Influence Of Stress And Cubic Anisotropy On The Angular Dependence Of The Exchange Bias

In recent years,giant magnetoresistance(GMR)and tunneling magnetoresistance(TMR)sensors grown on flexible substrates have received widespread attention due to the controllable mechanical deformability and the superior property.The bending ferromagnetic/antiferromagnetic film can be used to study the effect of the magnetic and transport properties on the mechanical stresses for the ferromagnetic/antiferromagnetic film grown on the flexible substrate,it is found that the hysteresis loops with different magnitudes and orientations of the stress can be classified into three types,which brings about the different exchange bias behaviors.The corresponding physical conditions for each type of the loop are deduced based on the principle of minimal energy.The equation of the critical stress is derived,which can be used to judge whether the loops show hysteresis or not.Numerical calculations suggest that except for the magnitude of the mechanical stress,the relative orientation of the stress is also an important factor to tune the exchange bias effectIn addition,we have investigated the effect of the cubic anisotropy on the exchange bias behavior of the ferromagnetic/antiferromagnetic bilayers.Based on the principle of minimal energy,the phase diagram of the initial states have been given.The corresponding physical equations about these initial states have been derived.Then,the types of the hysteresis loops and the angular dependence of the exchange bias have been discussed.It demonstrates that there are two different modes of the hysteresis loop: the whole planar and the half planar rotation modes.Additionally,the jump phenomenon can also be observed in the angular dependence of the exchange bias.We explain theoretically this jump phenomenon and the amplitude of the jump phenomenon together with the extreme value problem have also been discussed.Our investigations can be useful to understand the influence of the cubic anisotropy on the exchange bias.Different from the theoretical calculations,considering the constrain of the experimental installation,the pinning direction of the exchange bias will not be set randomly.Therefore,some common mutual angle between the pinning direction of the exchange bias and the applied field,which is set as 0°,45° and 90°,have been discussed in order to compare the theoretical results with the experimental measurements.The numerical results indicate that the larger coercivity can be achieved on the condition of the larger cubic anisotropy,while the larger exchange bias field can only be achieved by adjusting the direction of the cooling field,which does not need the magnetic material with a larger cubic anisotropy.