Numerical Study Of The Cooling Field And Temperature Dependent Exchange Bias Effect In Ferromagnet/spin Glass Systems

The EB effect in ferromagnet(FM)/antiferromagnet(AFM)bilayers has been studied extensively because of its central role in spintronic devices and intriguing physics.and the behavior of cooling field and temperature dependent exchange bias is obvious.In contrast,if systems are associated with the SG,the EB effect may be also influenced by HFC and T in a quite different manner.In the studies of EB in spin glass systems,Nanjing University Professor Du Jun experimentally studied the EB in FeNi/FeAu bilayers,and obtained a series of results.We report theoretical studies on the cooling field(HFC)and temperature(T)dependent exchange bias(EB)in spin glass(SG)/ferromagnet(FM)bilayers,and based on the result of Nanjing University and simulations were performed with the Heisenberg vecror model,using Monte Carlo techniques to re reproduce and interpret the EB phenomena governed by HFC and T.The following are our simulation results.First,the T dependences of EB in the FeAu/FeNi SG/FM bilayers have been investigated numerically.From the simulaitons,it is demonstrated that with elevating T the exchange bias field(HE)is initially negative and decreases in magnitude,then the HE rolls off to zero in blocking temperature.When T is increased further,HE changes its sign to a maximum positive value then decreases gradually.And finally vanishes at the EB blocking temperature.Meantime,with decreaseing the T the dependent coercivity(HC)exhibits decrease monotonous.And,in a relatively high temperature,it changes relatively flat,but in the low temperature zone will increase rapidly.Then,we also simulate the T dependences of EB in the FeAu/FeNi SG/FM bilayers,From the simulaitons,it is demonstrated that a negetive EB was established,and at the low T,with increasing the HFC,the HE decreases monotonously.This phenomenon is opposite to the traditional FM/AFM bilayers.Nevertheless,the HE value becomes positive at relatively high temperatures.And the HE value increases monotonouslly with increasing HFC,especially at the low T while HC is insensitive to HFC.In order to explain the above results,we take the advantages of theoretical simulation,we respectively Calculate the interface exchange at the low T and the interface exchange field at high T in the FM/SG bilayers systems.The results show that in the SG bulk after the field cooling process,the cooling field can improve the energy barrier.In contrast,the SG phase at low T can evolve spontaneously towards more stable states with lower exchange energies during the isothermally magnetizing process due to the low energy barrier in the SG bulk.Therefore,during the magnetization reversal at the descending branch of the M-H loops,under the weak HFC the H needs to overcome more interfacial exchange energy to reverse magnetization,so the HC is very strong.During the magnetization reversal process at the ascending branch of the M-H,it formates the noncollinearity of spin orientations due to the low energy barrier under the weak HFC.The interfacial coupling between SG spins and FM spins can weak the H when during the magnetization reversal and lead to the HC decrease.As a result,the weaker the cooling field,the stronger the exchange bias field.And the contribution of the cooling field to the magnetization process is constant,thereby He is independent of HFC.At the high temperature,Moreover,it is further demonstrated that a FM-to-AFM transition of types of interfacial couplings occurs only during isothermally magnetizing process in a narrow T region just below TB,and this is the reason why the HE value is positive at the temperature area.Meantime,due to the cooling field is constant when changing the SG spin energy barrier,this leads to the coupling enhance between the SG systems and FM under the strong HFc,In other words,it increases the positive HE value.The main significance of this paper lies in we obtain the EB effect in ferromagnet(FM)/antiferromagnet(AFM)bilayers,and clarify the cooling field(HFC)and temperature(T)dependent exchang bias.On the other hand,using a short-range SG vector model,we report a qualitative simulation on the cooling field(HFC)and temperature(T)dependent exchange bias(EB)in spin glass(SG)/ferromagnet(FM)bilayers.This not only enriches our understanding of the exchange bias effect,but provides a effective method to study EB effect in more complex systems.