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by Rok Dittrich

by Rok Dittrich

Minimum energy paths for the spontaneous thermal switching between stable magnetization states in a patterned recording media are calculated using the "nudged elastic band" method (NEB). The animations show a sequence of magnetization states when we take a "walk" trough the micromagnetic energy landscape following the minimum energy path from one energy minimum to the other. Along this walk we pass one ore more saddle points, so called "transition states", which determine the height of the energy barrier(s).

The patterned media is a granular CoCrPt, the anisotropy axes of the grains are aligned perpendicular to the film. The average grain diameter is 10 nm, and the thickness of the film 21 nm. Material parameters: Ku = 300 kJ/m*m*m, A=10 pJ/m, Js = 0.5 T. The colour code corresponds to the net magnetization perpendicular to the film.

Dependence of the energy barrier on the island size

The animations show magnetization states along the minimum energy paths. No external field was applied. The island size was varied while keeping the film thickness constant. The grains inside the island are perfectly exchange coupled. The reversal mode is inhomogeneous also at sizes down to 20 nm.
movie1 movie2 movie3 size
60 nm 32 nm 20 nm

The graph on the right shows the size dependency of the energy barrier which is obtained from the minimum energy path. In the analytical model we assume the 2-domain state as the transition state and neglect strayfield interactions between the two domains. The energy barrier then simply becomes the energy of the domain wall. The analytical model always overestimates the true energy barrier.

Intergranular exchange coupling

The animations show magnetization states along the minimum energy paths. No external field was applied. Intergrain exchange has a strong effect on the thermal reversal mode and the corresponding energy barrier(s) of the system. The island size is 70 nm, the height 21 nm and the grain boundary thickness 1 nm. The colour code corresponds to the out-of-plane magnetization direction. The table expresses the coupling strength "J" as a ratio ("h") of the maximum possible exchange energy due to intergrain coupling versus the average anisotropy energy KV of one grain.
movie4 movie5 table
J = 5 mJ/m*m J = 0.1 mJ/m*m

For weak intergrain exchange (right), the grains in the island switch individually. The thermal stability is determined by the thermal stability of the individual grains. At strong coupling the grains behave like one large grain. The resulting energy barrier is much higher than at weak coupling. The reversal starts with nucleation on one corner and the expansion of the reversed domain. This allows a further downscale of the bit size (= island size) in patterned media without running into problems of thermal stability.


Rok Dittrich, "Finite element computation of energy barriers in magnetic systems", Ph.D. thesis, Vienna University of Technology, 2003

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