Temperature dependence of exchange bias and coercivity in ferromagnetic/antiferromagnetic bilayers

A model for the temperature dependence of exchange bias and coercivity in epitaxial ferromagnetic (FM)/ antiferromagnetic (AFM) bilayers is developed. In this model, the interface coupling includes two contributions, the direct coupling and the spin-flop coupling. The temperature dependence arises from the thermal disturbance to the system, involved in the thermal fluctuations of magnetization of AFM grains and the temperature modulation of the relevant magnetic parameters. In addition, the randomness of original orientations of easy axes of AFM grains after field cooling is taken into account. A self-consistent calculation scheme is proposed and numerical treatment is carried out. The results show that the temperature dependence of exchange bias and coercivity is closely related to the sizes of AFM grains and the interface exchange coupling constants. Especially, the exchange bias will have a peak and the blocking temperature will increase if the spin-flop coupling plays a role. On the other hand, the original orientation distribution of easy axes of AFM grains will affect exchange bias and coercivity prominently. The prediction has been well supported by experiments.Received: 12 May 2004, Published online: 31 August 2004PACS: 75.30.Et Exchange and superexchange interactions - 75.50.Ee Antiferromagnetics - 75.30.Gw Magnetic anisotropy     

铁磁/反铁磁双层膜系统中的磁畴动力学行为

比较了铁磁单层膜与铁磁/反铁磁双层膜结构中的磁畴演化行为, 发现由于反铁磁层膜对铁磁层膜的耦合作用使得系统的磁畴壁厚度、 磁畴壁等效质量、磁畴壁移动速度等发生了改变, 系统的矫顽场增强, 并出现了交换偏置场. 文章具体研究了反铁磁层耦合作用下其磁畴壁厚度、 等效质量以及磁畴壁移动速度等与反铁磁层的净磁化、 磁各向异性、界面耦合强度以及温度等的关系; 并研究了其对铁磁/反铁磁双层膜中的交换偏置场、矫顽场的影响. 进而 从磁畴结构的形成及其演化上揭示了铁磁/反铁磁双 层膜中出现交换偏置以及矫顽场增加的物理机制.     

Simulating a perpendicular exchange-biased structure with a partially covering nonmagnetic insertion at the FM/AFM interface

The existence of minority spins, opposite to the perpendicular exchange bias, and majority spins aligned with this bias, and the dependence of the perpendicular exchange-bias field on the imprint effect, caused by the partially covering spacer at the ferromagnetic/antiferromagnetic (FM/AFM) interface, have been studied using Ising-type simulations. The present investigation suggests that the main factors influencing this phenomenon were dependent on the FM/AFM interface morphology, the balance between FM/AFM coupling and the FM-spins coupling, and the numerical balance between minority and majority spins. It was also determined that the imprint phenomenon can be used to enhance the perpendicular exchange-bias for small partial insertions at the FM/AFM interface. An erratum to this article is available at.     

Exchange coupling mechanism for magnetization reversal and thermal stability of Co nanoparticles embedded in a CoO matrix

A model providing a semi-quantitative account of the magnetic behavior of Co nanoparticles embedded in a CoO matrix is presented. The results confirm that exchange coupling at the interface between ferromagnetic (FM) and antiferromagnetic (AFM) nanostructures could provide an extra source of magnetic anisotropy, leading to thermal stability of the FM nanoparticles. It is shown that perpendicular coupling between the AFM and FM moments may result in large coercivities. The energy barrier, which works against reversal is due to the AFM susceptibility anisotropy. The experimentally observed exchange bias is tentatively ascribed to pre-existing intrinsic canting of the AFM moments at the interface.     

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.     

