Characterization of EUV periodic multilayers

Nanometric Co/Mg, Co/Mg/B₄C, Al/SiC and Al/Mo/SiC periodic multilayers deposited by magnetron sputtering are studied in order to correlate their optical performances in the extreme ultraviolet (EUV) range to their structural quality. To that purpose, our recently developed methodology based on high‐resolution X‐ray emission spectroscopy (XES) and X‐ray and EUV reflectometry is now extended to nuclear magnetic resonance (NMR) spectroscopy and time‐of‐flight secondary ions mass spectrometry (ToF‐SIMS). The analysis of the Co Lαβ and Mg Kβ emission spectra shows that the Co and Mg atoms within the multilayers are in a chemical state equivalent to that of the atoms in the pure Co and Mg references, respectively. But NMR spectra give evidence for a reaction between Co atoms and B and/or C atoms from B₄C. The Al and Si Kβ emission spectra do not reveal the formation of an interfacial compound in Al/SiC and Al/Mo/SiC. Only the roughness limits the optical quality of Al/SiC. The comparative analysis of the ToF‐SIMS spectra of Al/SiC and Al/Mo/SiC indicates that the structural quality is enhanced when Mo is introduced within the stack. Copyright © 2011 John Wiley & Sons, Ltd.     

Periodic structure of spin-transfer current in ferromagnetic multilayers

We show that the drift-diffusion mechanism in a normal-metal layer in combination with the resonance electron–magnon interactions at ferromagnet-normal interface of F–N–F heterostructure creates spatial instability modes and, out of these modes, a quasi-stable periodic structure of spin-transfer d.c. current can arise with certain channel step and step-to-radius ratio. The ferromagnetic resonance conditions determine spin-transfer current density. Independent nanooscillators creating intersecting arrays of channels can phase-lock on sub-micrometer distance, which depends on multilayer geometry and applied fields. By decreasing the layer thickness, the number of channels affected by each independent d.c.-current source and their radius may be diminished. Phase-locking of multiple independent nanooscillators can be used for enhancement of output power.     

Asymmetric reversal modes in ferromagnetic/antiferromagnetic multilayers

Experimentally an asymmetry of the reversal modes has been found in certain exchange bias systems. From a numerical investigation of the domain state model evidence is gained that this effect depends on the angle between the easy axis of the antiferromagnet and the applied magnetic field. Depending on this angle the ferromagnet reverses either symmetrically, e.g., by a coherent rotation on both sides of the loop, or the reversal is asymmetric with a nonuniform reversal mode for the ascending branch, which may even yield a zero perpendicular magnetization.     

General unit-disk representation for periodic multilayers

We suggest a geometrical framework in which to discuss periodic layered structures in the unit disk. Bandgaps appear when the point representing the system approaches the unit circle. We show that the trace of the matrix describing the basic period allows for a classification in three families of orbits with quite different properties. The laws of convergence of the iterates to the unit circle can then be considered universal features of the reflection.     

Filtering properties of defect-bearing periodic and triadic cantor multilayers

Defect-bearing periodic as well as pre-fractal dielectric multilayers can be designed to operate as narrow-band filters. For the same dielectric constituents and the same (or closest to same) number of layers, pre-fractal structures are remarkably better than the periodic ones, both in terms of filter bandwidth and transmittance peak, and are less sensitive to variations in the defect thickness. For structures having about 30 layers, optical losses do not significantly affect the filtering features of both morphologies if the loss tangent of the constituent materials is less than 10⁻⁵.     

Optical properties of hybrid periodic/quasiregular dielectric multilayers

Optical properties like transmission, omnidirectional reflection and localization of modes are theoretically investigated in hybrid periodic/quasiregular dielectric heterostructures based on porous silicon. It is shown that the fabrication of this class of multilayers would lead to an improvement of the formation of microcavities, the widening of the incidence angular interval for total reflection as well as the appearance of spatial localization of electric field intensity within specific regions of the structures.     

