic fields and much higher
frequencies. Further, we measure the susceptibility parallel to the magnetic
field. Most every resonance technique requires a measurement perpendicular to
the field. Needless to say, one can begin to see why this has been a problem
for more than 50 years.
Our current thoughts center on the lives of the electrons themselves. Electrons
are fermions. This classification carries some very important consequences, the
most important (for our purposes) is that no two fermions can have exactly the
same quantum state. This is not true for the other type of particles called
bosons. When you construct a crystal out of individual atoms, an electron band
structure forms. This band structure gives the quantum mechanical levels
available for the electrons. As you put electrons into the bands, those bands
start to fill up. The result is that even at zero kelvin, the electrons have a
finite kinetic energy. In a metal this energy corresponds to a temperature of
about 10,000 K.
We have progressed to the point that we think we understand what is going on in
itinerant systems. Typically when the conduction band spin polarizes, theories
consider two subbands. One subband is the majority spin and the other is the
minority spin. The magnetization is proportional to the difference in
population between the bands. We prefer to think of the subbands as the
uncompensated spins and the compensated spins. The population of the
uncompensated spin subband is just the difference between the majority and
minority subbands in conventional theories. It is the portion of the band that
is spin polarized. The populations of the compensated subband is just twice the
minority population. It is the portion of the band that is equally populated by
spin up and spin down electrons. The compensated subband carries no magnetic
moment. What is important about it, however, is that it has a very high
magnetic susceptibility. I will work on an explanation of the Stoner model of
itinerant ferromagnetism so that this is more self-contained. The Stoner model
gives an explanation for a lot of the properties seen in itinerant ferromagnets.
Yet it spectacularly fails on many other counts.
In any case, what we think we see with the TDR is the response of the
compensated subband. The basic idea is that this highly susceptible electron
gas sits in a static background field from the uncompensated subband. As the
temperature is reduced, the free electron like properties of the compensated
component dictate the behavior of the susceptibility. The difference is we now
have a relevant temperature in the problem, namely the Curie temperature. This
is the temperature below which the material exhibits ferromagnetism.
My Interpretations of Some Things
Local Moment vs. Itinerant Systems
Types of Magnetic Order
How a TDR Works
The Normal Skin Effect
Band Structure
Matt's Home
If you have any questions, feel free to email me at vannette@iastate.edu
Updated 18 July 2008 from the lab.