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Granular Co-Nanowires

by Hermann Forster



Co nanowires were grown in highly-ordered anodic aluminium templates using electrodeposition. This technique yields completely metal-filled aluminium membranes. The nanowires are arranged in a hexagonal lattice. The diameter of one nanowire is 55 nm and the lattice spacing is 100 nm. The typical length is 1000 nm. TEM  investigations show that there are two types of grains in these Co-nanowires, both with hcp structure, where the c-axis is the magnetocrystalline easy direction. The first type has the c-axis randomly oriented in a plane perpendicular to the long axis of the wire. The typical length of these grains is 100-250 nm. Grains of the second type have a length of less than 100 nm and the c-axes are parallel to the long axis. The first kind of grains has a total volume fraction of the Co nanowire of 70-90 %.

The simulation of an array of nanowires would exceed the computational power of our workstations. Therefore we just model three interacting nanowires. The influence of the other nanowires due to the strayfield is taken into account by a demagnetization factor. Our model of the nanowires consists of seven Co-grains. The total length of the sample is 1000 nm and the diameter is 55 nm.  The simulations show that the results are insensitive to a reduction of the exchange coupling between the grains. The smaller grains have a magnetocrystalline easy direction parallel to the long axis, instead in the bigger grains the easy axes are randomly distributed in a plane perpendicular to the long axis, which have a total volume fraction of 75 %.

In the simulation the external field is applied parallel and perpendicular to the long axis. Initially the Co nanowire is fully saturated parallel to the long axis. Then the external field is instantaneously applied with a strength of 1400 kA/m. For each applied field value we integrate the Gilbert equation of motion until the equilibrium state is reached and then the external field is reduced by steps of 28 kA/m. After the simulation of the total hysteresis curves, we have to consider that we just simulate three nanowire, whereas the experimental measurement is the result of the interaction within a 2D-array of nanowires.

We see a good qualitative agreement with the experimental results. The nanowires shows just a small hysteretic behaviour. The values for the coercive fields are by a factor 2 bigger than the experimental values. For the perpendicular case the magnetization starts to rotate in the smaller grains, which have a magnetocrystalline easy direction parallel to the long axis. As the external field is sufficiently decreased also the magnetization in the bigger grains with a magnetocrystalline easy direction perpendicular to the long axis starts to rotate. But in these grains the reversal is finished earlier, due to the fact that the external field has to be strong to rotate the magnetization out of the magnetocrystalline anisotropy direction in the smaller grains. Contrary in the parallel case the reversal starts in the bigger grains.

We also performed simulations neglecting the granular structure of the Co nanowire. This means that the nanowire is just one single crystal with uniaxial anisotropy either parallel or perpendicular to the long axis. The simulations clearly show that we have to take into account the granular structure to achieve a good qualitative agreement with the experiment.




[ References ]

H. Forster, T. Schrefl, R. Dittrich, D. Suess, W. Scholz, V. Tsiantos, J. Fidler, K. Nielsch, H. Hofmeister, H. Kronmuller, and S. Fischer, ``Magnetization reversal in granular nanowires,'' IEEE Trans. Magn., vol. 38, pp. 2580-2582, 2002. 
H. Forster, ``Reversal modes in mesoscopic structures,'' PhD-Thesis, TU Vienna, 2003. 


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