Frequency dispersive complex permittivity and permeability of ferromagnetic metallic granular composite at microwave frequencies

We experimentally studied the frequency dependent complex permittivity ε and permeability μ of composite composed of carbonyl iron powder (CIP) and epoxy resin in the frequency range 1-18 GHz. We found that the intrinsic ε and μ of CIP extracted from the measured ε and μ of composites follow the classical Maxwell equations and the Landau-Lifshitz-Gilbert (LLG) equation, respectively. The dependences of ε and μ of composites on the volume fraction of CIP (vf_CIP) were investigated using the two-exponent phenomenological percolation equation (TEPPE). We found that the TEPPE can fit the experimental results very well. Comparing the results of percolation parameters derived by experimental data at different frequencies, we show that the TEPPE is frequency independent for the composites at microwave frequencies. The results also show that the ε and μ spectrums of composites with definite vf_CIP can be correctly calculated by combining the TEPPE with the theoretical models of intrinsic ε and μ.     

Comparison of ferromagnetic resonance between amorphous wires and microwires

Measurements of magnetoimpedance in amorphous wires and microwires at the GHz region are presented here. The maxima observed in the magnetoimpedance of different samples in the high frequency range are attributed to the ferromagnetic resonance (FMR) that occurs when a sample is submitted to a longitudinal static magnetic field and an oscillating transversal field. While the appearance of a peak on the resistance and the drop of the inductance is explained by means of FMR, the dependence of the width of that resonance with different parameters (magnetic field, stress distribution, sample size, etc.) is not clearly understood, and therefore additional works to explain the value of the resonance width are needed. It is interesting to consider firstly, the influence of the diameter of the sample and thus the stress distribution on the FMR. The size and position of the FMR is found to be completely different for diameters ranging from 24 to 171 μm. The dependence of the frequency value at which the peak of the resistance is found can be explained by the different values of the anisotropy field in the sample. The width of the FMR changes drastically with the diameter of the sample and with the applied magnetic field and they will be discussed in this paper.     

Giant magnetoimpedance in glass-covered amorphous microwires at microwave frequencies

In this work, results on the giant magnetoimpedance (GMI) of a glass-covered amorphous microwires with nominal compositions Co_70.4Fe_4.6Si₁₅B₁₀ and Fe_77.5Si_7.5B₁₅ are presented. The impedance Z=R+iX has been investigated as function of frequency (up to 1.8 GHz) and magnetic field (up to ±400 Oe), using a HP4396B impedance analyzer and an appropriate coaxial microwave cavity. The effects of the thermal treatments (Joule heating, from 20 mA up to 100 mA for 10 min) for anisotropy induction and, as a consequence, for GMI effect have been investigated.     

AC-current-induced magnetization switching in amorphous microwires

We studied the influence of AC current flowing through microwires, on magnetization dynamics. We used a previously developed Sixtus-Tonks modified setup to evaluate the domain wall (DW) velocity within the microwire. However, instead of a magnetizing solenoid, we used a current flowing through the microwire. We observed that the AC current flowing through the annealed Co-rich microwire leads to remagnetization by fast domain wall propagation. The estimated DW velocity was approximately 4.5 km/s, which is similar to and even higher than that reported for the magnetic-field-driven domain wall propagation in Fe- and Co-rich microwires. We measured the DW velocity under tensile stress, and found that the DW velocity decreases under applied stress. An observed DW propagation induced by the current flowing through the microwire is explained considering the influence of an Oersted magnetic field on the outer domain shell. This field has a circular easy magnetization direction and magnetostatic interaction between the outer circumferentially magnetized shell and the inner axially magnetized core.     

Locally resolved photothermally modulated ferromagnetic resonance on epitaxial Fe-films deposited on laterally patterned GaAs

(0 0 1)Fe-mesa were grown on a GaAs high electron mobility transistor (HEMT)-structure. Magnetic properties were investigated by locally resolved photothermally modulated ferromagnetic resonance (PM-FMR). The surface and the in-plane anisotropy are decreased in HEMT-areas. The field independent response of PM-FMR provides information on the electrical properties of the GaAs-heterostructure and yields evidence of preparation dependent lifetime effects of the photo-carriers.     

