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Magnetic Moment of Cobalt Clusters

Motivation

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.

Objective

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?

Experimental Methods

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.

Stern-Gerlach field

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. cluster size.

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.

Quenching Effects

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 state.