Transverse susceptibility as the low-frequency limit of ferromagnetic resonance

A new theory of transverse susceptibility (TS) based on magnetization vector dynamics, as described by the Landau–Lifshitz equation of motion, is given. It is shown that the traditional TS experiment is, in fact, the zero-frequency limit of the ferromagnetic resonance (FMR). The importance of these results resides in the generality of the approach which allows one to find the TS for virtually any magnetic system if an expression for the magnetic free-energy density is known. Moreover, the effect of the frequency of excitatory AC field on the TS experiments and the effect of energy dissipation through the imaginary part of TS emerge coherently from the new TS model.     

Ferromagnetic resonance studies on (Co40Fe40B20)x(SiO2)1−x granular magnetic films

Magnetic properties of granular (Co₄₀Fe₄₀B₂₀)_x(SiO₂)_1−x   thin films (x=0.37-0.53$x=0.37-0.53$) have been studied by ferromagnetic resonance (FMR) technique. Samples have been prepared by ion-beam deposition of Co–Fe–B particles and SiO₂ on sitall ceramic substrate. The FMR measurements have been done for different orientations of DC magnetic field with respect to the sample plane. It was found that the deduced value of effective magnetization from FMR data of the thin granular film is reduced by the volume-filling factor of the bulk saturation magnetization. The overall magnetization changes from 152 to 515 G depending on the ratio of the magnetic nanoparticles in the SiO₂ matrix. From angular measurements an induced in-plane uniaxial anisotropy has been obtained due to the preparation of the film conditions as well.     

Spin-wave resonance and magnetic anisotropy in FePt thin films

Ferromagnetic Resonance (FMR) measurements at room temperature and X-band microwave frequency were performed on polycrystalline FePt thin films with face-centered cubic structure. With the external field perpendicular to the film plane, the absorption fields H_n of the odd and even spin-wave resonance modes n detected for the Fe_0.44Pt_0.56(45 nm)/Si(1 0 0) and Fe_0.51Pt_0.49(105 nm)/Pt(55 nm)/MgO(1 0 0) films, were found to obey the well-known H_n×n² ratio, giving for these films the exchange stiffness constant values of 3.9×10⁻⁸ and 4.4×10^–7 erg/cm, respectively. The study of the out-of-plane angular dependence of the absorption field of the uniform FMR mode allowed the measurement of the effective magnetic anisotropy constants of 5.3×10⁶ , 6.4×10⁶ , and 6.7×10⁶ erg/cm³, related, respectively, to the [1 1 1], [1 0 0], and [1 1 0] textures present in the films.     

Magnetic anisotropy in colossal magnetoresistive FeCr2S4 single crystals

The magnetic properties of spinel FeCr₂S₄ single crystals were investigated by ferromagnetic resonance (FMR). The FMR spectrum displays a single absorption line in the whole temperature range measured for both H∥(111) and H⊥(111). With decreasing temperature, the line with H∥(111) shifts to lower fields, while that with H⊥(111) shifts to higher fields. By superposing all the FMR spectra measured in different directions at 110 K, a double-peak is obtained, which clarifies the origin of the FMR double-peak in polycrystalline sample. By taking account of magnetic anisotropy and demagnetizing effect, the orientation dependence of resonance field is well fitted. It is found that the magnetic anisotropy strengthens with decreasing temperature; however, it has no evident influence on transport and colossal magnetoresistance behavior.     

A new perturbation method for determining the broadband complex permeability of magnetic thin films

In this paper, a new one-port microstrip line permeameter using the perturbation method is presented. A short-ended circuited microstrip line fixture was designed and implemented. Completely new analytical calculation formulas and a two-step measurement procedure were applied to deduce the complex permeability of the material in the frequency range from 100 MHz to 5 GHz. The measured results showed good agreement with the Landau–Lifchitz–Gilbert theory.     

Magnetic phase transitions and structures of Co3V 2O8

Co₃V ₂O₈ is a spin- 3/2 system on a Kagomé staircase and is known to undergo two magnetic phase transitions between 6 and 11 K. The H-T phase diagram of Co₃V ₂O₈ derived by magnetization measurements on a single crystal is presented. Additionally both ordered magnetic structures were investigated by neutron powder diffraction experiments and solved using Bertaut’s macroscopic theory. For the ferromagnetic phase the magnetic moments of the Co²⁺ ions were found to be 1.5(3)μ_B and 2.7(1)μ_B at 3.5 K along the crystallographic a axis for the (4a) and (8e) sites, respectively. The antiferromagnetic phase exhibits a magnetic cell with a doubled b axis with respect to the nuclear one. The magnetic moments point along the a axis being 1.8(2)μ_B (4a) and 1.8(1)μ_B (8e) at 8 K.     

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.     

