The structure dependence of exchange bias in ferromagnetic/antiferromagnetic bilayers

The structure dependence of exchange bias in ferromagnetic/antiferromagnetic （FM/AF） bilayers has been investigated in detail by extending Slonczewski＇s ＇proximity magnetism＇ idea. Here three important parameters are discussed for FM/AF bilayers, i.e. interracial bilinear exchange coupling J1, interracial biquadratic （spin-flop） exchange coupling J2 and antiferromagnetic layer thickness tAF. The results show that both the occurrence and the variety of the exchange bias strongly depend on the above parameters. More importantly, the small spin-flop exchange coupling may result in an exchange bias without the interracial bilinear exchange coupling. However, in general, the spin-flop exchange coupling cannot result in the exchange bias. The corresponding critical parameters in which the exchange bias will occur or approach saturation are also presented.     

Thickness dependence of positive exchange bias in ferromagnetic/antiferromagnetic bilayers

For the ferromagnetic (FM)/antiferromagnetic (AFM) bilayers, both negative and positive exchange bias H_E have been observed for low and high cooling field H_CF, respectively. The thickness dependence of H_E and coercivity H_C have been investigated for the cases of negative and positive H_E. It is found that the negative H_E and the positive one have similar FM thickness dependence that is attributed to the interfacial nature of exchange bias. However, the AFM thickness dependence of positive H_E is completely contrary to that of the negative one, which clearly demonstrates that the AFM spins play different roles for the cases of positive and negative H_E. In particular, the AFM thickness of positive H_E was first highlighted by an AFM spin canting model. These results should be attributed to the interfacial spin configuration after field cooling procedure.     

Interfacial roughness and temperature effects on exchange bias properties in coupled ferromagnetic/antiferromagnetic bilayers

Monte Carlo simulations have been used to study the relationship between the exchange bias properties and the interface roughness in coupled ferromagnetic/antiferromagnetic (FM/AFM) films of classical Heisenberg spins. It is shown that the variation of the exchange bias field versus the AFM anisotropy strongly depends on the FM/AFM interface. Unlike the flat interface, a non-monotonic dependence is observed for the roughest FM/AFM interface. This is explained by canted magnetic configurations at the FM/AFM interface, which appear after the first reversal due to the magnetic frustration. The temperature dependence of the exchange field is also dependent on the roughness. While the exchange field is roughly constant for the flat interface, a decrease is observed for the roughest interface as the temperature increases. This has been interpreted as a significant decrease of the effective coupling between the FM and the AFM due to the disordering of the moments at the FM/AFM interface because of the combination of magnetic frustration and temperature activation.     

Spin-flop coupling and exchange anisotropy in ferromagnetic/antiferromagnetic bilayers

By investigating the antiferromagnetic spin configuration, the exchange anisotropy and the interfacial spin-flop coupling in ferromagnetic/antiferromagnetic (FM/AF) bilayers have been discussed in detail. The results show that there are four possible cases for the AF spins, namely the reversible recovering case, irreversible half-rotating case, irreversible reversing and irreversible half-reversing cases. Moreover, the realization of the cases strongly depends on interface quadratic coupling, interface spin-flop (biquadratic) coupling and AF thickness. The magnetic phase diagram in terms of the AF thickness t_AF, the interfacial bilinear coupling J₁ and the spin-flop coupling J₂ has been constructed. The corresponding critical parameters in which the exchange bias will occur or approach saturation have been also presented. Specially, the small spin-flop exchange coupling may result in an exchange bias without the interfacial bilinear exchange coupling. However, in general, the spin-flop exchange coupling can weaken or eliminate the exchange bias, but always enhances the coercivity greatly.     

Half-metallic exchange bias ferromagnetic/antiferromagnetic interfaces in transition-metal chalcogenides

To investigate half-metallic exchange bias interfaces, magnetic structures at ferromagnetic (FM)/antiferromagnetic (AFM) interfaces in the zinc blende transition-metal chalcogenides, and with compensated and uncompensated AFM interfaces, were determined by the full-potential linearized augmented plane-wave method. With the uncompensated AFM interface, an antiparallel alignment of the Cr and Mn moments induces an excellent half-metallicity. More striking still, in the compensated AFM interface the Cr moments in the FM layer lie perpendicular to the Mn moments in the AFM layer but the Mn moments strongly cant to induce a net moment so as to retain the half-metallicity. These findings may offer a key ingredient for exchange biased spintronic devices with 100% spin polarization, having a unidirectional anisotropy to control and manipulate spins at the nanoscale.     

