Ferromagnetic thickness dependence of exchange bias: breaking of the inverse proportionality law*

The exchange coupling between antiferromagnetic/ferromagnetic (AF/FM) materials shifts the hysteresis loop along the field axis by an amount known as exchange bias field. It is believed that the ferromagnetic thickness dependence of the exchange bias field follows an inverse proportionality law. This has experimentally and theoretically been confirmed for FM thicknesses below the FM domain wall width. In this work we demonstrate that this exchange bias dependence is broken for certain FM spin structures, even though in FM layers thinner than the FM domain wall width. We present experimental data of FeF$_{2}$/FeNi bilayers that deviate from the inverse proportionality law, as well as a theoretical calculation that accounts for the results.