The size and space arrangement roles on coercivity of electrodeposited Co1−xCux nanowires

Magnetization curves with various magnetic field orientations and nanowire diameters were measured at room temperature. The measured coercivity as a function of angle (θ) between the field and wire axis reveals that the coercivity decreases with increasing value of θ for various nanowires. Theoretically, based on Monte Carlo simulation we investigated the magnetization reversal modes of the Co_1−xCu_x nanowires and obtained also the θ dependence of the coercivity. Comparing the simulated with the experimental results, we find that the magnetocrystalline anisotropy plays an important role on the magnetic properties of Co_1−xCu_x nanowires, and the magnetization reversal process in the Co_1−xCu_x nanowires could not be understood by the classical uniform rotation mode in the chain-of-sphere model.     

Influence of grain growth on the high-frequency behaviour of ferromagnetic Fe-Co-(M)-N (M=Ta, Hf) nanocomposite films

The CMOS compatible ferromagnetic Fe-Co-(M)-N (M=Ta, Hf) films were investigated with regard to their grain size-dependent frequency behaviour. Predominantly Fe₃₃Co₄₀Ta₁₀N₁₇ films were deposited by reactive r.f. magnetron sputtering. These films were compared to Fe₃₆Co₄₄Hf₉N₁₁ films. In order to induce an in-plane uniaxial anisotropy H_u as well as to investigate the grain growth behaviour, the films were annealed in a static magnetic field. The in-plane uniaxial anisotropy field of around 4 mT as well as a good soft magnetic behaviour with a saturation polarisation of approximately 1.2-1.4 T could be observed after heat treatment. Ferromagnetic resonance frequencies (FMR) of approximately up to 2.4 GHz could be achieved according to the Kittel theory. Depending on the heat treatment, high-frequency losses through energy dissipation was made conspicuous by means of the full-width at half-maximum (FWHM) Δf_eff of the imaginary part of the frequency-dependent permeability which was between 0.4 and 1 GHz. This FWHM was basically discussed in terms of two-magnon scattering theories, in combination with the Herzer random anisotropy model. In order to correlate the resonance line broadening with a phenomenological damping parameter α_eff, which ranged from about 0.0125 to 0.028, the modified Landau-Lifschitz-Gilbert equation was used to fit and describe the permeability spectra of the ferromagnetic films.     

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.     

High-frequency response of nanostructured magnetic materials

This paper reports a brief overview on recent developments regarding the high-frequency response in the GHz range of nanostructured magnetic materials. Emphasis is placed on the linear regime in the frequency domain characterized by the dynamic susceptibility spectrum. Some modeling tools and experimental probes allowing determination of the dynamic susceptibility spectrum are first rapidly reviewed and their respective advantages and disadvantages are discussed. Next, some illustrative examples of the high-frequency response of nanopatterned materials based on recent works are presented. The role played by the shape of the element on the characteristics of excitation spectrum is underlined. Lastly, some prospects are proposed and promising trends are highlighted.     

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.     

Determination of anisotropy constants of protein encapsulated iron oxide nanoparticles by electron magnetic resonance

Angle-dependent electron magnetic resonance was performed on 4.9, 8.0, and 19 nm iron oxide nanoparticles encapsulated within protein capsids and suspended in water. Measurements were taken at liquid nitrogen temperature after cooling in a 1 T field to partially align the particles. The angle dependence of the shifts in the resonance field for the iron oxide nanoparticles (synthesized within Listeria-Dps, horse spleen ferritin, and cowpea chlorotic mottle virus) all show evidence of a uniaxial anisotropy. Using a Boltzmann distribution for the particles’ easy-axis direction, we are able to use the resonance field shifts to extract a value for the anisotropy energy, showing that the anisotropy energy density increases with decreasing particle size. This suggests that surface anisotropy plays a significant role in magnetic nanoparticles of this size.     

Possible anisotropy gap in La1.35Sr1.65Mn2O7 and La1.5Sr0.5NiO4 detected through specific heat and magnetization measurements

Magnetization and specific heat measurements, as a function of temperature, were performed on single crystals of La_1.35Sr_1.65Mn₂O₇ and La_1.5Sr_0.5NiO₄, under different applied magnetic fields (H). The specific heat in La_1.35Sr_1.65Mn₂O₇ was decreased for H=9 T parallel to the crystal c axis, compared with H=0, possibly due to a suppression of spin-wave excitations (magnons) in that ferromagnetic bilayer structure. On the other hand, the applied magnetic field had no effect in the specific heat of the antiferromagnetic La_1.5Sr_0.5NiO₄. For H=9 T and below the temperature of 4 K the specific heat data, for each crystal, was well fitted by an exponential decay law. This allowed the calculation of energy gaps around 1 meV for both compounds, in close agreement with Δ=2μ_BH for an expected energy gap in the magnon spectrum. Detailed magnetization measurements showed monotonic variations below 4 K and a steep increase close to 2 K. Both magnetization and specific heat measurements suggest the existence of an anisotropy gap in the energy spectrum of La_1.35Sr_1.65Mn₂O₇ and La_1.5Sr_0.5NiO₄.     

