The phases of the antiferromagnetic magnetization and the corresponding exchange bias and coercivity in exchange-biased bilayers(FM/AF) with interface quadratic and biquadratic exchange coupling have been studied comprehensively. The results show that there are four possible cases for the antiferromagnetic magnetization, namely the reversible recovering case, irreversible half-rotating case, irreversible reversing and irreversible half-reversing cases. However, the realization of the cases strongly depends on interface quadratic coupling, interface biquadratic coupling and AF thickness. In the reversible recovering case the exchange coupling between FM and AF results in the exchange bias, and there is no exchange bias in the other cases. Specially, for exchange-biased bilayers without interface quadratic coupling, there exists a critical value of the biquadratic coupling constant J2crit=0.1σw(σw denotes AF domain wall energy), below which the positive exchange bias appears, otherwise there is no exchange bias, and the coercivity can be enhanced. For the FM/AF bilayers with interface quadratic and biquadratic coupling, the interface biquadratic coupling can weaken or eliminate the exchange bias, but always enhances the coercivity.
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