铁磁/反铁磁双层膜系统中交换各向异性及其厚度依赖性

研究铁磁/反铁磁双层膜系统中交换偏置场和矫顽场的冷却磁场依赖性.结果表明,随着冷却磁场的增加,交换偏置场由负值向正值转变.在转变点附近,矫顽场有-个特别的增强,并达到最大值.结果同相关实验-致.研究铁磁层和反铁磁层厚度对交换偏置场和矫顽场的影响.发现,正负交换偏置场和矫顽场随着铁磁层厚度的增大而减小,但随反铁磁层厚度的变化关系复杂.在正交换偏置场的情形,随反铁磁层厚度的增大,交换偏置场增强,矫顽场减弱;在负交换偏置场的情形,随反铁磁层厚度的增大,交换偏置场减弱,矫顽场增强.     

铁磁/反铁磁双层膜系统中的交换偏置及矫顽场的温度特性

提出了一个讨论铁磁／反铁磁双层膜中的交换偏置及矫顽场温度特性的物理模型，该模型，假设铁磁层为具有单畴各向异性的单畴膜而反铁磁层由许多相互独立具有多晶各向异性的颗粒组成，其温度依赖性主要来源于系统态的热不稳定，包括反铁磁颗粒易轴取向的热涨落和相关磁学量的温度依赖性等。计算结果表明其交换偏置随温度的增加非线性地减少而其矫顽场在体阻截温度处达极大值，且其体阻截温度随反铁磁颗粒粒径的增加而增加。我们的计算结果和相关实验结果一致，通过本的讨论，我们建议通过铁磁膜耦合上大粒径硬反铁磁颗粒膜可获得高交换偏置、低矫顽场且近独立于温度的相关磁学器件。     

掺杂下铁磁/反铁磁双层膜中交换偏置的增强

采用了Monte-Carlo方法，讨论了反铁磁层中不同非磁性掺杂浓度下，铁磁/反铁磁双层膜中交换偏置的温度特性. 模拟结果显示：反铁磁层中非磁性掺杂能导致铁磁/反铁磁双层膜中交换偏置的增强. 同时，交换偏置随非磁性掺杂浓度的变化存在极大值，即同一温度下交换偏置随掺杂浓度的变化是非单调的. 并且，随着温度的升高交换偏置的最大值所对应的掺杂浓度向浓度低的方向移动. 它和Hong Jung-Il等人的实验结果完全一致. 究其原因在于反铁磁层相应的自旋排布、磁畴结构等随掺杂浓度的改变发生大的变化，当其正向磁畴和负向磁畴都形成连通的网络结构时，系统的交换偏置达最大. 比较了随机掺杂与规则掺杂的模拟结果. 模拟结果表明规则掺杂能够获得比随机掺杂更大的交换偏置，进一步表明了铁磁/反铁磁双层膜中交换偏置的特性与铁磁/反铁磁界面磁畴结构密切相关.     

Theoretical investigation of exchange bias

The exchange bias of bilayer magnetic films consisting of ferromagnetic (FM) and antiferromagnetic (AFM) layers in an uncompensated case is studied by use of the many-body Green's function method of quantum statistical theory. The effects of the layer thickness and temperature and the interfacial coupling strength on the exchange bias H_E are investigated. The dependence of the exchange bias H_E on the FM layer thickness and temperature is qualitatively in agreement with experimental results. When temperature varies, both the coercivity H_C and H_E decrease with the temperature increasing. For each FM thickness, there exists a least AFM thickness in which the exchange bias occurs, which is called pinning thickness.     

Exchange-coupling-induced fourfold magnetic anisotropy in CoFeB/FeRh bilayer grown on SrTiO3(001)