外应力对铁磁/反铁磁体系交换偏置的影响及阶跃现象

采用能量极小原理及S-W模型研究了外应力对铁磁/反铁磁（FM/AFM）双层薄膜体系交换偏置的影响.不施加外磁场时,根据能量与铁磁层磁化强度方向之间的关系,指出体系存在单稳态和双稳态两种不同的状态,是由交换各向异性与单轴各向异性之间的竞争控制的.体系处于单稳态还是双稳态直接决定着交换偏置的角度依赖关系.分析磁化过程发现,外磁场沿内禀易轴及内禀难轴方向施加时,磁滞回线的一支转换场发生突变,而另一支转换场则保持不变,最终导致交换偏置场和矫顽场出现阶跃行为.数值计算表明,交换偏置场和矫顽场在阶跃点均具有较大的数值 关键词： 单稳态 双稳态 外应力     

Exchange bias for ferromagnetic/antiferromagnetic bilayers with the uniaxial anisotropy being misaligned with the exchange anisotropy

Using the principle of minimal energy and S-W model, the exchange bias for ferromagnetic/antiferromagnetic 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 ferromagnetic 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.     

Pt插层对铁磁/反铁磁界面交换耦合的影响

在铁磁层(FM)/反铁磁层(FeMn)耦合体系中插入Pt 插层或对靠近FM/FeMn界面处的FeMn掺杂Pt元素,研究了体系的交换偏置场 H_ex及矫顽力H_c随Pt插层深度 d_Pt与Pt掺杂层厚度t_PtFeMn的变化关系. 实验结果表明,引入Pt插层后NiFe/FeMn(d_Pt)/Pt/FeMn体系的未补偿磁矩(UCS)的数量得到很大的提高,从而对H_ex与H_c 起到增强的作用; 同时, 从实验结果可以推测FeMn层内部UCS的分布深度约为1.3 nm. 另外,对靠近FM/FeMn界面处的FeMn掺杂Pt元素,发现掺入Pt元素后体系的H_ex 得到有效增强, 这是因为掺入Pt元素后体系UCS的数量也得到很大的提高.     

Resultant exchange bias and coercivity on rotatable antiferromagnetic anisotropy in ellipsoidal core/shell nanoparticles

A special consideration has been conducted on the dependencies of exchange bias and coercivity on rotatable antiferromagnetic anisotropy with respect to the collinear ferromagnetic anisotropy and field-cooling directions in ellipsoidal core/shell nanoparticles. With increasing the angle between antiferromagnetic and ferromagnetic easy axes, exchange bias field and coercivity both exhibit biaxial symmetries about the ferromagnetic easy and hard axes. Moreover, the variations of the antiferromagnetic anisotropy constant cannot change the trends of these novel behaviors, but only control their occurrences by dominating the coercive field behaviors. This new exchange-biased feature obtained by means of the special nanoparticle shape and the relative angle between anisotropies is of technological importance for maximizing exchange bias, in order to optimize the designs of the involved devices.     

铁磁/反铁磁双层膜中的磁锻炼效应

采用Monte Carlo 方法,研究铁磁/反铁磁双层膜中的磁锻炼效应.结果表明,反铁磁层中冷场诱发的界面净磁化(钉扎效应)的磁弛豫可导致系统中的交换偏置场的磁锻炼效应.进一步研究表明,反铁磁层中掺杂可调控交换偏置场的磁锻炼效应,原因在于反铁磁层中掺杂能有效地改变冷场诱发的净磁化的磁弛豫过程.     

外应力场下铁磁/反铁磁双层膜系统中的交换偏置

采用自由能极小的方法研究了铁磁/反铁磁双层膜系统在外应力场下的交换各向异性.本模型中铁磁层具有单轴磁晶各向异性和立方磁晶各向异性，而反铁磁层仅具有单轴磁晶各向异性，但其厚度趋于半无穷.理论上解析地给出了系统的等效交换偏置和钉扎角(它显示了反铁磁层对铁磁层磁化的钉扎作用)与外应力场之间的关系.数值计算表明：系统的等效交换偏置与外磁场的方向有关，而与其大小无关；然而外应力场的大小和方向均对系统的等效交换偏置有影响，其根源在于外应力场的大小和方向都影响着钉扎角. 关键词： 铁磁/反铁磁双层膜 交换偏置 钉扎角 应力场     

Relative-thickness dependence of exchange bias in bilayers and trilayers

We consider the models of ferromagnetic (FM)/antiferromagnetic (AFM) bilayers and trilayers and perform a modified Monte Carlo method to study their exchange bias (EB) properties at low temperature after field cooling on increasing one component thickness at the expense of the other one. The results indicate that EB is insensitive to the thickness variations as the FM layer is thicker than the AFM one. Otherwise, it has a steep increase with the decrease of FM thickness, but the purely inverse proportion is no longer valid due to the dual influences of FM and AFM thicknesses. EB in trilayers should be approximately twice larger than that in bilayers because there is a double interfacial area in the trilayers compared with the bilayers, but the dispersed FM/AFM distributions may break this relation as a result of thermal destabilization. Moreover, EB is independent of FM/AFM stacking sequences probably because of the ideal interface between them. It has been clarified unambiguously that such control of EB through varying the FM/AFM dimensions in heterostructures is attractive for spintronics applications.     

