Magnetic anisotropy in IrMn/Co structures with an alternative sequence of deposition of antiferromagnetic and ferromagnetic layers

The preparation conditions and the magnitudes of the uniaxial and unidirectional magnetic anisotropies of IrMn/Co structures with an alternative sequence of deposition of antiferromagnetic and ferromagnetic layers upon heat treatment and cooling in an external magnetic field have been investigated. It has been revealed that the unidirectional anisotropy (exchange bias) arises in the structure with an antiferromagnetic layer deposited on a ferromagnetic layer (TS structure) at an annealing temperature of higher than 100°C. In structures with a ferromagnetic layer deposited on an antiferromagnetic layer (BS structure), the exchange bias does not arise in the annealing temperature range under investigation. The possible factors responsible for this effect and the ratio between the temperature of the appearance of the exchange bias and the Néel temperature have been discussed.     

Angular and NiFe thickness dependence of exchange bias in IrMn/NiFe/IrMn thin film

Exchange biased IrMn/NiFe/IrMn thin films were studied as a function of NiFe thickness. In plane angular dependence of a resonance field distribution which is measured by FMR was analyzed as a combined effect of an unidirectional anisotropy and an uniaxial anisotropy. The unidirectional anisotropic field and the uniaxial anisotropic field were linearly varied with NiFe thickness while the films with a thicker NiFe layer do not follow the linear variation. Resonance field and linewidth variations were also analysed with NiFe thickness.     

Effect of Ta buffer and NiFe seed layers on pulsed-DC magnetron sputtered Ir20Mn80/Co90Fe10 exchange bias

A systematic investigation has been done on the correlation between texture, grain size evolution and magnetic properties in Ta/Ni₈₁Fe₁₉/Ir₂₀Mn₈₀/Co₉₀Fe₁₀/Ta exchange bias in dependence of Ta buffer and NiFe seed layer thickness in the range of 2-10 nm, deposited by pulsed DC magnetron sputtering technique. A strong dependence of 〈1 1 1〉 texture on the Ta/NiFe thicknesses was found, where the reducing and increasing texture was correlated with exchange bias field and unidirectional anisotropy energy constant at both NiFe/IrMn and IrMn/CoFe interfaces. However, a direct correlation between average grain size in IrMn and H_ex and H_c was not observed. L1₂ phase IrMn₃ could be formed by thickness optimization of Ta/NiFe layers by deposition at room temperature, for which the maximum exchange coupling parameters were achieved. We conclude finally that the coercivity is mainly influenced by texture induced interfacial effects at NiFe/IrMn/CoFe interfaces developing with Ta/NiFe thicknesses.     

Extracting uniaxial anisotropy of ferromagnetic layer in exchange-biased system

Effective anisotropy of the ferromagnetic pinned layer of ferro(FM)-antiferromagnetic (AF)-coupled NiFe(FM)/FeMn(AF) exchange-biased system was investigated in a broad frequency range (100 MHz-5 GHz) using a complex permeability spectrum. The exchange bias and effective uniaxial anisotropy fields of the thin film have been computed theoretically using the Landau-Lifschitz-Gilbert (LLG) equation. From the measurements, uniaxial anisotropy of the pinned FM layer has been extracted to understand the nature of the exchange bias in the system. It is found that the uniaxial anisotropy field of NiFe layer when exchange biased with the AF layer increases from 5 to 15 Oe at different external magnetic fields.     

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.     

Antiferromagnet IrMn thickness dependence in exchange-biased perpendicular magnetic anisotropy based on CoFe/Pt/CoFe/[IrMn(tIrMn)] multilayers

The effect of the antiferromagnetic IrMn thickness upon the magnetic properties of CoFe/Pt/CoFe/[IrMn(t_IrMn)] multilayers is studied. An oscillatory interlayer coupling (IEC) has been shown in pinned CoFe/Pt(t_Pt)/CoFe/IrMn multilayers with perpendicular anisotropy. The period of oscillation corresponds to about 2 monolayers of Pt. The oscillatory behavior of IEC depends on the nonmagnetic metallic Pt thickness and is thought to be related to the antiferromagnetic ordering induced by the IrMn layer. From the extraordinary Hall voltage amplitude (EHA) curves as function of IrMn thickness, we report that the oscillation dependence of IEC for the [CoFe/Pt/CoFe] multilayer system induced by IrMn with spacer-layer thickness is a important features of perpendicular exchange biased system.     

