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The rigid vortex model assumes a ``rigid vortex'', which does not
change its shape in an external field. Together with a certain
magnetization distribution it gives an approximation for the
magnetization distribution of a curling state (vortex state) in a
fine cylindrical particle. An analytical model for the
magnetization distribution
in zero field has been
developed using a variational principle by Usov and
coworkers [113,114]. It is split into two parts (cf. Fig. 9.2)
Figure 9.2:
Geometry of a flat cylindrical nanodot.
![\includegraphics[scale=0.5]{fig/papers/icfpm02/fig/dotgeom.eps}](img568.png) |
The first part describes the
magnetization in the core of the vortex (
,
is the
vortex core radius), which is defined by
:
where
,
are the polar coordinates. The other part
describes the magnetization outside the core (
):
denotes the radius of the core and it is given by
where
(the exchange length) is given by
is the radius of the nanodot,
is a numerical constant (cf. [113]) and
is the ratio
, where
is the height of the nanodot. For permalloy we find
and with
and
we get
. The core radius is obtained from the minimization of the total energy (exchange and magnetostatic energy).
There are some typical properties of the rigid vortex model with Usov's magnetization distribution:
- In equilibrium in zero field there are surface charges only on the top and bottom surface within the vortex core.
- For shifted vortices surface charges are induced on the circumference of the nanodot.
- There are no volume charges in the model.
Next: 9.2.2 Numerical Finite Element
Up: 9.2 Analytical and Numerical
Previous: 9.2 Analytical and Numerical
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Werner Scholz
2003-06-08