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.     

Effect of annealing treatments on the microwave electromagnetic properties of amorphous FeCuNbSiB microwires

The amorphous FeCuNbSiB microwires are fabricated by using the melt extraction method and annealed separately at temperatures T = 573, 673, 723 and 773K for 1h. The effect of annealing treatment on the microwave electromagnetic properties of FeCuNbSiB wires/wax composites has been investigated for the first time. It is found that in a frequency range of 0.5--4.0GHz, the complex permittivity, permeability, magnetic and electric loss tangents of FeCuNbSiB wires/wax composites are strongly dependent on the annealing temperature and frequency. For T = 573, 723 and 773K, two resonance peaks are found at frequency f = 1.2 and 3.3GHz. However, for T = 673K, only one resonance peak occurs at f = 3.3GHz. The resonance peak at f = 1.2GHz is believed to be due to the stress-induced anisotropy, while the resonance peak at f = 3.3GHz is attributed to the random anisotropy.     

Dependence of the ferromagnetic resonance modes on the coupling strength in exchange-coupled trilayer structures

The dependence of the dispersion relation and the magnetization on the exchange coupling strength was calculated for a system consisting of two ferromagnetic layers exchange-coupled through a nonmagnetic spacer layer. The magnetic layers are characterized by both uniaxial and cubic magnetocrystalline anisotropies. A minimization procedure was developed which allows the resonance modes to be obtained for any magnetic field orientation and strength, as well as for any exchange coupling strength. If the antiparallel coupled film is unsaturated at resonance, the dispersion relation for both acoustic and optic modes could be rather complex, especially when the field is applied in the plane of the film.     

The role of dipolar interactions for the magnetic properties of ferromagnetic nanoring

We investigate numerically the effects of the dipolar interactions on magnetic properties in small ferromagnetic nanorings using a Monte Carlo technique. Our simulated results show that the strength of dipolar interaction in the magnetic nanoring has an important influence on the magnetization reversal processes and further the coercivity and the remanence. As the dipolar interaction increases, the transition of magnetization reversal processes from the onion-rotation state to the vortex state can occur, which results in an increase in coercivity and a decrease in remanence. On the other hand, it is found that the coercivity and the remanence depend more strongly on the strength of dipolar coupling for the relatively small size nanoring than for the large size nanoring in width. This can be attributed to the stable vortex state without core in smaller width nanoring in contrast to the metastable vortex state with core in larger width nanoring, induced by strong dipolar interactions. Additionally, the temperature dependence of coercivity and remanence in magnetic nanoring is also studied at a fixed dipolar interaction.     

Annealing temperature effect on microstructure,magnetic and microwave properties of Fe-based amorphous alloy powders

Fe₇₄Ni₃Si₁₃Cr₆W₄ amorphous alloy powders were annealed at different temperature (T) for 1.5 h to fabricate the corresponding amorphous and nanocrystalline powders. The influences of T on the crystalline structure, morphology, magnetic and microwave electromagnetic properties of the resultant samples were investigated via X-ray diffraction, scanning electron microscopy, vibrating sample magnetometer and vector network analyzer. The results show that the powder samples obtained at T of 650 °C or more are composed of lots of ultra-fine α-Fe(Si) grains embedded in an amorphous matrix. When T increases from 350 to 750 °C, the saturated magnetization and coercivity of the as-annealed powder samples both increase monotonously whereas the relative real permittivity shows a minimal value and the relative real permeability shows a maximal value at T of 650 °C. Thus the powder samples annealed at 650 °C show optimal reflection loss under −10 dB in the whole C-band. These results here suggest that the annealing heat treatment of Fe-based amorphous alloy is an effective approach to fabricate high performance microwave absorber with reasonable permittivity and large permeability simultaneously via adjusting T.     

