10.4 Experimental results

The measurement of thermally activated magnetization reversal is a very tricky task for several reasons. First, it is very difficult to produce ``perfect'' monocrystalline single domain particles of cobalt or iron. As the particles have to be only a few nanometres in diameter, the surface to volume ratio is large and surface effects are very important. Thus, the particles should have a sufficiently smooth surface. Furthermore, they must not contain too many lattice defects, which act as nucleation sites for magnetization reversal processes and pinning sites for domain walls.

The second main obstacle is the measurement of the magnetization of these small particles. Only superconducting quantum interference devices (SQUIDs) have a sufficiently high sensitivity to measure the flux changes during the magnetization reversal process of single domain particles.

Only in recent years it has become possible to measure the magnetization of individual single-domain particles. The first study of the dynamics and temperature dependence of magnetization reversal in individual submicronic single-domain Co particles at very low temperatures was done by Wernsdorfer et al. [60].

They used a planar Nb micro-bridge dc-SQUID of 1 $\mu$m diameter on which the ferromagnetic particle was placed. The SQUID loop collects the flux produced by the samples magnetization. The close proximity between sample and SQUID results in a very efficient and direct flux coupling, which allows the detection of magnetization reversals corresponding to $10^4 \mu_B$. The elliptic ferromagnetic particles were fabricated by electron beam lithography and lift-off techniques out of sputtered thin films. A 10 nm thin Si film protected them against oxidation.

The dynamics of magnetization reversal is studied by two types of experiments: Switching field measurements and switching time measurements.

In the case of switching field measurements, the external field is increased at a given rate and fixed temperature until the sample's magnetization switches. The value of the switching field is stored. This experiment is repeated 100 to 200 times to obtain a switching field histogram. From that, the mean switching field and a width of the switching field distribution can be obtained.

For switching time measurements, the magnetic field is applied antiparallel to the magnetization of the sample and increased to a set value at fixed temperature. After the magnetic field is stabilized, the time until the magnetization switches, is measured. This experiment has to be repeated many times again to obtain a switching time histogram. The integral of this histogram gives the probability of switching.

The results [61] show good agreement with the Arrhenius-Néel law and the validity of the Néel-Brown theory for thermally assisted switching over a single energy barrier. Figure  gives the probability of not-switching of magnetization as a function of time at different applied fields at 0.5 K for a single crystalline Co particle of 20 nm. Full lines are fits to the data with an exponential.

Figure: Probability of not-switching of magnetization as a function of the time for a 20 nm single crystalline Co particle at $0.5$ K. The full lines are fits to the data with an exponential [61]

However, the quality of the samples has great influence on the measurements. For particles with antiferromagnetic components (due to, e.g., oxidation) or ferrimagnetic materials disagreement with the Néel-Brown theory has been observed. In these cases, the probability of not switching was flatter than exponential at low temperature (typically $T<1$ K) and steeper at higher temperatures. Furthermore, the width of the switching field distribution increased for lower temperatures, which might be explained by surface spin disorder.

Another interesting property is described by the Barkhausen volume, which is the smallest switching unit in magnetization reversal. It is also called ``activation volume'' and can be estimated from the energy barrier at zero field [61] or from the coercive field at different sweeping speeds of the external field [62].

Lederman et al. [63] used a magnetic force microscope to study the angular dependence of the switching field and switching time behaviour of a rectangular single-domain permalloy particle. It was found, that the angular dependence differs significantly from that expected for coherent rotation. In addition, the dependence of the probability for not switching cannot be fit with a simple exponential for applied fields close to the switching field. This indicates, that multiple-energy barriers of similar height are involved in the thermally activated process responsible for the reversal. The rectangular shape of the particle results in vortices at both ends of the particle. This complex magnetization distribution results in complicated switching dynamics, which cannot be described by the Arrhenius-Néel law any more.