Effect of Mechanical Stresses and Annealing on the Magnetic Structure and the Magnetic Impedance of Amorphous CoFeSiBCr Microwires

The structural and magnetic properties of amorphous ferromagnetic microwires can undergo significant measurements under the action of external mechanical stresses and heat treatment. The study of transformations occurring in this case is important for designing various sensors of mechanical stresses, loading, and temperature and also for inducing in the wires a certain type of magnetic anisotropy that plays a significant role in the realization of various effects in them. In this work, the influence of external stresses and annealing on the processes of the magnetization and the magnetic impedance of Co₇₁Fe₅B₁₁Si₁₀Cr₃ microwires having a low positive magnetostriction (~10^-8) in amorphous state has been studied. The influence of external stresses leads to a sharp change in the character of the magnetization reversal curve, which was due to the change in the sign of the magnetostriction and the type of magnetic anisotropy. The amplitude of higher harmonics and the value of the magnetic impedance, respectively, are sensitive to mechanical stresses. Elastic stresses in the wires with a partial crystallization do not lead to a marked change in the magnetic properties; however, annealing can lead to a substantial increase in the axial magnetic anisotropy of the wires existing in the stressed state. The experimental results are analyzed in the framework of a magnetostriction model of induced magnetic anisotropy.     

Cylindrical magnetization model for glass-coated microwires with circular anisotropy: Statics

The static magnetization profile of glass-coated microwires with effective circular anisotropy is investigated using micromagnetics. In this family of microwires, the ferromagnetic nucleus with an amorphous character presents a magnetic structure composed of an inner region with axial domains and an outer region with circular domains, due to magnetoelastic anisotropy. A one-dimensional micromagnetic model is developed, taking into account both the exchange and magnetoelastic anisotropy energies, and solved quasi analytically. The total energy, magnetization profiles and magnetization curves are investigated as a function of radius and anisotropy constant of the nucleus. This work represents a fundamental study of the magnetization process in these amorphous microwires and provides guidelines for the production of microwires with tailored magnetic properties. En passant, the nucleation problem in an infinite cylinder, introduced by W.F. Brown, is revisited.     

Magnetoelastic interactions in multilayer microwires

Amorphous magnetic microwires exhibit outstanding magnetic characteristics as giant Barkhausen jump or nearly non-hysteretic behaviour that make them very suitable as sensing elements in various devices. In this article, we overview the different families of microwires and summarise most relevant results in connection with the magnetoelastic interlayer interactions in multilayer microwires. Improved magnetic behaviour can be observed in bi-layer microwires consisting of a magnetic nucleus coated by insulating cover. By employing combined sputtering and electroplating techniques, a novel series of multilayered magnetic microwires have been recently introduced. They consist typically of a magnetic nucleus and several shells having insulating and/or metallic nature, the latter magnetic or not. The magnetic character of the multilayer microwire will then depend on the magnetoelastic coupling between layers. External layers induce compressive stresses on the soft amorphous nucleus resulting in induced axial or circular anisotropies depending on magnetostriction sign. In a similar way, reduction of measuring temperature results in tensile stress as a consequence of different thermal expansion coefficients of various layers.     

Surface magnetic anisotropy in glass-coated amorphous microwires as determined from ferromagnetic resonance measurements

The ferromagnetic resonance frequency of different Co base glass-coated amorphous magnetic microwires about 3.5 μm in diameter with negative, vanishing and positive magnetostriction has been investigated from power absorption measurements in the microwave frequency range. The experimental technique employed here involves the replacement of the dielectric of a coaxial transmission line by the sample to be measured. From the evolution of the resonance frequency with DC applied magnetic field, the surface magnetic anisotropy field of the microwires has been quantitatively obtained and, as expected, found to depend on the sign and strength of the magnetostriction. Similar values for the surface anisotropy are obtained in comparison with bulk anisotropy as determined from quasi-static hysteresis loops measurements.     

Effect of torsional stresses on the magnetoimpedance of amorphous wires with negative magnetostriction

A model to describe the effect of torsional stresses on the magnetoimpedance of amorphous wires with negative magnetostriction is suggested. An approximate expression for the impedance with regard to the spatial distribution of magnetoelastic anisotropy induced by torsional stresses is derived. It is shown that the relative variation of the impedance is maximal near a critical stress value at which the surface magnetic structure of the wire changes. The calculated dependences of the impedance on the external magnetic field and torsional stress are in good qualitative agreement with experimental data for amorphous wires with negative magnetostriction.     

Recent advances in studies of magnetically soft amorphous microwires

In this paper, we present the giant magneto-impedance (GMI) effect (real part of longitudinal impedance, Z, and of the off-diagonal impedance) and hysteretic magnetic properties of amorphous glass-coated microwires with different compositions possessing nearly zero, positive and negative magnetostriction constant and metallic nucleus diameter ranging between 6 and 16 μm. Enhanced soft magnetic properties (low coercivity of about 4 A/m) and high-GMI effect have been observed in Co-rich microwires with vanishing magnetostriction constant. The magnetic anisotropy field of these microwires depends on the ratio between metallic diameter, d and total microwires diameter, D. Stress-sensitive magnetic properties have been obtained in Fe-rich microwires after stress annealing: hysteresis loop stress-annealed (SA) microwires drastically changes under applied stress. A variety of hysteresis loops with different hysteresis loops can be obtained in Fe-rich microwires changing the conditions (time and/or temperature) of the stress annealing. The obtained results allow us to tailor the microwire magnetic properties for magnetic sensors applications through selection of their composition and/or geometry and by thermal treatment.     

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.     