Exchange coupling across the interface between a ferromagnetic (FM) layer and an antiferromagnetic (AFM) or another FM layer may induce a unidirectional magnetic anisotropy and/or a uniaxial magnetic anisotropy, which has been extensively studied due to the important application in magnetic materials and devices. In this work, we observed a fourfold magnetic anisotropy in amorphous CoFeB layer when exchange coupling to an adjacent FeRh layer which is epitaxially grown on an SrTiO₃(001) substrate. As the temperature rises from 300 K to 400 K, FeRh film undergoes a phase transition from AFM to FM phase, the induced fourfold magnetic anisotropy in the CoFeB layer switches the orientation from the FeRh$\langle 110\rangle $ to FeRh$\langle 100\rangle $ directions and the strength is obviously reduced. In addition, the effective magnetic damping as well as the two-magnon scattering of the CoFeB/FeRh bilayer also remarkably increase with the occurrence of magnetic phase transition of FeRh. No exchange bias is observed in the bilayer even when FeRh is in the nominal AFM state, which is probably because the residual FM FeRh moments located at the interface can well separate the exchange coupling between the below pinned FeRh moments and the CoFeB moments.     

Exchange bias mechanism in FM/FM/AF spin valve systems in the presence of random unidirectional anisotropy field at the AF interface: The role played by the interface roughness due to randomness

We propose an atomistic model and present Monte Carlo simulation results regarding the influence of FM/AF interface structure on the hysteresis mechanism and exchange bias behavior for a spin valve type FM/FM/AF magnetic junction. We simulate perfectly flat and roughened interface structures both with uncompensated interfacial AF moments. In order to simulate rough interface effect, we introduce the concept of random exchange anisotropy field induced at the interface, and acting on the interface AF spins. Our results yield that different types of the random field distributions of anisotropy field may lead to different behavior of exchange bias.     

Modeling of magnetization processes in exchange coupled fluoride bilayers

The angular dependence of the hysteresis loops of ferromagnetic/antiferromagnetic (FM/AF) bilayer with a compensated interface is investigated by means of numerical simulation for a perfect single-crystalline AF layer having no AF domains at the FM/AF interface, as well as for a twinned AF layer. For applied magnetic field direction nearly parallel to the AF easy axis the completely reversible loops with finite exchange bias field have been obtained for the uniform case, while a large exchange bias has been found for the twinned case, in agreement with experimental results.     

Experimental magnetic study and evidence of the exchange bias effect in unidimensional Co arrays produced by interference lithography

A simple process for fabricating submicrometric magnetic arrays employing interference lithography, sputtering deposition and lift-off processes is proposed and demonstrated. The magnetic properties of cobalt (Co) arrays were measured and compared with those of a continuous Co magnetic film. The results show a dependence of the hysteresis curve on the orientation of the field as regards the array, which is correlated with the anisotropy of the structures and a dependence of the coercive field on the periodicity of the arrays. Moreover, an exchange bias effect was observed, which is ascribed to a ferromagnetic/antiferromagnetic (FM/AFM) coupling between Co and a thin surface cobalt oxide (CoO) layer.     

Room temperature exchange bias in multiferroic BiFeO<Subscript>3</Subscript> nano- and microcrystals with antiferromagnetic core and two-dimensional diluted antiferromagnetic shell

Exchange bias (EB) of multiferroics presents many potential opportunities for magnetic devices. However, instead of using low-temperature field cooling in the hysteresis loop measurement, which usually shows an effective approach to obtain obvious EB phenomenon, there are few room temperature EB. In this article, extensive studies on room temperature EB without field cooling were observed in BiFeO₃ nano- and microcrystals. Moreover, with increasing size the hysteresis loops shift from horizontal negative exchange bias (NEB) to positive exchange bias (PEB). In order to explain the tunable EB behaviors with size dependence, a phenomenological qualitative model based on the framework of antiferromagnetic (AFM) core-two-dimensional diluted antiferromagnet in a field (2D-DAFF) shell structure was proposed. The training effect (TE) ascertained the validity of model and the presence of unstable magnetic structure using Binek’s model. Experimental results show that the tunable EB effect can be explained by the competition of ferromagnetic (FM) exchange coupling and AFM exchange coupling interaction between AFM core and 2D-DAFF shell. Additionally, the local distortion of lattice fringes was observed in hexagonal-shaped BiFeO₃ nanocrystals with well-dispersed behavior. The electrical conduction properties agreed well with the space charge-limited conduction mechanism.     