Exchange anisotropy in Co/NiO bilayers: time-dependent effects

The time dependence of the exchange anisotropy was studied in Co/NiO bilayers. In order to only observe the relaxation phenomena inside the antiferromagnetic (AF) layer and to eliminate the dynamic behaviour inside the ferromagnetic (F) layer, we have developed an experimental method where a small a.c. magnetic field is applied perpendicular to the main anisotropy axis. All data are obtained by magneto-optical (m.o.) experiments. We observe a logarithmic time dependence of Hud, the exchange unidirectional anisotropy. We prove that the key parameter for the rate of relaxation is the anisotropy of the AF layer which depends strongly of the preparation method. We use the random field model as proposed by Malozemoff and suppose a breakdown of the AF interface into regular domains of size close to the crystallite size (10 nm width). If we further develop a Fulcomer and Charap relaxation model, we can propose from the distribution of relaxation times an analysis in terms of a spread of AF anisotropy energies. High magnetic pulsed field experiments (55 T) complete the experimental study and the results are analysed assuming that the Zeeman energy balances the anisotropy energy of the AF domains and switches them into the opposite direction.     

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.     

Surface modes with biquadratic coupling and uniaxial anisotropy in semi-infinite Heisenberg antiferromagnet

We address the role and the influence of both biquadratic exchange and uniaxial anisotropy in the study of bulk and surface magnetic excitations for a two-sublattices semi-infinite Heisenberg antiferromagnet. The calculations apply to combined effect and are based on a matching technique within the framework of both non-interacting spin-wave theory and random phase approximation. Emphasis has been laid upon the advantage of handling bulk and surface spin precessional fields, characterized by their symmetry in particular. Analytic expressions for the bulk and surface equations of motion are also derived which enables us to analyze qualitatively the nature of the modes by observing the response of the energy branches to the variation of both biquadratic exchange and single-ion anisotropy field as well as exchange parameters occurring on the surface. Two numerical applications of the theoretical formalism developed in this work are described. First concerns the situation when the free surface model is assumed. The second application considers the existence of surface perturbations and treats the effects of the presence of biquadratic exchange term on the bulk and surface spin-wave spectra showing two kinds of surface propagating modes which depend on the presence or not of the uniaxial anisotropy contribution and also on the variations of the bulk-surface exchange parameters. A significant conclusion which this work reached relates to the checking of the results obtained in the literature by using our own theoretical formalism. We show that this formalism is very well adapted to calculations of localized bulk and surface spin-wave modes associated with the simultaneous presence of biquadratic exchange and uniaxial anisotropy. Also, the results obtained for the bulk spin fluctuations field as well as for the magnetic surface waves, are found to be in qualitative agreement with those obtained in the literature. The analytic formulation presented in this work provides an accurate and practical scheme for calculating the surface spin dynamics under the influence of surface exchange parameters, biquadratic coupling and uniaxial anisotropy terms.     

铁磁共振法测磁各向异性

采用铁磁共振方法,研究了铁磁/反铁磁双层膜系统中,因交换耦合以及磁晶各向异性而产生的有效各向异性场.结果表明:被测系统有无交换偏置场以及其正负号性质等均能在共振谱中得到辨析.结果还显示:沿着不同结晶方向施加外磁场,共振场的行为与磁晶各向异性以及铁磁/反铁磁交换耦合作用而诱发的单向各向异性等密切相关.将共振频率的变化看成外磁场(包括其方向和大小)的函数,研究得到了单向各向异性,立方各向异性等对共振频率的影响,并同实验结果做了很好的比较. 关键词： 铁磁/反铁磁双层膜 交换耦合 铁磁共振 单向各向异性     

The origin of noncollinear anisotropies and asymmetric magnetization reversal in FM/AFM bilayer system

