Interface biquadratic coupling and magnon scattering in exchange-biased ferromagnetic thin films grown on epitaxial FeF2

The magnetic anisotropy of ferromagnetic (FM) Ni, Co, and Fe polycrystalline thin films grown on antiferromagnetic (AF) FeF(2)(110) epitaxial layers was studied, as a function of temperature, using ferromagnetic resonance. In addition to an in-plane anisotropy in the FM induced by fluctuations in the AF short-range order, a perpendicular (biquadratic) magnetic anisotropy, with an out-of-plane component, was found which increased with decreasing temperature above the AF Neél temperature (T(N) = 78.4 K). This is a surprising result given that the AF's uniaxial anisotropy axis was in the plane of the sample, but is consistent with prior experimental and theoretical work. The resonance linewidth had a strong dependence on the direction of the external magnetic field with respect to in-plane FeF(2) crystallographic directions, consistent with interface magnon scattering due to defect-induced demagnetizing fields. Below T(N), the exchange bias field H(E) measured via FMR for the Ni sample was in good agreement with H(E) determined from magnetization measurements if the perpendicular out-of-plane anisotropy was taken into account. A low field resonance line normally observed at H ≈ 0, associated with domain formation during magnetization in ferromagnets, coincided with the exchange bias field for T < T(N), indicating domain formation with the in-plane FM magnetization perpendicular to the AF easy axis. Thus, biquadratic FM-AF coupling is important at temperatures below and above T(N).     

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.     

First-principles calculations of magnetic and electronic structures around surfaces and interfaces of magnetic multi-layered structure

Electronic and magnetic structures of ferromagnetic (FM)/non-magnetic (NM) and FM/antiferromagnetic (AF) bi-layer systems are calculated by the first principles approach. For the FM/NM system, we focus on the Co/Cu multi-layered structure whose interfacial layer is assumed to have a mixed composition of Co and Cu atoms, and show a possibility that Co atoms at the interface play a significant role as the spin-dependent scattering potentials. In the FM/AF system, we consider Fe or Co monolayer as FM layer and MnNi as AF layers. It is predicted that the Mn moments adjacent to FM layer are forced to align the FM moments, and those of under layer go gradually to anti-parallel alignment as in the bulk MnNi.     

Structure and magnetic properties of Fe/Fe oxide clusters

Fe clusters have been synthesised in ultra-high-vacuum chamber using a gas-stabilized cluster aggregation method that ensures good control of the cluster size and naturally oxidized in order to obtain Fe/Fe oxide core-shell nanoparticles. The morphology of an individual nanoparticle, as revealed by transmission electron microscopy, consists of a Fe core of an average diameter of 4.4 nm surrounded by an oxide shell of uniform thickness of about 1.2 nm in average. The nanoparticles may be assimilated with a ferro-/antiferromagnetic (FM/AF) system. The morpho-structural features have been correlated with magnetic measurements on the core-shell nanoparticles. A significant exchange bias effect has been measured, when the sample was field-cooled under an applied field of 3 T. As the morphology of core-shell nanoclusters is much more complicated than in FM/AF bilayers of regular thickness due to the particular geometry of the coronal AF layer, the shape and surface anisotropy have to be taken into account for a correct interpretation of the magnetic data.     

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.     

Asymmetric reversal in inhomogeneous magnetic heterostructures

Asymmetric magnetization reversal is an unusual phenomenon in antiferromagnet/ferromagnet (AF/FM) exchange biased bilayers. We investigated this phenomenon in a simple model system experimentally and by simulation assuming inhomogeneously distributed interfacial AF moments. The results suggest that the observed asymmetry originates from the intrinsic broken symmetry of the system, which results in local incomplete domain walls parallel to the interface in reversal to negative saturation of the FM. The magneto-optical Kerr effect unambiguously confirms such an asymmetric reversal and a depth-dependent FM domain wall in accord with the magnetometry and simulations.     

Exact diagonalization of Hubbard clusters at finite temperatures

Finite temperature electronic and magnetic properties of small clusters are investigated in the framework of the Hubbard model by using exact diagonalization methods and by sampling the different cluster topologies exhaustively. Results are discussed for the specific heat C(T), magnetic susceptibility χ(T), local magnetic moments μ_i(T), average magnetic moments $\overline\mu_N(T)$ and spin-correlation functions γ_ij(T). Representative cluster sizes and band-fillings are considered showing antiferromagnetic-like (AF) and ferromagnetic-like (FM) behaviors. For half-band filling ν= N the susceptibility shows an AF high-temperature behavior of the form χ≈1/(T + T_N) from which the cluster `Néel’ temperature T<sub>N</sub> is derived. In contrast, for ν= N + 1 a FM high-temperature behavior of the form χ≈1/(T - T<sub>C</sub>) is found, where T<sub>C</sub> can be interpreted as the cluster `Curie’ temperature. In both cases one also observes peaks in C(T), either at T?T_N or T?T_C, which reflect the development of spin fluctuationsand the breakdown of the low-temperature short-range magnetic order. The dependence of T_N and T_C on cluster size N and interaction strength U/t is analyzed in terms of effective Heisenberg spin interactions. Finally, the effects of temperature-induced structural fluctuations are discussed.     

