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.     

交换偏置双层膜中的反铁磁自旋结构及其交换各向异性

研究了交换偏置双层膜中界面存在二次以及双二次交换耦合下反铁磁磁矩转动及其交换各向异性.结果表明，其反铁磁膜中的磁矩转动存在可逆“恢复行为”、不可逆“半转动行为”、不可逆“倒转行为”以及不可逆“半倒转行为”四种情形，四种情形的出现强烈地依赖于界面二次、双二次耦合以及反铁磁膜厚度.其中可逆恢复行为情况下，系统出现交换偏置，而不可逆的半转、半倒转以及倒转情形，系统不出现交换偏置.特别地,在界面处仅存在双二次耦合的情形下，其界面双二次耦合常数J₂≤0.1 σ关键词： 反铁磁自旋结构 交换各向异性 界面双二次耦合 交换偏置     

铁磁/反铁磁/铁磁三层膜系统中反铁磁自旋结构及其交换各向异性

研究铁磁/反铁磁/铁磁三层膜中界面存在二次以及双二次交换耦合下反铁磁磁矩转动及其交换各向异性.结果表明,其反铁磁膜中的磁矩转动存在可逆"恢复行为"、不可逆"连续倒转行为"以及不可逆"中断倒转行为"三种情形,三种情形的出现强烈地依赖于两界面处的线性耦合和双二次耦合.钉扎界面的交换耦合与旋转界面的交换耦合相互竞争,当钉扎界面耦合占主导时,反铁磁磁矩发生可逆"恢复行为",系统出现交换偏置.在旋转界面耦合占主导情形下,其线性耦合与双二次耦合也相互竞争,分别导致反铁磁磁矩发生不可逆"连续倒转行为"和不可逆"中断倒转行为",系统都不出现交换偏置,但矫顽场都得以增强.相关结论为实验上观测的磁滞能耗以及界面垂直耦合提供了可能的解释.     

Influence of magnetic field sweep rate on the hysteresis loops of Ni0.8Fe0.2/Fe0.5Mn0.5 exchange bias bilayer

The influence of the magnetic field sweep rate on the hysteresis loops of exchange bias Ni0.8Fe0.2/Fe0.5Mn0.5 bilayers has been investigated with a vibrating sample magnetometer. It was found that the sweep rate of 13.6 kA/4πms is high enough to bring about obvious changes in the hysteresis loops of the exchange bias bilayer. High sweep rate in the magnetization reversal stage enlarges the coercivity of the sample, while high sweep rate in the saturation state reduces the coercivity. The above phenomena were attributed to magnetic viscosity in the ferromagnetic layer enhanced by the interface exchange interaction and domain magnetization reversals assisted by thermal fluctuation in the antiferromagnetic layer respectively.     

Ru thickness-dependent interlayer coupling and ultrahigh FMR frequency in FeCoB/Ru/FeCoB sandwich trilayers

The antiferromagnetic (AFM) interlayer coupling effective field in a ferromagnetic/non-magnetic/ferromagnetic (FM/NM/FM) sandwich structure, as a driving force, can dramatically enhance the ferromagnetic resonance (FMR) frequency. Changing the non-magnetic spacer thickness is an effective way to control the interlayer coupling type and intensity, as well as the FMR frequency. In this study, FeCoB/Ru/FeCoB sandwich trilayers with Ru thickness ($t_{\rm Ru}$) ranging from 1 Å to 16 Å are prepared by a compositional gradient sputtering (CGS) method. It is revealed that a stress-induced anisotropy is present in the FeCoB films due to the B composition gradient in the samples. A $t_{\mathrm{Ru}}$-dependent oscillation of interlayer coupling from FM to AFM with two periods is observed. An AFM coupling occurs in a range of $2 {\rm Å} \le t_{\rm Ru} \le 8 {\rm Å}$ and over 16 $\mathrm{Å}$, while an FM coupling is present in a range of $t_{\rm Ru}< 2$ Å and $9 {\rm Å} \le t_{\rm Ru} \le 14.5 Å$. It is interesting that an ultrahigh optical mode (OM) FMR frequency in excess of 20 GHz is obtained in the sample with ${t}_{\mathrm{Ru}}= 2.5 \mathrm{Å}$ under an AFM coupling. The dynamic coupling mechanism in trilayers is simulated, and the corresponding coupling types at different values of $t_{\mathrm{Ru}}$ are verified by Layadi's rigid model. This study provides a controllable way to prepare and investigate the ultrahigh FMR films.     

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.     

