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Micromagnetic simulation of nucleation and domain wall motion in small particles and wires

T Schrefl, H Forster, D Suess, W Scholz, V Tsiantos, J Fidler

Proc. of Int. Workshop on Wires (IWMW), San Sebastian, Spain, June 2001, (2001) submitted

Finite element micromagnetics is an effective tool to investigate the
magnetization reversal process of small magnetic structures. A detailed
understanding of the reversal process becomes increasingly important for
ultra high density magnetic storage and sensor applica-tions. These
applications require the control of various properties such as the
switching time and the energy barrier of thermally activated reversal
which both depend significantly on the reversal mode. Irregular shaped
particles like polyhedral, columnar grains of perpendicular media or
cylindrical wires can be easily modeled using tetrahedral finite elements.
The solu-tion of the Gilbert equation of motion resolves the magnetization
in space and in time during the magnetization reversal process. In addition
energy barriers for thermally activated magne-tization reversal can be
estimated by plotting the energy along different reversal paths or by
Langevin dynamics. The deterministic Gilbert equation of motion transforms
to a stochastic partial differential equation adding a random thermal field
to the effective field. The space dis-cretization leads to a system of
stochastic differential equations with multiplicative noise which is
interpreted in the sense of Stratonovich and solved using the method of
Heun. The irreversible switching of magnetic particles occurs either by
the rotation of the magnetiza-tion or by the expansion of a nucleus of
reverse magnetization. The numerical results show that the Gilbert damping
constant, *alpha*, drastically changes the reversal mode of elongated
particles. A Co-Cr grain of a perpendicular recording media with a column
length of 40 nm rotates quasi-uniformly for *alpha* = 1, whereas a nucleation
process occurs for *alpha* = 1 and *alpha* = 0.01 respectively. Below this
critical length the maximum exchange energy found during reversal increases
with the column length, indicating a smooth transition between coherent
rotation and nucleation. In addition thermal fluctuation may change the
reversal mode. At finite temperature inhomogeneous reversal pro-cesses
become dominant if the column length exceeds 30 nm. Below this value
non-uniform rotation shows a lower energy barrier than the nucleation
of a reversed domain. The activation energy for Co nanowires with a
diameter of 2 nm was found to depend linearly on the applied field.
This behavior indicates that magnetization reversal occurs by the
formation of a nucleus of reverse magnetization. The analysis of
the calculated magnetization configurations as a function of time
confirms a nucleation mechanism. The magnetization starts to reverse
within a finite volume at one end of the wire. The calculated activation
volume, v = (2.1 nm), was found to be independent of the length of the
nanowire. Once a reversed domain has formed, it expands along the entire
wire. Adaptive refinement schemes are used to simulate the wall motion.
Thus it is possible to resolve the domain wall structure while keep the
total number of finite elements to a minimum. The effect of the diameter
of the wire and the Gilbert damping constant on the domain wall velocity
will be discussed. The calculated wall velocity in Co wires with a diameter
of 40 nm was 400 m/s for *alpha* = 0.1 and for an external field of 80 kA/m.
This work was supported by the Austrian Science Fund (Y-132 PHY).

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Oct. 18, 2001