Dependence of exchange bias on core/shell relative dimension in ferromagnetic/antiferromagnetic nanoparticles

We employ a modified Metropolis Monte Carlo simulation to study the effect of bimagnetic core/shell relative dimension on exchange bias in ferromagnetic/antiferromagnetic nanoparticles. The exchange bias field is inversely proportional to the ferromagnetic shell thickness in the antiferromagnetic (core)/ferromagnetic (shell) nanoparticles, while in the nanoparticles with an opposite core/shell structure the exchange bias behavior is complex and distinguished in different ranges of the ferromagnetic core radius. The work elucidates unambiguously how the core and shell dimensions optimize the exchange bias in nanoparticles.     

Numerical study of exchange bias in antiferromagnetic/ferromagnetic core/shell nanoparticles with non-magnetic defects

We perform Monte Carlo simulations for an antiferromagnetic/ferromagnetic core/shell nanoparticle with a doubly inverted structure. We investigate the dependence of the exchange bias field and coercivity on the magnetic dilution of the shell-interface and shell part. It is demonstrated that exchange bias and coercivity can exhibit monotonic or non-monotonic behavior depending on the location of the non-magnetic components. Also, temperature dependence of the exchange bias and coercivity of the system are studied for a particular defect concentration value. Our results provide an alternative way for tunning the magnetic properties of doubly inverted nanoparticles.     

Tunning exchange bias in inverted antiferromagnetic/ferromagnetic core/shell nanoparticles by binary alloy shells

A detailed investigation of exchange bias properties of an inverted nanoparticle with an antiferromagnetic core and a ferromagnetic binary alloy shell of the type $B_x{C}_{1?x}$ is presented by benefiting from Monte Carlo simulations. Exchange bias displays a non-monotonic behavior with the varying value of the concentration the type-B magnetic components, x. Coercivity exhibits a monotonic or a non-monotonic variation with x depending on the relative strength between unlike magnetic components in the shell. Particular attention has also been given to determine the effects of the cooling field process on the magnetic properties of the nanoparticle. Numerical results obtained in this work present a different physical mechanism and an alternative way for tuning the exchange bias and coercivity of bimagnetic core/shell nanoparticles.     

Hysteretic behavior of angular dependence of exchange bias in FeNi/FeMn bilayers

For FeNi/FeMn bilayers, the angular dependence of exchange bias shows hysteresis between clockwise and counterclockwise rotations, as a new signature. The hysteresis decreases for thick antiferromagnet layers. Calculations have clearly shown that the orientation of antiferromagnet spins also exhibits hysteresis between clockwise and counterclockwise rotations. This furnishes an interpretation of the macroscopic behavior of the ferromagnetic layer in terms of the thermally driven evolution of the magnetic state of the antiferromagnet layer.     

Model of hybrid interfacial domain wall in ferromagnetic/antiferromagnetic bilayers

A general model of a hybrid interfacial domain wall(HIDW) in ferromagnetic/antiferromagnetic exchange biased bilayers is proposed, where an interfacial domain wall is allowed to extend into either the ferromagnetic or antiferromagnetic layer or across both. The proposition is based on our theoretical investigation on thickness and field dependences of ferromagnetic domain wall(FMDW) and antiferromagnetic domain wall(AFDW), respectively. Good match of the simulation to the hysteresis loops of a series of Ni Fe/Fe Mn exchange-biased bilayers confirms the existence of the HIDW, where the AFDW part is found to preferentially occupy the entire antiferromagnetic layer while the FMDW shrinks with the increased magnetic field as expected. The observed asymmetry between the ascending and descending branches of the hysteresis loop is explained naturally as a consequence of different partition ratios between AFDW and FMDW.     

外应力场下铁磁/反铁磁双层膜系统的铁磁共振性质

从系统能量出发，采用Smith和Beljers理论方法研究了铁磁/反铁磁双层膜系统在外应力场下的铁磁共振现象.本模型中铁磁薄层具有单轴磁晶各向异性和立方磁晶各向异性，而反铁磁层非常薄因而其能量可忽略.推导出了该系统的铁磁共振频率和频谱宽度的解析式.结果表明：外应力场仅在低磁场下对具有立方磁晶各向异性系统的铁磁共振有影响，且区分弱磁场和强磁场的临界场依赖于外应力场的方向. 关键词： 铁磁/反铁磁双层膜 交换偏置 铁磁共振 应力场     

Interfacial spin interactions of ferromagnetic and antiferromagnetic manganite bilayers

A pulsed laser deposition technique was used to grow ferromagnetic La_0.7Sr_0.3MnO₃ (LSMO) films on antiferromagnetic La_0.33Ca_0.67MnO₃ (LCMO) and Pr_0.7Ca_0.3MnO₃ (PCMO) films in bilayer forms. The LSMO film on the PCMO layer had a more elongated out-of-plane lattice than that on the LCMO layer. The former had a lower ferromagnetic transition temperature (320 K) than the latter (350 K). The enhanced low-temperature magnetoresistance of the LSMO/PCMO bilayer suggests that the spin frustration is stronger at this bilayer than in the LSMO/LCMO bilayer. These differences indicate that strain state and defect concentration play important roles in governing interfacial spin interactions.