The eigenproblems of spin waves in a symmetrical ferromagnetic bilayered system with periodic boundary conditions are solved using the interface-rescaling approach (IRA).The results show that interface coupling between two sublayers would not change the excitation energy of odd bulk modes,but change excitation energy of even bulk modes.We call this peculiar phenomenon the phenomenon of even bulk mode variance (PEBMV).There are two kinds of mechanisms which cause PEBMV:phase reversal and phase translation of the magnon at the interface,corresponding,respectively,to the antiferromagnetic and ferromagnetic interface coupling cases.PEBMV embodies the selective effect of the interface on different bulk magnons.
Using the principle of minimal energy and S-W model,the exchange bias for ferromagnetic/antiferro-magnetic bilayers has been investigated when the uniaxial anisotropy is misaligned with the exchange anisotropy. According to the relation between the energy of the bilayer and the orientation of ferro-magnetic magnetization,it is found that the bilayer will be in the monostable state or bistable state when the external field is absent in the initial magnetization state. The monostable state or bistable state of the bilayer,which determines the angular dependence of exchange bias directly,is controlled by the competition between the exchange anisotropy and uniaxial anisotropy. When the applied field is parallel to the intrinsic easy axes and intrinsic hard axes,one of the switching fields of the hysteresis loop shows an abrupt change,while the other keep continuous by analyzing the magnetization reversal processes. Consequently,the exchange bias field and the coercivity will show a jump phenomenon. The numerical calculations indicate that both the magnitude and direction of the exchange anisotropy will significantly affect the angular dependence of exchange bias. The jump phenomenon of exchange bias is an intrinsic property of the bilayer,which is dependent on the interfacial exchange-coupling constant,the orientation of the exchange anisotropy,the thickness and uniaxial anisotropy constant of the ferromagnetic layer.
BAI YuHao1 & YUN GuoHong1,2 1 College of Physical Science and Technology,Inner Mongolia University,Hohhot 010021,China