Perpendicular antiferromagnetic ordering of Mn and exchange anisotropy in Fe/Mn multilayers

Fe/Mn is a model system in which to study exchange bias, since the antiferromagnetic (AF) Mn layers are believed to have uncompensated moments with all spins aligned in the plane and parallel to those of the Fe. We have determined the microscopic AF ordering at the interfaces using single-crystal neutron diffraction. An unexpected magnetic structure is obtained, with out-of-plane Mn moments perpendicular to those of Fe. This explains the low bias field and shows that the simple AF ordering assumed in a variety of exchange-biased systems may well have to be revised.     

Ab initio calculations of interfacial magnetism in Fe/Mo superlattices

Ab initio calculations have been performed on Fe/Mo(1 0 0) superlattices in order to study the interfacial magnetic properties and layer thickness effect on the magnetic moments. In most cases, the magnetic moments of interfacial Fe monolayers are always smaller than those of the inner layers, and the induced magnetic moments of interfacial Mo monolayers oriented in the opposite direction. Calculation results show that the Fe layers are ferromagnetic when n = 3. As the thickness of the Mo layers increases, the influence of the Mo layer increases and the magnetic state of the Fe layer gradually changes into an antiferromagnetic or non-magnetic state. The change of magnetic moments of Fe/Mo superlattices is in agreement with the experimentally observed oscillation periods.     

Molecular-Dynamics Approach to the Magnetic Structure of Competing Magnetic Alloys: Fe-Cr Alloys

A molecular dynamics (MD) approach which determines automatically the complex magnetic structures in itinerant electron systems is applied to Fe-Cr alloys with use of 250 atoms in a MD unit cell (5×5×5 bcc lattice). It is demonstrated that the Fe-Cr alloys show various complex magnetic structures due to competing interactions: the collinear ferromagnetism (F) of matrix Fe with antiparallel Cr moments beyond 80 at.% Fe, the coexistence of non-collinear structure of Cr and collinear F of Fe between 50 and 75 at.% Fe, the coexistence of broken antiferromagnetism (AF) of Cr and the F of Fe between 25 and 45 at.% Fe, the coexistence of F of Fe and antiferromagnetic long-range order of Cr around 20 at.% Fe, the AF of Cr matrix with non-collinear Fe moments (spin-glass like structure) between 5 and 15 at.% Fe, and the AF below 5 at.% Fe. In the concentration region between 5 and 20 at.% Fe, ferromagnetic Fe pairs which are stabilized with different amplitudes of local moments are found. The magnetic phase diagram and calculated magnetic moments are shown to be consistent with the neutron, Mössbauer, and photoemission experiments.     

An estimation of the magnetic disorder at Fe/Cr interfaces in coupled and non-coupled Fe/Cr multilayers

The antiferromagnetic coupling at the Fe/Cr interfaces, inferred from the orientation of the Cr magnetic moments, is used to estimate the magnetic disorder resulting from the interfacial roughness in Fe/Cr multilayers. A crossover from in-plane to out-of-plane orientation of Cr moments depends on the energy cost in either case: (i) to break the interfacial Fe–Cr antiferromagnetic coupling or (ii) having sites with frustrated Cr–Cr antiferromagnetic coupling in the Cr interlayers. A quantitative model of the magnetic frustration due to interfacial disorder in Fe/Cr multilayer systems is described. The step edge density, or terrace size, required to break the interfacial Fe–Cr coupling and destroy the Fe–Fe interlayer exchange coupling is estimated.     

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.     

Interface-induced states with an incommensurate spin-density wave in Fe/Cr-type multilayers

A model is proposed for magnetic ordering in Fe/Cr-type multilayers substantially above the Néel temperature of bulk chromium. Redistribution of the charge (and, hence, spin) density near the Fe/Cr interfaces gives rise to the formation of an essentially inhomogeneous spin-density-wave (SDW) state in the chromium spacer. The spatial structure of the antiferromagnetic order parameter in thick spacers is described. The SDW contribution to the effective exchange coupling between the moments in adjacent iron layers is calculated. The data obtained are used in the interpretation of experimental data on the tunneling spectroscopy of trilayers and neutron diffraction from Fe/Cr superlattices.     

