Modern microwave magnetic materials: Recent advances and trends

In recent years, a large variety of microwave magnetic materials has been developed, with different compositions, shapes, and fabrication processes. The physics of the dynamic magnetic responses of these materials is very rich, due to the interplay between the intrinsic magnetic properties of the materials, the domain structure, and dynamic shape effects. These materials are associated to a variety of applications, some of them well-established, for direct interaction with rf waves; others corresponding to etablished uses of magnetic materials, but at higher speeds or higher frequencies; and some in association with hot topics in the magnetic or rf communities including metamaterials, nanoscale structures, and nonlinear devices.     

A novel formulation for the numerical computation of magnetization modes in complex micromagnetic systems

The small oscillation modes in complex micromagnetic systems around an equilibrium are numerically evaluated in the frequency domain by using a novel formulation, which naturally preserves the main physical properties of the problem. The Landau–Lifshitz–Gilbert (LLG) equation, which describes magnetization dynamics, is linearized around a stable equilibrium configuration and the stability of micromagnetic equilibria is discussed. Special attention is paid to take into account the property of conservation of magnetization magnitude in the continuum as well as discrete model. The linear equation is recast in the frequency domain as a generalized eigenvalue problem for suitable self-adjoint operators connected to the micromagnetic effective field. This allows one to determine the normal oscillation modes and natural frequencies circumventing the difficulties arising in time-domain analysis. The generalized eigenvalue problem may be conveniently discretized by finite difference or finite element methods depending on the geometry of the magnetic system. The spectral properties of the eigenvalue problem are derived in the lossless limit. Perturbation analysis is developed in order to compute the changes in the natural frequencies and oscillation modes arising from the dissipative effects. It is shown that the discrete approximation of the eigenvalue problem obtained either by finite difference or finite element methods has a structure which preserves relevant properties of the continuum formulation. Finally, the generalized eigenvalue problem is solved for a rectangular magnetic thin-film by using the finite differences and for a linear chain of magnetic nanospheres by using the finite elements. The natural frequencies and the spatial distribution of the natural modes are numerically computed.     

Magnetic study of CaMn0.96Mo0.04O3, canting vs. phase separation

CaMn_0.96Mo_0.04O₃ is an example of Mn⁴⁺ rich perovskite manganites, which exhibits a net ferromagnetic component at low temperature, observed by dc magnetization and ac susceptibility. To characterize the magnetic state of this compound, neutron powder diffraction was carried out in the 2-400 K temperature range, showing that it is necessary to use three components (ferromagnetic and G- and A-type antiferromagnetic) to describe it. This particular state is in agreement with the unusual magnetic behaviour observed by macroscopic measurements and is compared to the one observed for manganites with similar Mn valence but obtained by A-site substitution.     

Temperature dependence of electron magnetic resonance and magnetization in NiO nanorods

For NiO nanorods of 5 nm diameter prepared by sol-gel technique, variations of the magnetization M with temperature T (5-370 K) and magnetic field H up to 55 kOe are reported. Also, temperature variations of the EMR (electron magnetic resonance) parameters (intensity I₀, linewidth ΔH and resonance field H_r) of an observed line due to uncompensated spins are followed for The M vs. H and T variations yield a blocking above which the data fits modified Langevin function with magnetic moment μ_p?1240 μ_B/particle. For the EMR line, I₀ decreases rapidly for T<T_B, and the line broadens and shifts to lower H with lowering T, following the lineshift δH_r=(ΔH)ⁿ with n?2.8. This is close to the value of n=3 expected for randomly oriented particles.     

High-frequency magnetic properties and attenuation characteristics for barium ferrite composites

High-frequency magnetic properties and attenuation characteristics for barium-ferrite/epoxy composites have been studied. The methods for increasing μ′ and μ″ and controlling f_R, including ion substitution, doping of small amount of oxides, effect of damping, as well as the modification of particle sizes and shapes, are introduced. The results show that the composites are potential candidates for use as electromagnetic (EM) attenuation materials with low reflectivity and broad bandwidth at 2-18 GHz.     

Influence of transverse fields on surface and bulk polaritons in antiferromagnetic films

We study the behavior of surface and bulk polaritons in thin antiferromagnetic films when a dc magnetic field is applied perpendicular to the easy axis. Dispersion relations are obtained for magnetostatic modes, as well as for retarded polaritons. It is shown that, the dispersion relations of localized modes exhibit reciprocity, i.e. but they are non equivalent since they are localized in different regions. The non reciprocal character of surface modes in a semi infinite sample is regained for very thick films.     