Magnetic structures of exchange bias Ni/FeF2(1 1 0) interface

Electronic and magnetic structures of ferromagnetic (FM)/antiferromagnetic (AFM), Ni/FeF₂(1 1 0), with a compensated AFM interface are investigated by using the full-potential linearized augmented plane-wave method. We find that magnetic structures at the AFM interface are perturbed by a contact with the FM material, where the superexchange interaction through the interface F excites and induces a small net moment at the AFM interface. These results predicted may play an important role for explaining the exchange bias in this system, and rule out the exchange bias mechanisms with the spin-flop coupling and the magnetic moment reorientation.     

Numerical simulation of magnetization process in antiferromagnetic–ferromagnetic bilayer with compensated interface

The properties of antiferromagnetic (AFM)–ferromagnetic (FM) bilayer have been studied using self-consistent mean-field approximation for Heisenberg Hamiltonian. The perpendicular exchange coupling has been revealed in a bilayer with a compensated interface. For a uniform AFM film a symmetrical hysteresis loop has been calculated, because the transverse instability develops within the AFM film at certain critical value of external magnetic field. On the other hand, shifted hysteresis loop with a finite exchange bias field has been obtained for a non-uniform AFM film consisting of various AFM domains with perpendicular directions of the easy anisotropy axes.     

Asymmetric magnetization reversal behavior and noncollinear anisotropies in exchange-bias system

The effect of noncollinearity between unidirectional and uniaxial anisotropies on asymmetric magnetization reversal of ferromagnet/antiferromagnet (FM/AFM) bilayer has been investigated. The results show the emergence of noncollinear anisotropies comes from the competition among applied magnetic field, magnetic anisotropy and exchange coupling in FM/AFM interface. The noncollinearity can lead to the asymmetry of hysteresis loop of FM/AFM bilayer. However, when the magnetic field is applied along the uniaxial anisotropy axis of FM layer, the hysteresis loop of FM/AFM bilayer is always symmetry independence of the noncollinear angle. Our results indicate that the asymmetry not only originates from the noncollinearity but also depends on the applied magnetic field orientation. Moreover, the asymmetry of hysteresis loop is always along with the appearance of unequivalence for magnetization reversal of FM/AFM bilayer, and there is a periodicity of π with orientation of applied field for its periodicity independence of the angle of the noncollinearity between the uniaxial and unidirectional anisotropies. The results can help us to open additional avenues to tailor the future advance magnetic device.     

Interface induced exchange bias effect in La0.67Sr0.33MnO3/SrIrO3 multilayer

Epitaxial superlattices of ferromagnetic/paramagnetic La_0.67Sr_0.33MnO₃/SrIrO₃ materials have been prepared on SrTiO₃ (100) substrate using pulse laser deposition technique. An unexpected onset of interface magnetic interaction has been observed around 40 K. Interestingly, magnetic exchange bias effect has been observed in both field cooled and zero field cooled magnetization loops, however, the shifting of loop is opposite in both measurements. Exchange bias field vanishes as temperature increases to interface magnetic ordering temperature. Moreover, exchange bias field is found to decrease with increasing cooling field. We believe that tuning of magnetic exchange at interface during field cooling induces this evolution in nature of exchange bias field.     

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     

Defect-tuning exchange bias of ferromagnet/antiferromagnet core/shell nanoparticles by numerical study

The influence of non-magnetic defects on the exchange bias (EB) of ferromagnet?(FM)/antiferromagnet?(AFM) core/shell nanoparticles is studied by Monte Carlo simulations. It is found that the EB can be tuned by defects in different positions. Defects at both the AFM and FM interfaces reduce the EB field while they enhance the coercive field by decreasing the effective interface coupling. However, the EB field and the coercive field show respectively a non-monotonic and a monotonic dependence on the defect concentration when the defects are located inside the AFM shell, indicating a similar microscopic mechanism to that proposed in the domain state model. These results suggest a way to optimize the EB effect for applications.