Quantitative micromagnetics simulations of exchange bias in the NiFe/NiMn system

Developing a predictive understanding of the exchange biasing of a ferromagnet (FM) by its interaction with an antiferromagnet (AF) is a long-standing problem of great technological and scientific interest. Several competing theories to explain the FM/AF coupling have been proposed in the literature but a quantitative application of these theories to a particular FM/AF pair with industrial relevance has been lacking. In this work, we investigate the specific system of NiFe and polycrystalline NiMn using a micromagnetics approach. The NiFe is represented by an array of uniformly magnetized cubes with two-dimensional periodic boundary conditions, i.e., an infinite slab. We incorporate appropriate treatments of the magnetostatic interaction, the exchange interaction within the FM, and the external applied field. We include the presence of the polycrystalline NiMn by an additional term that represents the energy of direct coupling to a NiMn grain. We consider that some NiMn grains are hysteretic as the applied field is rotated. We calculate a hysteresis loop that shows an exchange bias of 272 Oe and an enhanced coercivity of 121 Oe. These results compare favorably to the relevant experiments. We believe that this is the first demonstration of such agreement. Index Terms--Exchange bias, ferromagnet-antiferromagnet bi-layers, micromagnetics, unidirectional anisotropy.