Raman study of BiFeO3 with different excitation wavelengths

Raman spectra of bismuth ferrite (BiFeO₃) over the frequency range of 100-1500 cm⁻¹ have been systematically investigated with different excitation wavelengths. The intensities of the two-phonon modes are enhanced obviously under the excitation of 532 nm wavelength. This is attributed to the resonant behavior when incident laser energy closes to the intrinsic bandgap of BiFeO₃. The Raman spectra of BiFeO₃ excited at 532 nm were measured over the temperature range from 77 to 678 K. Besides the abnormal changes of the peak position and the linewidth of the A₁ mode at 139 cm⁻¹, the prominent frequency shift, the line broadening and the decrease of the intensity for the two-phonon mode at 1250 cm⁻¹ were observed as the temperature increased to Néel temperature (T_N). All these results indicate the existence of strong spin-phonon coupling in BiFeO₃.     

Photon confinement in one-dimensional photonic quantum-well structures of nanoporous silicon

Various combinations of periodically assembled nanoporous silicon layers with different refractive indices and thicknesses have been used to fabricate one-dimensional photonic quantum well structures, in which both the well and barrier regions consist of photonic crystals. The structures are operational in the regime of visible light. Quantized states resulting from the photonic confinement effect are observed, consistent with calculations using the transfer-matrix method. Behaviors of the photons in the structures can be well described by the effective wave-vector approach.     

Effect of zinc nitrate concentration on the structural and the optical properties of ZnO nanostructures

ZnO nanorods and nanodisks were formed on indium-tin-oxide-coated glass substrates by using an electrochemical deposition method. Scanning electron microscopy images showed that the ZnO nanorods were transformed into nanodisks with increasing Zn(NO₃)₂ concentration. X-ray diffraction patterns showed that the ZnO nanostructures had wurzite structures. The full widths at half maxima of the near band-edge emission peak of photoluminescence spectra at 300 K for ZnO nanorods were small, indicative of the high quality of the nanorods. These results indicate that the structural and the optical properties of ZnO nanostructures vary by changing Zn(NO₃)₂ concentration.     

Preparation and FMR analysis of Co nanowires in alumina templates

Magnetic and structural properties of a high aspect ratio Co nanowire (NW) array electrodeposited in free-standing porous alumina template with a pore diameter of ∼200 nm are studied. Considered collectively, X-ray diffraction analysis, magnetometer and ferromagnetic resonance (FMR) measurements indicate that both the c-axis of crystal structure and the easy axis of magnetization are aligned preferentially perpendicular to the NW axis. The FMR spectra are characterized with very broad (a few kG) breadths and exhibit asymmetric shape in low field region due to under-saturation effects. Surprisingly, FMR spectra also revealed the presence of a spin-wave mode (SWM) as the applied field direction approached parallel to the film plane, i.e. perpendicular to the NWs. A brief discussion on this observation is provided. Further, characteristic magnetic parameters of the studied NW array were obtained by fitting the field angle-dependent FMR spectra and resonance field by using an analytical model that considers various factors affecting the total anisotropy.     

Shape controllable synthesis of ZnO nanorod arrays via vapor phase growth

ZnO nanorod arrays with peculiar morphologies were synthesized on (111)-oriented Si substrate and glass via a vapor phase growth. The morphology of the individual nanorod can be flat-headed bottle-like, and needle-like, which depends on the deposition positions relative to the source materials in the presence of a controlling element Se. In addition, the arrays of all the three morphologies exhibit good alignment and high coverage. This fabrication technique can be also used to direct the controllable growth of other nanomaterials with similar morphologies.     

Yafet-Kittel-type magnetic ordering in Ni0.35Zn0.65Fe2O4 ferrite detected by magnetosensitive microwave absorption measurements

Magnetosensitive microwave absorption measurements of polycrystalline ferrite Ni_0.35Zn_0.65Fe₂O₄ was carried out at 9.4 GHz (X-band) as a function of temperature. Temperature dependence of the total linewidth (ΔH_pp) deduced from the resonance spectra showed the passage through the Curie point (T_c~430 K). Additionally, the plot ΔH_pp vs. T also indicated the existence of another magnetic phase transition at ~240 K, which can be associated with a Yafet-Kittel-type canting of the magnetic moments. Low-field microwave absorption (LFMA) and the magnetically modulated microwave absorption spectroscopy (MAMMAS) were used to give a further knowledge on this material. For low temperature, these techniques give evidence of a Yafet-Kittel-type canting of the magnetic moments.     