The influence of annealing on the bimodal distribution of blocking temperatures of exchange biased bilayers

The exchange bias effect at the interface between antiferromagnetic (AFM) and ferromagnetic (FM) layers is of paramount importance in state‐of‐the‐art spintronic devices. However, a complete account of the physics behind exchange bias remains elusive and new effects are constantly unraveled. In particular, a bimodal distribution of blocking temperatures $ (T_{\rm B})$ was recently discovered, associated with the bulk of the AFM layer and interfacial AFM/FM regions with spin‐glass‐like properties. Here we study exchange bias in MnIr (25, 60 Å)/CoFe (50 Å) bilayers annealed at high temperatures (623 K and 673 K). We observe, for all samples and annealing temperatures, the existence of a large exchange bias variation at low temperatures associated with interfacial disorder. Such variation is more significative in the thinnest samples, where it is found to be independent on annealing temperature. On the other hand, in the thickest samples the contribution of the low temperature distribution largely increases with annealing temperature, due to enhanced disorder arising from Mn diffusion. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Co-Ni/FeMn双层膜中磁化强度对交换偏置的影响

固定CoNiFeMn双层膜中反铁磁层的厚度,改变CoNi铁磁层的成分来调节磁化强度,从而研究铁磁层的饱和磁化强度对CoNiFeMn双层膜中交换偏置的影响.研究表明,CoNiFeMn界面的交换耦合能U不是一个常量,而是随(MFM)12的增加而线性增加.其原因是铁磁层磁矩通过界面相互作用在反铁磁层中形成的局域交换磁场,在磁场冷却时影响反铁磁层的自旋结构或磁畴结构及双层膜中的交换偏置 关键词： 交换偏置 磁化强度     

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.     

Parallel versus antiparallel interfacial coupling in exchange biased Co/FeF2

By using the surface and element specificity of soft x-ray magnetic dichroism we provide direct experimental evidence for two different types of interfacial uncompensated Fe moments in exchange biased Co/FeF2 bilayers. Some moments are pinned and coupled antiparallel to the ferromagnet (FM). They give rise to a positive exchange bias and vanish above T(N) = 78 together with the antiferromagnet (AF) order. Other interfacial Fe moments are unpinned and coupled parallel to the FM. They persist up to 300 K and give rise to magnetic order at the AF surface even above T(N) .     

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.     

Unified nonequilibrium dynamical theory for exchange bias and training effects

We have investigated the exchange bias and training effect in the ferromagnetic/antiferromagnetic (FM/AF) heterostructures using a unified Monte Carlo dynamical approach. The magnetization of the uncompensated AF layer is still open after the first field cycling is finished. Our simulated results show obvious shift of hysteresis loops (exchange bias) and cycling dependence of exchange bias (training effect) when the temperature is below 45~K. The exchange bias field decreases with decreasing cooling rate or increasing temperature and the number of the field cycling. Essentially, these two effects can be explained on the basis of the microscopical coexistence of both reversible and irreversible moment reversals of the AF domains. Our simulations are useful to understand the real magnetization dynamics of such magnetic heterostructures.     

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.     

Enhancement of spin-orbit torque efficiency by tailoring interfacial spin-orbit coupling in Pt-based magnetic multilayers

We study inserting Co layer thickness-dependent spin transport and spin-orbit torques (SOTs) in the Pt/Co/Py trilayers by spin-torque ferromagnetic resonance. The interfacial perpendicular magnetic anisotropy (IPMA) energy density ($K_{\rm s}= 2.7 $ erg/cm$^{2}$, 1 erg = 10$^{-7}$ J), which is dominated by interfacial spin-orbit coupling (ISOC) in the Pt/Co interface, total effective spin-mixing conductance $(G_{\mathrm{eff,tot}}^{\mathrm{\uparrow \downarrow }}=\mathrm{0.42\times }{10}^{15} \mathrm{\Omega }^{-1}\cdot\mathrm{m}^{-2}$) and two-magnon scattering ($\beta_{\mathrm{TMS}}= 0.46 {\mathrm{nm}}^{2}$) are first characterized, and the damping-like torque ($\xi_{\mathrm{DL}}= 0.103$) and field-like torque ($\xi _{\mathrm{FL}}=-0.017$) efficiencies are also calculated quantitatively by varying the thickness of the inserting Co layer. The significant enhancement of $\xi_{\mathrm{DL}}$ and $\xi_{\mathrm{FL}}$ in Pt/Co/Py than Pt/Py bilayer system originates from the interfacial Rashba-Edelstein effect due to the strong ISOC between Co-3d and Pt-5d orbitals at the Pt/Co interface. Additionally, we find a considerable out-of-plane spin polarization SOT, which is ascribed to the spin anomalous Hall effect and possible spin precession effect due to IPMA-induced perpendicular magnetization at the Pt/Co interface. Our results demonstrate that the ISOC of the Pt/Co interface plays a vital role in spin transport and SOTs-generation. Our finds offer an alternative approach to improve the conventional SOTs efficiencies and generate unconventional SOTs with out-of-plane spin polarization to develop low power Pt-based spintronic via tailoring the Pt/FM interface.     