Theory of ferromagnetic polariton linewidths

The interaction between magnons and photons which is responsible for magnetic polariton formation is expressed in terms of second quantized operators, and it is confirmed that the polariton dispersion curve obtained by diagonalizing the Hamiltonian is the same as that found classically. A term describing relaxation of the polariton by the two magnon mechanism which is often dominant in ferromagnetic resonance is then introduced. The lineshape function for inelastic light scattering is calculated by a Greens function technique. On the assumption that the lineshape can be approximated as a Lorentzian an expression for the linewidth is derived. The linewidth is zero when the polariton frequency Ω lies outside the magnon manifold, and increases discontinuously from zero at w = ¦γ¦H₀, where H₀ is the (internal) static field.     

Angular dependence of the ferromagnetic resonance spectrum in continuous/heterogeneous multilayers

We present here a study of the angular dependence of the ferromagnetic resonance (FMR) spectra in trilayers formed by two continuous ferromagnetic layers, Fe and Ni₈₀Fe₂₀ (permalloy), separated by a granular film of Fe(x)–SiO₂(1–x). The study of the Fe/Fe-SiO₂/Ni₈₀Fe₂₀ trilayer was made for an Fe volume concentration x=0.75 and two thicknesses (t=1 and 18 nm) of the granular layer. One microwave absorption line is in general found close to the field expected for Fe, while the other is coincident with the resonance field of permalloy. However, the Fe-like absorption is considerably wider than what is usually observed in pure Fe films, which suggests the presence of a strong exchange interaction between this layer and the granular spacer. The angular dependence of the resonance field and the line width could be very well fitted with a model that assumes an effective in-plane anisotropy for each layer, indicating that the shape anisotropy dominates the angular response of both modes. When the excitation frequency is increased, the line width of the permalloy-like mode increases by a similar factor. The width of the Fe-like mode is very similar at different frequencies because of the effect of the granular layer.     

Introduction of Zr in nanometric periodic Mg/Co multilayers

We study the introduction of a third material, namely Zr, within a nanometric periodic Mg/Co structure designed to work as optical component in the extreme UV (EUV) spectral range. Mg/Co, Mg/Zr/Co, Mg/Co/Zr and Mg/Zr/Co/Zr multilayers are designed, and then characterized in terms of structural quality and optical performances through X-ray and EUV reflectometry measurements, respectively. For the Mg/Co/Zr structure, the reflectance value is equal to 50% at 25.1?nm and 45° of grazing incidence and reaches 51.3% upon annealing at 200°C. Measured EUV reflectivity values of tri-layered systems are discussed in terms of material order within a period and compared to the predictions of the theoretical model of Larruquert. Possible applications are pointed out.     

A long-range ferromagnetic spin model with periodic boundary conditions

A possible way to study long-range interacting particles in finite–infinite periodic systems is applied to a modified Ising model with ferromagnetic interaction that decays as a 1/r^α law. We verify, by Monte Carlo heat-bath simulations for cases in D dimensions, that the thermodynamic quantities scale in a way proposed by Tsallis, and that the mean field theory is exact in the last model for all 0⩽α⩽D/2 suggested previously by other authors.     

Modulational instability and gap solitons in periodic ferromagnetic films

The modulational instability and gap solitons are theoretically studied in the ferromagnetic films under a periodic magnetic field. By multiple scale expansion, the envelope soliton solutions are obtained naturally. Due to the periodic modulation of dispersion, the solitons may be pushed into the gap region. For the easy-axis magnetic film, the red-shift of frequency leads to a modulational instability in the bottom of band and generates a bright gap soliton. For the easy-plane case, the blue-shift leads to an instability in the top of band and a dark gap soliton emerges. The weak damping produces an attenuation factor and a small oscillation.     

Large mode area OmniGuide fiber with superconductor-dielectric periodic multilayers cladding

An OmniGuide fiber consisting of superconductor–dielectric cladding periodic multilayers is investigated. The theoretical results of the OmniGuide fiber are presented and compared with that of multicore photonic crystal fiber and step-index fiber. The large mode area and low loss with small bending radius are observed by the OmniGuide fiber.     

Modes of periodic domain wall motion in ultrathin ferromagnetic layers

Magnetization reversal in a periodic magnetic field is studied on an ultrathin, ultrasoft ferromagnetic Pt/Co(0.5 nm)/Pt trilayer exhibiting weak random domain wall (DW) pinning. The DW motion is imaged by polar magneto-optic Kerr effect microscopy and monitored by superconducting quantum interference device susceptometry. In close agreement with model predictions, the complex linear ac susceptibility corroborates the dynamic DW modes segmental relaxation, creep, slide, and switching.     