Magnetic and spectroscopic characteristics of ZnMnO system

We report on the observation of room-temperature ferromagnetism in epitaxial (Zn,Mn)O films grown by a pulsed-laser deposition technique using high-density targets. The X-ray, microscopic, spectroscopic and magnetic properties of target material containing 6 at.% of Mn and films were compared. The target shows the presence of large clusters exhibiting paramagnetic behavior. However, ferromagnetic properties were observed in (Zn,Mn)O films grown at a substrate temperature of 500 °C and with an oxygen partial pressure of 1 mTorr. Although, crystalline quality of the film improves with increasing substrate temperature, the ferromagnetism becomes weaker.     

Theoretical modeling of hard X-ray surface modes in a periodic multilayer

The excitation of hard X-ray surface modes of a periodic multilayer is studied with the help of theoretical modeling. It is found that a hard X-ray surface mode can appear in a specific periodic multilayer coated with a high-density reflecting layer. The generation of the hard X-ray surface modes is shown to be effective only at a certain set of the structural parameters of the multilayer. A method for the calculation of the propagation (attenuation) length of the surface mode running in the periodic multilayer is described. The excitation of the hard X-ray surface modes is compared with that of optical surface modes in photonic crystals. The relationship between the surface modes and guided modes of periodic multilayers is discussed.     

Magnetic resonance in crystalline La0.9Ca0.1MnO3: Comparative study of bulk and nanometer-sized samples

X-band electron magnetic resonance (EMR) measurements were done at 115?T?600 K on bulk and nanometer size-grain powder single-crystalline samples of La_0.9Ca_0.1MnO₃, in order to study an impact of structural inhomogeneity on magnetic ordering. For the nano-crystal sample, two superimposed EMR lines are observed below 240 K, while for bulk-crystal one, a second line emerges in narrow temperature interval below 130 K. Temperature dependences of resonance field and line width of the main and the secondary line are drastically different. EMR data and complementary magnetic measurements of bulk-crystal sample reveal mixed-magnetic phase, which agrees with the published phase diagram of bulk La_1−xCa_xMnO₃. In a marked contrast, the same analysis for nano-crystal sample shows two phases one of which is definitely ferromagnetic (FM) and other is likely such, or super paramagnetic. The data obtained are interpreted in terms of very different magnetic ground states in the two samples, that is attributed to different randomness of the indirect FM exchange interactions mediated by bound holes.     

Transport equations for chiral fermions to order ? and electroweak baryogenesis: Part I

This is the first in a series of two papers. In this first part, we use the Schwinger-Keldysh formalism to derive semiclassical Boltzmann transport equations, accurate to order ?, for massive chiral fermions, scalar particles, and for the corresponding CP-conjugate states. Our considerations include complex mass terms and mixing fermion and scalar fields, such that CP-violation is naturally included, rendering the equations particularly suitable for studies of baryogenesis at a first order electroweak phase transition. We provide a quantitative criterion in which case the reduction to the diagonal kinetic equations in the mass eigenbasis is justified, leading to a quasiparticle picture even in the case of mixing scalar or fermionic particles. Within the approximations we make, it is possible to first study the Boltzmann equations without the collision term. In a second paper [Ann. Phys. xxx (2004) xxx] we discuss the collision terms and reduce the Boltzmann equations to fluid equations.     

Transport equations for chiral fermions to order ? and electroweak baryogenesis: Part II

This is the second in a series of two papers. While in Paper I [Ann. Phys. 314 (2004) 208] we derive semiclassical Boltzmann transport equations and study their flow terms, here we make use of the results from that paper and address the collision terms. We use a model Lagrangean, in which fermions couple to scalars through Yukawa interactions and approximate the self-energies by the one-loop expressions. This approximation already contains important aspects of thermalization and scatterings required for quantitative studies of transport in plasmas. We compute the CP-violating contributions to both the scalar and the fermionic collision term. CP-violating sources appear at order ? in gradient and in a weak coupling expansion, as a consequence of a CP-violating split in the fermionic dispersion relation. This represents the first controlled calculation of CP-violating collisional sources, thus establishing the existence of `spontaneous' baryogenesis sources in the collision term. The calculation is performed by the use of the spin quasiparticle states established in Paper I. Next, we present the relevant leading order calculation of the relaxation rates for the spin states and relate them to the more standard relaxation rates for the helicity states. We also analyze the associated fluid equations, make a comparison between the source arising from the semiclassical force in the flow term and the collisional source, and observe that the semiclassical source tends to be more important in the limit of inefficient diffusion/transport.     

