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Exchange Bias

by Markus Kirschner


Introduction

The phenomena of exchange  anisotropy and exchange bias, particularly, were discovered in the year 1956 by Meiklejohn and Bean when studying Co particles surrounded with antiferromagnetic oxide (CoO).  They found that the field required to switch the ferromagnet from the field cooled state into the reversed state is larger than that to rotate the ferromagnet back to its original direction.

Our present work concerning exchange bias focus on bilayer systems with perfectly compensated interfaces.

schematic
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Interacting Grain Model

The model consists of 60 x 60 antiferromagnetic grains with randomly distributed easy axes coupled to a ferromagnetic film. It starts from the total energy for each grain which is composed of the exchange energy terms, the AF anisotropy energy, an in-plane anisotropy energy in the F-layer (approximating shape effects of the ferromagnetic film), and the Zeeman energy. We assume a fully compensated interface which leads to spin flop coupling.

First the system undergoes a field cooling process simulated by a Metropolis Monte Carlo algorithm. Then the hysteresis loop is calculated by time integrating the Landau-Lifshitz-Gilbert equation for different applied fields at zero Kelvin.
 

 

sample
  [ Animation ]


Hysteresis and Training Effect

The first hysteresis loop always shows the largest bias field and coercivity. With the number of cycles both fields fall off quickly (training effect) until the system reaches the steady state. Further cycling then does not change the hysteresis curve anymore.

hysterese
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360° Domain Walls

For certain material parameters our simulations resulted in substantially stable 360° domain wall loops or lines within the ferromagnet, similar to those observed experimentally. 

domain walls
[ Animation ]


Textured Antiferromagnetic Films

Due to the fact that several experimental samples show on average a preferred orientation of the antiferromagnetic easy directions, simulations of bilayers with textured AF films were performed. The diagram compares the behavior of the bias field of  <111> textured AF films with Gaussian distributed crystalline axes and a standard deviation of 20° with the untextured case. The maximum bias field clearly shifts towards lower AF thicknesses for textured films. Experiments of van Driel et al. confirm our results.

textured


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Mar. 05, 2003