A new paradigm for exchange bias in polycrystalline thin films

In this paper we provide a review and overview of a series of works generated in our laboratory over the last 5 years. These works have described the development and evolution of a new paradigm for exchange bias in polycrystalline thin films with grain sizes in the range 5-15 nm. We have shown that the individual grains in the antiferromagnetic (AF) layer of exchange bias systems contain a single AF domain and reverse over an energy barrier which is grain volume dependent. We show that the AF grains are not coupled to each other and behave independently. Understanding this process and using designed measurement protocols has enabled us to determine unambiguously the blocking temperature distribution of the AF grains, the anisotropy constant (K_AF) of the AF, understand the AF grain-setting process, and predict its magnetic viscosity. We can explain and predict the grain size and film thickness dependence of the exchange field H_ex. We have also studied interfacial effects and shown that there are processes at the interface, which can occur independently of the bulk of the AF grains. We have seen these effects via studies of trilayers and also via the field dependence of the setting process which does not affect the blocking. From separate experiments we have shown that the disordered interfacial spins exist as spin clusters analogous to a spin glass. These clusters can order spontaneously at low temperatures or can be ordered by the setting field. We believe it is the degree of order of the interfacial spins that gives rise to the coercivity in exchange bias systems. Based on this new understanding of the behaviour of the bulk of the grains in the antiferromagnet and the interfacial spins we believe that we have now a new paradigm for the phenomenon of exchange bias in sputtered polycrystalline thin films. We emphasize that the phenomenological model does not apply to core-shell particles, epitaxial single-crystal films and large grain polycrystalline films.     

The structure and magnetism of Fe/Mo(0 0 1) surface: A pseudopotential calculation

The effect of structure on the magnetism of iron monolayers (MLs) on molybdenum is investigated using the density functional theory (DFT) with norm conserving pseudopotentials and a plane wave basis, under the local spin density approximation (LSDA). Relaxation of 5 and 7 ML of Mo resulted in a contraction of 11.3% and 11.7%, respectively, for the top Mo–Mo interlayer spacing in close agreement with experimental results. In the case of one Fe overlayer, the top Fe–Mo interlayer spacing contracted by 15.8% for a ferromagnetic (FM) p(1×1) and 20.6% for an antiferromagnetic (AF) c(2×2) configuration. The magnetic moment of the surface (Fe) layer is enhanced from its theoretically calculated bulk value. Total energy calculations show that the AF c(2×2) is the stable state with a magnetic moment of 2.53 μ_B. The surface Fe atoms are AF coupled with each other and with the Mo layers below, showing layered AF coupling. The present study demonstrates the reliability of the pseudopotential approach under LSDA with core corrections included to the calculation of magnetic properties of combined transition metal systems.     

Magnetic properties and electronic structures of hcp Fe,Co and Ni nanowires encapsulated in a zigzag (12,0) BN nanotube

The magnetic properties and electronic structures of ferromagnetic nanowires (FM=Fe, Co and Ni) encapsulated inside a zigzag (12,0) boron nitride nanotube (BNNT) are investigated by first-principle calculations. The relaxed geometry structures of FM/BNNT systems have only slightly changed. Formation energy analysis shows that the combining processes of Co/BNNT and Ni/BNNT systems are exothermic, and therefore the Co and Ni nanowires can be encapsulated into a semiconducting zigzag (12,0) BNNT and form stable hybrid structures. The charges are transferred from ferromagnetic nanowires to more electronegative BNNTs, and the formed FM–N bonds have covalent bond characteristics. The magnetic moments of FM/BNNT systems are smaller than those of the freestanding ferromagnetic nanowires, especially for the atoms on the outermost shell of the nanowires. The stable FM/BNNT systems exhibit higher magnetic moments, which can be useful for a wide variety of next-generation nanoelectronic device components.     

Magnetic structure of (Fe0.97Cr0.03)2P

Magnetic behaviour of di-metal iron phosphide with a small substitution of iron by chromium, (Fe_0.97Cr_0.03)₂P, has been studied using SQUID magnetometry and powder neutron diffraction. It is paramagnetic at temperatures above ∼180 K with persisting short range ferromagnetic (FM) order. At lower temperatures three different regions of magnetic behaviour are identified. FM order evolves in the region 180 K-120 K but much more slowly and with much less magnetic moments than in Fe₂P. In the region 120 K-50 K negative exchange interactions gain some importance leading to a loss of FM order. Below 50 K FM interactions again dominate. Pinning centres influence the behaviour at low temperature up to ∼100 K.     

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.     

Increased surface spin stability in γ-Fe2O3 nanoparticles with a Cu shell

γ-Fe(2)O(3) nanoparticles were coated with a Cu shell in situ during synthesis. An interfacial monolayer of CuO in the Cu-coated γ-Fe(2)O(3) nanoparticles was discovered that stabilized the disordered surface spins of γ-Fe(2)O(3) nanoparticles. Element-specific x-ray absorption spectroscopy at the L-edges for Cu and Fe indicated the magnetic moment of the Cu in the shell interacted with the γ-Fe(2)O(3) nanoparticle's surface magnetic moments. This exchange interaction between the Fe and Cu at the interface permitted an overall Cu moment in CuO (an antiferromagnet typically) that altered the γ-Fe(2)O(3) nanomagnetism. Increasing the Cu shell thickness also increased the total Fe magnetism of the nanoparticles.