Exchange bias in ferromagnetic/antiferromagnetic bilayers

We present a theoretical investigation on the thickness dependence of exchange bias in ferromagnetic (FM)/antiferromagnetic (AFM) bilayer systems, in which the exchange coupling at the interface between the FM layer and the AFM layer includes both bilinear (direct exchange) and biquadratic (spin-flop) terms. Based on the above model, the basic formula is derived for the first time. From the formula, a lot of interesting facts can be extracted, and a number of recent experimental results can be illustrated. We find that the exchange bias linearly depends on the reciprocal of FM layer thickness. However, another factor is the switching thickness of the AFM layer to display exchange bias, which approaches saturation with a relatively thick AFM layer. In general, the biquadratic term reduces exchange bias. When the biquadratic coupling is properly selected, the discrepancies in the previous theories and experiments can be efficiently eliminated.