The origin of spin current in YIG/nonmagnetic metal multilayers at ferromagnetic resonance

Spin pumping in yttrium-iron-garnet(YIG)/nonmagnetic-metal(NM) layer systems under ferromagnetic resonance(FMR) conditions is a popular method of generating spin current in the NM layer.A good understanding of the spin current source is essential in extracting spin Hall angle of the NM and in potential spintronics applications.It is widely believed that spin current is pumped from precessing YIG magnetization into NM layer.Here,by combining microwave absorption and DC-voltage measurements on thin YIG/Pt and YIG/NM_1/NM_2(NM_1 =Cu or Al,NM_2 =Pt or Ta),we unambiguously showed that spin current in NM,instead of from the precessing YIG magnetization,came from the magnetized NM surface(in contact with thin YIG),either due to the magnetic proximity effect(MPE) or from the inevitable diffused Fe ions from YIG to NM.This conclusion is reached through analyzing the FMR microwave absorption peaks with the DC-voltage peak from the inverse spin Hall effect(ISHE).The voltage signal is attributed to the magnetized NM surface,hardly observed in the conventional FMR experiments,and was greatly amplified when the electrical detection circuit was switched on.     

Microscopic properties of Co/Pd multilayers studied by ferromagnetic and nuclear magnetic resonance

The microscopic properties of Co/Pd multilayers were studied by ferromagnetic and nuclear magnetic resonance. The anisotropy of the layer is found to decrease for decreasing Co sublayer thickness and a switching of the magnetic preferential direction occurs below 8Å. The anisotropy is also a function of the Pd layer thickness: below 20Å it increases with decreasing thickness. This is attributed to a decrease in the Pd/Co interface contribution to the anisotropy. Hyperfine field spectra show the layers with [111] texture to be mainly polycrystalline fcc. The spectra shift to lower hyperfine fields upon decreasing Co sublayer thickness. This is attributed to a decrease in the magnetic moment caused by stretching of the Co lattice due to neighbouring Pd atoms. The results were checked by experiments on almost single phased [100] fcc Co/Pd multilayers. The similarity with the results on the [111] layers suggests that the expansion of the Co lattice is nearly isotropic.     

Theory of magnetooptical effects in ferromagnetic metals

Magnetooptical effects in ferromagnetic metals have been studied by the Kohn-Luttinger method, by means of electron scattering by impurity centers. There is a discussion of the more general case, in which the external agent has both a frequency and a wave vector. Solution of the corresponding kinetic equation with an account of the diffusion term reveals the symmetric and antisymmetric parts of the complex average velocity, valid for both high and low frequencies.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 12, No. 7, pp. 47–50, July, 1969.     

Theory of ferromagnetic resonances in thin wires

A phenomenological theory of ferromagnetic resonances in a ferromagnetic metallic cylinder magnetized along its axis is based on the simultaneous solution of the equation of motion and Maxwell's equations. A general relaxation term in the equation of motion is used. The boundary conditions correspond to the dynamic surface anisotropy with the preferred direction parallel to the static magnetization. It is shown that the solution yields an infinite number of resonance modes of different spatial symmetry. Formulas for the surface impedance and the relative absorption of individual modes are derived. The effect of the finite radius of the cylinder on the resonance, antiresonance and spin wave resonance behaviour is discussed.     

Theory of magnetooptical effects in ferromagnetic nickel

A theory is developed for magnetooptical effects in ferromagnetic nickel with allowance for the topology of the Fermi surface at low temperatures, when the carriers are scattered on ionized impurity centers. The contribution to the frequency conductivity tensor due to the anisotropy of the Fermi surfaces of nickel is found and it is shown that this contribution in the first approximation of perturbation theory reduces to a decrease of the tensor . An estimate is made of the influence of the density of states of nickel on the anomalous frequency-dependent Hall current and a study is also made of the case of low and high frequencies, when, respectively, ^{2 2} « 1 and ^{2 2} » 1.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 29–33, May, 1972.