A new generation of CMOS-compatible high frequency micro-inductors with ferromagnetic cores: Theory,fabrication and characterisation

A new generation of CMOS-compatible micro-inductor prototypes with magnetic cores were realized, characterised as well as theoretically modelled in a frequency range up to 4 GHz, a frequency range where, e.g., mobile communication and global positioning systems (GPS) are operated. The micro-inductor's electrical magnitudes like inductance (L) and quality factor (Q) were theoretically described by means of an equivalent circuit model taking the frequency behaviour of the magnetic film core, expressed by the Landau-Lifschitz and Maxwell equations, into account. Six inch targets were used to deposit metallic layers (Al₉₉Si_0.5Cu_0.5), diffusion barriers (Si₃N₄), insulating layers (SiO₂) and magnetic films (Fe₃₉Co₃₀Ta₈N₂₃) by DC or reactive r.-f.-magnetron sputtering. All film materials were patterned by NUV-lithography (Near Ultra Violet), plasma beam milling and reactive ion etching to form the micro-inductors on 4-inch silicon wafers. The inductor windings are arranged in a way that they possess a low resistance and generate a quasi closed flux at the end of the cores to minimise eddy current losses in the silicon substrate. In order to diminish demagnetising effects in an efficient working core the magnetic films were patterned into micro squares with lateral dimensions of 20 and 100 μm with 100 nm in thickness. More magnetic volume and a higher micro-inductor cross-section was achieved by producing 100 nm magnetic double layers separated by a 800 nm thick Si₃N₄ inter-layer. To guarantee a sufficiently high cut-off frequency of the magnetic films, they were annealed in a static magnetic field at a temperature of 400 °C for uniaxial anisotropy induction. This represents a temperature treatment where aluminium CMOS processes take place. As a result of patterning, the magnetic film material exhibited a remarkable increase of the cut-off frequency from 2 GHz in laterally extended films up to 3.2 GHz which could be also observed in the measured frequency dependent inductance and quality factor. This was accompanied by an acceptable decrease of the initial permeability that still enabled initial inductances between 1 and 2 nH to be attained.     

Effect of barrier thickness on strain uniformity of wire in laterally aligned InGaAs/GaAs quantum wire nanostructures

The effect of barrier thickness on strain uniformity of a laterally aligned array of InGaAs quantum wire in GaAs matrix has been investigated with the finite elements method. A decrease in GaAs barrier thickness was predicted to assist the InGaAs wire to maintain its strain state in the central region up to a longer distance towards the edge of the wire along the width direction. It is suggested that, by reducing the spacing between the quantum wires, it is possible to improve uniformity of strains within the wire, thereby yielding more uniform opto-electronic properties such as sharp and narrow peaks in photoluminescence spectra.     

Electronic and magnetic behavior of ultrathin Ti nanowires

We report theoretical results on the magnetic behavior of free standing nanowires of Ti. Four different structures of Ti nanowires-linear, ladder, dimerized, and zigzag-with nonmagnetic, ferromagnetic, and anti-ferromagnetic configurations were considered. Exploration of magnetism in these atomic chains leads to ferromagnetic behavior for all the structures: zigzag structure shows almost degenerate ferromagnetic and anti-ferromagnetic states though. The zigzag structure of Ti nanowires is favored of all for low values of nearest neighbor distances, whereas the dimerized structure is favored at larger atomic separations. Our work helps to resolve the controversy in the predicted ground state magnetic nature of zigzag chains of Ti as reported in recent previous works. The maximum value of magnetic moment (0.93 μ_B/atom) occurs in the ladder chains while the zigzag chains show the minimum value (0.17 μ_B/atom). Interestingly, all the structures in the magnetic configuration show metastable state except the dimerized structure. Ferromagnetic dimerized nanowires seem to be a potential candidate for use in spintronics. The projected density of states shows that d_x²_−y² and d_xy bands play a leading role in magnetism of linear and ladder structures, whereas there is no outstanding contribution from a particular d-orbital for zigzag and dimerized nanowires. The charge density plots suggest that linear and zigzag structures have metallic bonding whereas covalent bonding is predominant in the dimerized and ladder structures. The estimated diameters for the favored ferromagnetic configuration of these ultrathin nanowires lie in the range 1.9-3.4 Å and indicate the instability of the ladder structure, as also projected by the relative cohesive energy and relative break force values.