The Exchange Bias Field In The Ferromagnetic/Antiferromagnetic Bilayers

In order to clearly understand the nature of exchange bias of the FM/AFMbilayers, we first discuss the influence of the biquadratic coupling field on both thehysteresis loops and the dependence of exchange bias field on the applied magneticfield angle. The result shows: the maximum of the exchange bias field moves towardsthe easy axis with increasing the biquadratic coupling field or bilinear coupling field;additionally, the oscillations of the curves for the angular dependence of exchangebias field become weak and gradually resembles the sine function with increasing thebiquadratic coupling field. It results from the fact that the biquadratic coupling fieldand uniaxial anisotropy of the ferromagnetic counteract each other, so the oscillationsare weakend and the curves are smoothened. The hysteresis loops are also changed bythe biquadratic coupling field.Secondly, it was found that the stress has great impact to the physical propertiesof magnetic materials. Therefore it is essential to perform a further discussion on theproblem of the film stress. Here the hysteresis loops and the dependence of exchangebias field on the applied magnetic field angle were studied by changing themagnitude and direction of the stress field respectively. The results show: when thedirection of the stress field along the easy axis, the angular dependence of exchange bias field can be characterized as the oscillations of the curves become strong withincreasing the stress field. When the direction of the stress field rotates90°, theangular dependence of exchange bias field can be characterized as the oscillations ofthe curves become weak with increasing the stress field. The hysteresis loops are alsochanged by the stress field.Futhermore, we consider the angular dependence of exchange bias field in theFM/AFM bilayers on both the biquadratic coupling and the stress when they arepresent in the system simultaneously, here we assume the AFM layer has a stronguniaxial anisotropy constant, and deduce the analytical expression of the exchangebias field. The result shows: the exchange bias field depends on the direction of theapplied magnetic field and has nothing to do with the magnitude of the appliedmagnetic field. However, the exchange bias field is influenced by the magnitude andthe direction of the stress, the magnitude of biquadratic coupling field, and the angleof the ferromagnetic and antiferromagnetic easy axes.