The effects of the magnitude of the uniaxial anisotropy of a ferromagnet and the cooling field on the noncollinearity between uniaxial anisotropy and induced unidirectional anisotropy in a ferromagnet/antiferromagnet bilayer system are investigated. A diagram of noncollinear anisotropies and relative negative (positive) exchange bias field dependence upon cooling field and uniaxial anisotropy of the ferromagnet is obtained. The numerical result shows that the emergence of noncollinear anisotropies originates from the action of the cooling field and uniaxial anisotropy of the ferromagnet. The noncollinearity strongly depends on the magnitude of cooling field and uniaxial anisotropy of the ferromagnet. Moreover, the effect of noncollinear anisotropies and applied field on asymmetric magnetization reversal is also investigated. Amazingly, when the magnetic field is applied collinearly with unidirectional anisotropy, the hysteresis loop of ferromagnet/antiferromagnet bilayers is always symmetric even if there are noncollinear anisotropies. Our results indicate that the asymmetry of the hysteresis loop only originates from the noncollinearity between the induced unidirectional anisotropy and the applied field, rather than from the noncollinearity between the uniaxial and unidirectional anisotropies.     

量子自旋波本征值及易轴型各向异性对其的影响

本文考虑体单轴各向异性利用界面重参数化方法从理论上严格推导了两层异质铁磁质中量子自旋波的本征值,并模拟计算了简立方晶格结构 (100) 第一布里渊区的能带结构,特别研究了易轴型体单轴各向异性对本征值的影响.结果发现在这样的体系中存在体模、禁闭模和界面模;各种本征模与体交换作用、界面交换作用、晶格自旋、原子层数有关,而且各向异性直接影响各种本征模的存在条件. 关键词： 铁磁薄膜 自旋波 各向异性     

Magnetization reversal in perpendicular exchange-biased multilayers

Co/Pt multilayers with perpendicular magnetic anisotropy exhibit an exchange bias when covered with an IrMn layer. The exchange bias field, which is about 7 mT for 3 Co/Pt bilayer repetitions and a Co layer thickness of 5 Å, can be increased up to 16.5 mT by the insertion of a thin Pt layer at the Co/IrMn interface. The interfacial magnetic anisotropy of the Co/IrMn interface (KSCo/IrMn =-0.09 mJ/m2) favours in-plane magnetization and tends to tilt the Co spins away from the film normal. Dynamical measurements of the magnetization reversal process reveal that both thermally activated spin reversal in the IrMn layer and domain wall nucleation in the Co/Pt multilayer influence the interfacial spin structure and therefore the strength of the perpendicular exchange bias field.     

The energy bands of quantized spin waves and the uniaxial anisotropy in a biferromagnetic system

The eigenproblems of quantized spin waves in a (100) ferromagnetic bilayer system have been investigated theoretically using the interface rescaling approach. The energy-band structure of the system has been obtained and the effect of the uniaxial bulk anisotropy field of easy-axis type on the energy bands are explored thoroughly. It is found that all kinds of eigenmodes of the spin waves in the biferromagnetic system are determined by the bulk exchange coupling constant, the interface exchange coupling constant, the spin of lattice, the number of atomic layers and the uniaxial bulk anisotropy. Especially, we explore the effect of the uniaxial bulk anisotropy field of easy-axis type on the energy bands of first Brillouin zone and the existence condition of all kinds of the eigenmodes.     

Phase transition in antiferromagnets with anisotropic exchange interactions and uniaxial anisotropy

Abstract

Following the Bogoliubov variational principle, the equilibrium and stability equations of the free energy for the two sublattice antiferromagnetic system with inter- and intrasublattice exchange interactions and with an external magnetic field are investigated. For the Ising spin system with uniaxial anisotropy, the phase diagrams have been calculated for various values of anisotropy constant d and the ratio of intra- to intersublattice interaction constants γ. It is shown that first-order, as well as second-order transitions, occur for γ > 0, whereas only a second-order transition occurs for γ ≦ 0, irrespective of the sign of d. Furthermore, similar calculations are extended for the anisotropic Heisenberg spin system and quite interesting phase diagrams have been obtained. Next, the effects of the anisotropic exchange interactions on the magnetic ordered states and the magnetizations of the singlet ground state system of spin one and with a uniaxial anisotropy term are investigated in the vicinity of the level crossing field H ? D/gμ _B . A field-induced ordered state without the transverse component of magnetization is shown to appear in a certain range of magnetic field as the spin dimensionality decreases. It has also turned out that the phase transition between this ordered state and the canted antiferromagnetic state ordinarily found for the isotropic singlet ground state system is of first order. Lastly, the stable spin configurations at a temperature of absolute zero for a two-sublattice uniaxial antiferromagnet under an external magnetic field of arbitrary direction are studied. In particular, the effects of a single ionic anisotropy D-term and anisotropy in the exchange interactions on the magnetic phases are investigated. The antiferromagnetic state has turned out to appear only for the external magnetic field along the easy axis of sublattice magnetization, and makes a first-order phase transition to the canted-spin state or the ferromagnetic state. For other field directions, no antiferromagnetic state appears and only a second-order phase transition between the canted-spin and the ferromagnetic states occurs. The critical field as a function of external field direction has been calculated for several D-values.     