Magnetic polarons in Ca1−xYxMnO3

Experimental evidence shows that in the magnetoresistive manganite Ca_1−xY_xMnO₃, ferromagnetic (FM) polarons arises in an antiferromagnetic (AF) background, as a result of the doping with yttrium. This hypothesis is supported in this work by classical Monte Carlo calculations performed on a model where FM double exchange and AF superexchange compete.     

Observation of exchange bias and spin-glass-like ordering in ɛ-Fe2.8Cr0.2N nanoparticles

Nanoparticles of ɛ-Fe_2.8Cr_0.2N system exhibit the exchange bias phenomenon due to the exchange coupling of the spins of the antiferromagnetic (AF) oxide/oxynitride surface layer and the ferromagnetic (FM) nitride core. Exchange bias is observed at 10 K both in the absence and presence of cooling field. Due to the interface disorder, a mixture of parallel and anti-parallel/perpendicular coupling of the AF and FM spins is observed. The roughness of AF-FM interface induces disorder due to the random exchange anisotropy. The saturation magnetization is also found to be drastically lowered as compared to parent ɛ-Fe₃N. Below 58 K, the broad peak (T _E ≅ T _f ) in zero-field cooled (ZFC) magnetization curves indicates the presence of unidirectional anisotropy and spinglass-like ordering, that arises from the freezing of localized frustrated spins.      

中层大气中脉冲点源产生的声重力波

本文从脉冲点源出发,利用广义函数的理论,将象函数作高频近似和低频近似,求得了早时响应和长时响应,从而将目前已有的结果由特殊推广到一般。再巧妙地引入含参变量的积分,可以得到(1/ω_ct₀)ⁿ的因子,此因子有极其重要的物理意义。本文的结果是:1.Row^[1]是在特殊情况下作近似,只能得到$J_{c}\\left(\\omega_{c} \\sqrt{t^{2}-t_{0}^{2}}\\right)$,本文不作近似而是在一般情况下就可得到结果。此结果除了包含特殊情况下的$J_{0}\\left(\\omega_{c} \\sqrt{(t-\\alpha)^{2}-t_{0}^{2}}\\right)$外,还得到了一个修正项$J_{1}\\left(\\omega_{c} \\sqrt{(t-\\alpha)^{2}-t_{0}^{2}}\\right)$,t-α-t₀越小,修正效应越大。2.Row^[1]的(12)式中$J_{0}\\left(\\omega_{c} \\sqrt{t^{2}-t_{0}^{2}}\\right) H\\left(t-t_{0}\\right)$的应改为$J_{0}\\left(\\omega_{c} \\sqrt{(t-\\alpha)^{2}-t_{0}^{2}}\\right)\\cdot H\\left(t-\\alpha-t_{0}\\right)$,α表示一向后的推迟时间。3.(1/ω₀t₀)ⁿ表示离源越远,t₀越大,修正效应越小。而ω_c越小周期T_c越长,修正效应越强,越低频率声重力波衰减愈慢而愈容易观察。4.从推导过程可以看到Row^[1]文章的(20)式不是长周期近似,而是高频近似。5.实验与理论一致。     

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.     

Dimensionality driven spin-flop transition in layered iridates

Using resonant x-ray diffraction, we observe an easy c-axis collinear antiferromagnetic structure for the bilayer Sr_{3}Ir_{2}O_{7}, a significant contrast to the single layer Sr_{2}IrO_{4} with in-plane canted moments. Based on a microscopic model Hamiltonian, we show that the observed spin-flop transition as a function of number of IrO_{2} layers is due to strong competition among intra- and interlayer bond-directional pseudodipolar interactions of the spin-orbit entangled J_{eff}=1/2 moments. With this we unravel the origin of anisotropic exchange interactions in a Mott insulator in the strong spin-orbit coupling regime, which holds the key to the various types of unconventional magnetism proposed in 5d transition metal oxides.