Magnetic Moment of Cobalt Clusters
Xiaoshan Xu, Shuangye Yin, Anthony Liang, and Walt de Heer
Magnetism is an ancient subject - and the origin of bulk magnetism in
transition metals is still filled with theoretical difficulties. Atomic
magnetism is comparitively well understood, with its origin in Hund's
rules and partially filled orbitals. Experiments using cluster beams
may provide a connection between the two, as magnetic
properties of a crystal can be tested as it approaches the bulk one atom
at a time.
There are also many potential applications of nanomagnetism in
data storage technologies. These experiments should thus be of
interest to physicists, chemists, and engineers.
The objective of our experiment is to measure how the magnetic moment
of clusters (expressed as Bohr magnetons per atom) varies with the
size of the clusters in atoms. We are also interested in the
magnetization curves of the clusters. How does the magnetic
moment of a cluster vary with the magnitude and direction of an
applied magnetic field? Does this magnetization curve show any
hysteresis or saturation like the bulk?
A diagram of our experimental apparatus is given below.
The three main components are:
- Molecular beam source and flight chamber
- Stern - Gerlach magnet
- Time of flight mass spectrometer
First the Cobalt sample is vaporized by a high intensity pulse of light from a
Nd:YAG laser. As the Cobalt vapor expands, high pressure inert gas is injected
into the chamber which causes the Cobalt to condense into clusters. These
clusters continue to expand out of a hole in the sample chamber where they
are then collimated into a beam. The distribution of cluster sizes and
energies can be controlled by the temperature and pressure of the inert gas.
At the end of the beam, the clusters are ionized by an eximer laser and
accellerated toward a detector by the strong electric field between two high
voltage plates. Each cluster's time of flight from the beam to the
detector depends on the transverse deflection of the beam and the mass of the
cluster. Thus the signal from the detector in time corresponds to the mass
spectrum of cluster beam. An example spectrum is shown below
The spikes in the figure above correspond to the signal generated in the
detector by the impact of a cluster with a single mass. The amplitude of the
space depends on the number of clusters in the beam with that mass. The
spike's position on the horizontal axis corresponds to mass of the cluster.
The magnetic properties of the clusters are studied by passing the beam
through a magnetic field. A uniform magnetic field can exert no net force
on a magnetized object, so the magnet is designed so that the field strength
increases in a direction transverse to the beam. This type of magnet is
familiar from the famous Stern-Gerlach experiment. In a non-uniform field
the deflection of a magnetized cluster away from the beam axis is
proportional to the gradient of magnetic field. The deflection can be
measured in the mass spectrum because the deflected clusters will arrive
earlier or later depending on whether they were deflected toward or away from
the detector. (Think of the magnet as giving the magnetized clusters a
head start or delay in the race toward the detector, depending on the
orientation of their magnetic moment)
The deflection profile of a single cobalt cluster (37 atoms) is shown in
the figure above. This graph is a close up of one of the single spikes in the
spectrum shown earlier. The blue curve is the profile of a single cluster
species with the magnetic field turned off. Note that the the curve is
centered on zero. The dispersion around the center represents the
differences in time of flight due to the thickness of the cluster beam (~1mm).
The red curve is the delection profile with the magnetic field turned on.
If we extrapolate from the known properties of bulk Cobalt
we would expect there to be one peak with no broadening. Instead, and
completely unexpectedly, there are two peaks. This suggests that the ensemble of
clusters contains two species with this mass - one with a high magnetic moment,
and one with a low magnetic moment.
It is interesting to ask how the deflection profile varies with the
cluster size. Below is a three dimensional plot of the deflection profile vs.
From the above graph we see that the high magnetic moment and low magnetic
moment clusters coexist for all cluster sizes, and as the cluster size approaches
200 atoms both converge to the bulk value.
More interestingly, it seems that the relative intensity of the two
deflection peaks depends on the conditions under which the clusters are
formed. By varying the amount of the carrier gas in the chamber where
the sample is vaporized, it is possible to select for the high moment
species, the low moment species, or a mixture of the two. As the density
of the carrier gas increases, the low magnetic moment species is gradually
replaced by the high moment species. This is illustrated by the
three pictures below
Increasing the density of the carrier gas must increase the number of
collisions that each cluster will undergo before it enters the beam.
More collisions means more opportunities to exchange energy and come to
equilibrium with the carrier gas. It is therefore quite plausible that
the low magnetic moment state represents a quenched non-equilibrium