Magnetic anisotropy and geometrical frustration in the Ising spin-chain system Sr5Rh4O12

A structural and thermodynamic study of the newly synthesized single crystal Sr₅Rh₄O₁₂ is reported. Sr₅Rh₄O₁₂ consists of a triangular lattice of spin chains running along the c-axis. It is antiferromagnetically ordered below 23 K with the intrachain and interchain coupling being ferromagnetic (FM) and antiferromagnetic (AFM), respectively. There is strong evidence for an Ising character in the interaction and geometrical frustration that causes incomplete long-range AFM order. The isothermal magnetization exhibits two step-like transitions leading to a ferrimagnetic state at 2.4 T and a FM state at 4.8 T, respectively. Sr₅Rh₄O₁₂ is a unique frustrated spin-chain system ever found in 4d and 5d based materials without a presence of an incomplete 3d-electron shell.     

Investigation of magnetic properties for oblique deposited granular films by magnetic field annealing

A series of (Fe₅₇Co₂₄Ni₄Nb₂B₁₃)_x-(SiO₂)_1−x nano-granular thin films were fabricated by magnetron sputtering with different oblique incidence angle θ and excellent soft magnetic properties are achieved. Based on the results of magnetic field anneal at different temperature T_a, it is evidenced that orientation of atomic pairs contributes to the annealing treatment, and could manipulate magnetic anisotropy. The damping coefficient α decreases with increasing angle θ and this is ascribed to the anisotropy dissipation.     

On the relation between the effective ferromagnetic resonance linewidth Δfeff and damping parameter αeff in ferromagnetic Fe-Co-Hf-N nanocomposite films

Ferromagnetic Fe-Co-Hf-N nanocomposite films were investigated concerning their microstructure-dependent frequency behaviour. To modify the composition, the films were deposited by reactive RF magnetron sputtering by using three different 6 in. targets with various Hf fractions. The films were post-annealed up to 600 °C in a static magnetic field to induce an in-plane uniaxial anisotropy and to obtain different crystal sizes. Depending on the annealing temperature, high-frequency losses were investigated by considering the full-width at half-maximum (FWHM) Δf_eff of the imaginary part of the frequency-dependent permeability which showed a resonance frequency f_FMR of 2.3 GHz for an in-plane uniaxial anisotropy field H_u of 4 mT. The FWHM in correlation with the damping parameter α_eff is discussed, e.g., in terms of two-magnon scattering. Damping occurs due to film inhomogeneity in magnetisation and uniaxial anisotropy caused by a magnetocrystalline anisotropy H_a and/or non-magnetic phases. This will result in homogenous or even inhomogeneous resonance line broadening if additional and resonance as well as precession frequencies of independent grains arise.     

Damping and ferromagnetic resonance linewidth broadening in nanocrystalline soft ferromagnetic Fe–Co–Hf–N films

In order to describe high-frequency damping mechanisms of ferromagnetic films by means of the imaginary part of the frequency-dependant permeability, CMOS compatible ferromagnetic Fe₃₆Co₄₄Hf₉N₁₁ films were deposited by reactive r.f. magnetron sputtering on oxidised 5×5 mm²×380 μm (1 0 0)-silicon substrates with a 6-in. Fe₃₈Co₄₇Hf₁₅ target, as well as magnetic field annealing between 300 and 600 °C. An in-plane uniaxial anisotropy of around 4.5 mT as well as an excellent soft magnetic behaviour with a saturation polarisation of approximately 1.4 T could be observed after heat treatment at the above-mentioned temperatures, which drives these films to a high-frequency suitability. Ferromagnetic resonance frequencies of approximately up to 2.4 GHz could be obtained. The frequency-dependant permeability was measured with a broadband permeameter. Depending on the heat treatment, an increase of the full-width at half-maximum (FWHM) of the imaginary part of the frequency-dependant permeability is discussed in terms of two-magnon scattering, anisotropy-type competition and local resonance generation through predominant grain growth causing magnetisation and anisotropy inhomogeneities in the magnetic films. The grain size of the films was determined by (HRTEM) imaging and amounts from a few nanometres for films heat treated at 300 °C to more than 10 nm at 600 °C where the FWHM Δf_eff and the Landau–Lifschitz–Gilbert equation damping parameter α_eff increases with d_nm² and d_nm (e.g. d_nm is the grain diameter of the nonmagnetic Hf–N phase), respectively.