Random anisotropy in ising spin glass

The theory of Ghatak and Sherrington for the Ising spin glass with uniform uniaxial anisotropy has been extended for the random uniaxial anisotropy (RUA). The magnitude of the RUA is assumed to fluctuate randomly with gaussian probability distribution. The susceptibility and the specific heat have been calculated for a system of spin one and zero mean values of the anisotropy and the exchange interaction. It is found that the random fluctuations of the anisotropy produce a cusp in the susceptibility and a broad maximum in the specific heat.     

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.     

Interlayer coupling between out-of-plane magnetized multilayers across a thin antiferromagnetic spacer

The interlayer exchange coupling between Co/Pt perpendicular-to-plane magnetized layers across a thin IrMn spacer layer was experimentally studied. In contrast to earlier studies on interlayer coupling through antiferromagnetic NiO, which revealed an oscillatory coupling behavior as a function of NiO thickness, a ferromagnetic coupling was observed here in the range of IrMn thickness between 0.6 and 1.5 nm and antiferromagnetic between 1.5 and 2.5 nm. The antiferromagnetic coupling is attributed to an orange peel magnetostatic mechanism whereas the ferromagnetic coupling is attributed to an out-of-plane polarization of the antiferromagnetic IrMn layer induced by the interfacial exchange interaction with the adjacent out-of-plane ferromagnetic layers. Measurements of hysteresis loops versus temperature show that the coupling vanishes at 510 K for t_IrMn=1 nm. This critical temperature is far below the Néel temperature of bulk IrMn, but above the blocking temperature of IrMn/Co bilayers at such thickness. Using a one-dimensional model describing a partial domain wall in the antiferromagnet, we explain the coupling in terms of an out-of-plane tilt of the Mn moments at the IrMn/(Co/Pt) interfaces yielding a weak net polarization of the IrMn. Finally, the non-oscillatory decay of the coupling was attributed to the compensated spin structure of the IrMn in the parallel to the interfaces.     

Thickness dependence of exchange anisotropy in NiFe/IrMn bilayers studied by Planar Hall Effect

Planar Hall Effect (PHE) in NiFe(t)/IrMn(10.0 nm) thin film structures has been experimentally investigated as a function of NiFe thickness in the range from 3 to 20 nm, under the applied magnetic field perpendicular to the easy axis. The PHE voltage change and its field sensitivity increase with NiFe thickness, but the field interval of two voltage maxima decreases with the thickness. There are good agreements between measured and calculated PHE voltage profiles, where the parameters of exchange-biased and effective anisotropy fields have been characterized to decrease with NiFe thickness. However, an anisotropic resistivity change increases as the NiFe thickness increases. These analyses suggest that PHE is the effective method, inferred to single domain, to determine the electrical and magnetic parameters in magnetic devices.     

Influence of induced uniaxial anisotropy on the domain structure and phase transitions of yttrium-iron garnet films

The effect of induced uniaxial anisotropy on the properties and parameters of the domain structure and phase transitions in yttrium-iron garnet (YIG) films is investigated. Based on the measurements and the derived formulas we determine the difference between the magnetization and the uniaxial anisotropy field for each of the films. We have also measured the parameters of the domain structures and phase transitions of the films for the magnetization parallel and perpendicular to the projections of the [111] crystallographic axes onto the plane of the film. We find that films of pure YIG films grown in (111) are characterized by the existence of some critical value of the uniaxial anisotropy field. It is found that for films in which the uniaxial anisotropy field is larger than this critical value and films in which it is less than this critical value, such parameters of the domain structures as the ratio of the width of the domains to the film thickness, the orientation of the magnetization of the domains, the orientation of the domain boundaries, and the magnitudes of the phase transition fields differ substantially. Fiz. Tverd. Tela (St. Petersburg) 41, 2034–2041 (November 1999)