Theoretical investigations of magnetic properties of ferromagnetic single-walled nanotubes

The magnetic behaviors of ferromagnetic single-walled nanotubes are systematically investigated by use of the many-body Green's function method of quantum statistical theory. The spontaneous magnetization, absolute value of ferromagnetic energy, area of hysteresis loop and coercivity increase with diameter of the tubes and spin quantum number, and decrease with temperature. Curie temperature increases with diameter and spin quantum number. As the diameter of the tube tends to infinity, all the numerical results approach to those of a two-dimensional monolayer. The dependences of initial susceptibility on temperature and diameter below and above Curie point are contrary. The calculated results are compared with experimental results where possible, and are qualitatively in agreement with the latter. The Curie temperature is determined by the tube diameter and independent of rolling helicities.     

Intermartensitic transformation and magnetic field effect in NiMnInSb ferromagnetic shape memory alloys

Partially substituting Sb for In, we found an irreversible transformation of martensite to intermartensite at 90 K in Ni₅₀Mn₃₄In₁₂Sb₄ alloy during heating. The reverse transformation of martensite and intermartensite to the parent phase induced by a magnetic field has been investigated. The results indicate that, if a sufficiently high magnetic field is applied, the intermartensite state is no longer necessary as an intermediate state. Thus, a difference of the transformation originating from magnetic and from thermal energies has been found. In this competition, lattice distortions play an important role to promote the occurrence of the intermediate intermartensitic path.     

Characterization of magnetic materials by low-field microwave absorption techniques

A low-field non-resonant microwave absorption has recently been observed in a variety of magnetically ordered materials at low DC fields (−1000 Oe H_DC+1000 Oe), which is known as low-field microwave absorption (LFA). It has been shown that LFA is essentially similar to giant magnetoimpedance (GMI), and clearly different from ferromagnetic resonance (FMR). LFA strongly depends on the anisotropy field of the sample. In contrast with FMR (which can be described as the homogeneous precession of spins in the saturated state), LFA can be thought as a spin rotation process occurring during the magnetic saturation. In this work, we present a detailed study of the basic features of LFA in several types of materials: ferrites and amorphous microwires and ribbons; in particular the effects sample shape, temperature up to the Curie transition, the influence of easy axis and the effects of annealings. These examples show that once LFA is fully understood, it can become a powerful characterization tool.     

Complex permittivity, permeability and microwave absorbing properties of (Mn2−xZnx)U-type hexaferrite

Complex permittivity, permeability and microwave absorbing properties of a U-type hexaferrite series Ba₄Mn_(2−x)Zn_xFe₃₆O₆₀ (with 0≤x≤2 in step of 0.5) have been examined in the X-band (8.2-12.4 GHz) frequency range. The series have been prepared using conventional solid state reaction route. Microstructural variations with composition have been found with X-ray diffraction (XRD) and scanning electron microgram (SEM). The complex permittivity (ε^?=ε′−jε″) and permeability (μ^?=μ′−jμ″) were measured using vector network analyzer (Agilient Make model PNA E8364B). These parameters were then used for calculating the reflection loss for determination of microwave absorbing properties. Addition of Zn resulted in an increase in reflection loss from −4 dB (or 60 % absorption) in sample with x= 0 to −32 dB (99.92% absorption) in sample with x=1 when the sample thickness was 1.7 mm. Multiple peaks of resonance were obtained in the dielectric and magnetic loss spectra for all samples with x>0. The result indicates that the sample with composition Ba₄MnZnFe₃₆O₆₀, i.e., x=1, can be used effectively for microwave absorption and suppression of electromagnetic interference.     

Physical properties and giant magnetoimpedance sensitivity of rapidly solidified magnetic microwires

The relation between the magnetoimpedance and the magnetic properties of a wide set of soft magnetic microwires from several sources has been studied. Magnetic properties were obtained by vibrating sample magnetometry and ferromagnetic resonance spectroscopy. The magnetoimpedance voltage sensitivity of each sample, the criterion of interest for high sensitivity magnetometer design, was then evaluated at several frequencies and drive currents. It appears that all samples possess roughly similar properties, regardless of their fabrication process or chemical composition. The voltage sensitivity of the samples obtained from experimental measurement is compared with a simple model of sensitivity. The general trends predicted by the model provide useful insights for materials optimization. Averaged sensitivity over the sample set is around 10 kV/T/cm at 10 MHz. The critical importance for sensitive magnetometry of the maximum excitation current permissible in each wire is also highlighted.     

