Measurement of exchange anisotropy in exchange-bias bilayers

Recently, experimental results for ferromagnetic (FM) and antiferromagnetic (AFM) bilayers show that the measured exchange anisotropy depends on what measurement is done. In this article, we theoretically investigate how the interface exchange coupling including bilinear and biquadratic terms manifests itself in different measurements such as hysteresis loop, ac susceptibility, and ferromagnetic resonance in FM/AFM bilayers. In the semi-infinite limit for the AFM layer, the analytical expressions for measured exchange anisotropy from the hysteresis loop, ac susceptibility and ferromagnetic resonance are derived. It is found that the intrinsic magnetic parameters, such as FM anisotropy constant, AFM domain wall energy, and the interface exchange coupling including the bilinear and biquadratic contributions, can play different roles in different measurement techniques. However, by comparing different measurements the intrinsic magnetic parameters, the domain energy σAFMσAFM and the bilinear and biquadratic exchange coupling constants JE1JE1 and JE2JE2, can be determined, respectively