Investigation of ferromagnetic resonance and damping properties of CoFeB

In this study, the influences of thin film thickness and post-annealing process on the magnetic properties of CoFeB thin films were investigated. The angular dependency and linewidth of the ferromagnetic resonance signal were used to explore the magnetic behavior of sputtered single-layer and trilayer thin film stacks of CoFeB. A micromagnetic simulation model was employed based on the metropolis algorithm comprising the demagnetizing field and in-plane induced uniaxial anisotropy terms with all relevant contributions. Our results reveal that the direction of magnetization changes from in-plane to out-of-plane as a result of the annealing process and induces a perpendicular magnetic anisotropy in the 1-nm thick CoFeB thin film. The ferromagnetic resonance (FMR) linewidth can be defined well by the intrinsic Gilbert damping effect and the magnetic inhomogeneity contribution in both as-grown and annealed samples. The difference between the linewidths of the single and trilayer film is mainly caused by the spin pumping effect on damping which is associated with the interface layers.     

Study of domain structure and magnetization reversal after thermal treatments in Fe40Co38Mo4B18 microwires

We have studied the effect of thermal treatment on the magnetic domain structure and magnetic reversal process of amorphous and nanocrystalline Fe₄₀Co₃₈Mo₄B₁₈ microwires. The domain structure and the magnetization reversal of amorphous FeCoMoB microwires reflect the complex stress distribution introduced by the glass coating. Hence, the thickness of radial domain structure decreases with temperature and the temperature dependence of the switching field presents a discontinuous behavior. After nanocrystallization, the domain structure of FeCoMoB microwire is almost constant within the temperature range 10-400 K and the switching field decreases almost linearly with temperature mostly because of the decrease of saturation magnetization.     

Identifying magnetic response of split-ring resonators at microwave frequencies

In this study we provide experimental methods to identify the magnetic resonance of split ring resonantors (SRR) at the microwave frequency regime. Transmission measurements were performed on both single SRR unit cell and periodic arrays of SRRs. The magnetic response of the SRR structure was demonstrated by comparing the transmission spectra of SRRs with closed ring resonators (CRR). Effects of the changes in the effective dielectric constant of the SRR medium on the band-gaps of SRR are investigated experimentally. SRRs not only exhibit a magnetic resonance band gap but also a band gap due to the electric resonance. Finally, we present the effect of electric coupling to the magnetic resonance of bianisotropic SRRs by utilizing SRRs with different orientations, and incident electromagnetic wave polarizations.     

On the comparison of the polarisation behaviour of exchange-biased AF/F NiMn/Fe37Co48Hf15 bi-layer and multi-layer films with increased ferromagnetic cut-off frequencies

Antiferromagnetic/ferromagnetic (AF/F) NiMn/Fe₃₇Co₄₈Hf₁₅ films were investigated with respect to their exchange bias, in-plane unidirectional anisotropy, polarisation and high frequency behaviour. After deposition, carried out by r.f. magnetron sputtering, the films were post-annealed for 4 h at 300 °C in a static magnetic field, in order to induce exchange-bias, which results in a unidirectional anisotropy. Dependent on the presence of a bi-layer or multi-layer sandwich structure the films show a different exchange-bias field-ferromagnetic inter-layer thickness behaviour with exchange-bias fields μ₀?H_eb between 2 and 10 mT. The in-plane uniaxial (single film) or unidirectional anisotropy fields μ₀*H_UF were between 4 and 18 mT. This results in a significant increase of the cut-off frequency in the GHz range in comparison to a single Fe₃₇Co₄₈Hf₁₅ film, which is shown by frequency-dependent permeability plots. High damping in the imaginary part of the permeability, i.e., high resonance line broadening could be observed for films with high coercivity μ₀*H_c of around 7 mT in the easy axis of magnetisation.