Giant magnetoimpedance in thin amorphous and nanocrystalline microwires

We present the results on Giant magneto-impedance effect (GMI) in amorphous and nanocrystalline microwires at frequencies until 4 GHz, paying special attention to tailoring the frequency and magnetic field dependence of the GMI effect. Correlation between magnetoelastic anisotropy and magnetic field dependences of diagonal and off-diagonal impedance components are observed.     

A contribution from the magnetoelastic effect to measured microwave permeability of thin ferromagnetic films

Microwave magnetic performance of thin ferromagnetic films is of interest in view of many technical problems. For measuring the microwave permeability, a shorted stripline technique is in common use. Recently, a coaxial technique has been developed for permeability measurements of films deposited onto a flexible substrate. The coaxial technique is reported to be advantageous over the conventional stripline method in wideband operating range and accuracy. In this paper, measurement results are presented which are obtained with these two techniques for Fe–N films. It is found that the magnetoelastic effect contributes greatly to the measured microwave permeability of the films. With the coaxial measurements under an external magnetic bias, this effect may be accounted for to estimate the permeability of a plane film sample. Additional information on the properties of the film can also be extracted from these data, such as estimations of average magnetic anisotropy field and of the magnetostriction constant of the film.     

Anisotropy of constrained magnetostrictive materials

The magnetic anisotropy of a ferromagnetic material that is free to deform is defined as the effective anisotropy, which is the sum of intrinsic anisotropy and magnetostriction-induced anisotropy. Prior works [1] and [2] (Baltzer, 1957; Kittel, 1949) indicate that if the material is undeformed then the measured anisotropy is same as its intrinsic anisotropy. When magnetostrictive materials are used as actuators or sensors they are often mechanically loaded, resulting in a restriction on the deformation. To capture their behavior in such scenarios, a modelling approach is required. Therefore, in this work, the thermodynamic accuracy of the common expressions for magnetostriction-induced and stress-induced anisotropies is first investigated. A 3D magnetoelastic model is then developed using Armstrong's implementation of an energy model. This 3D magnetoelastic model is capable of predicting the stresses induced when the magnetostriction of these materials is constrained. Using this model, it is shown that when the bulk magnetostriction of the material is clamped, the measured anisotropy will not in general be the same as the intrinsic anisotropy. It is also shown that when the magnetostriction is clamped at the microscopic level, i.e. if the material is locally constrained at the exchange length scales, then the measured anisotropy is the intrinsic anisotropy.     

Nanomechanical measurement of magnetostriction and magnetic anisotropy in (Ga,Mn)As

A GaMnAs nanoelectromechanical resonator is used to obtain the first measurement of magnetostriction in a dilute magnetic semiconductor. Resonance frequency shifts induced by field-dependent magnetoelastic stress are used to simultaneously map the magnetostriction and magnetic anisotropy constants over a wide range of temperatures. Owing to the central role of carriers in controlling ferromagnetic interactions in this material, the results appear to provide insight into a unique form of magnetoelastic behavior mediated by holes.     

Enhancement of GMI effect in magnetic microwires through the relative temperature dependence of magnetization and anisotropy

We present the study of Giant Magneto Impedance (GMI) effect in magnetic microwires with zero magnetostriction. It is shown that the temperature response of GMI effect can be enhanced by 80% through the relative temperature dependence of magnetization and anisotropy. However, such effect appears only for low amplitudes of exciting current that induces exciting magnetic field below the anisotropy field of the wire. On the other hand, when measuring at high exciting current (when the exciting field exceeds the anisotropy field), the GMI response decreases monotonically with temperature.     

Strain-induced modification of magnetic structure and new magnetic phases in rare-earth epitaxial films

Rare earths exhibit complex magnetic phase diagrams resulting from the competition between various contributions to the magnetic energy: exchange, anisotropy and magnetostriction. The epitaxy of a rare-earth film on a substrate induces (i) a clamping to the substrate and (ii) pseudomorphic strains. Both these effects are shown to lead to modifications of the magnetic properties in (0 0 1)Dy, (0 0 1)Tb and (1 1 0)Eu films. In Dy and Tb films, spectacular variations of the Curie temperature have been evidenced. Additionally, Tb films exhibit a new large wavelength magnetic modulation. In Eu films, one of the helical magnetic domains disappears at low temperature whereas the propagation vectors of the other helices are tilted. The link between structural and magnetic properties is underlined via magnetoelastic models. Moreover, molecular beam epitaxy permits the growth of Sm in a metastable dhcp phase. The magnetic structure of dhcp Sm has been elucidated for the first time. In this review, neutron scattering is shown to be a powerful technique to reveal the magnetic structures of rare-earth films.     

A model for torsion-stress effect on nonlinear magnetoimpedance in amorphous wires with negative magnetostriction

A model to describe the influence of torsional stress on nonlinear magnetoimpedance in amorphous wires with negative magnetostriction is proposed. The nonlinear voltage response is found in the framework of the low-frequency approximation taking into account the spatial distribution of the circular magnetic field and the magnetoelastic anisotropy induced by the torsional stress. It is demonstrated that the application of torsional stress results in an increase of the second harmonic amplitude in voltage due to a reinforcement of helical anisotropy in the wire. The second harmonic amplitude is analyzed as a function of external field, torsional stress and current amplitude. The ranges of torsional stress and current amplitude to achieve maximal field sensitivity of the second harmonic are found.     

Magnetoelastic effects at the interface of CoP nanostructured multilayers

Summary The role of magnetoelastic energy to determine the causes which affect the magnetic anisotropy are reviewed. The simple model used to describe magnetostriction in the new nanostructured materials is reported. Starting from this model the magnetostriction in multilayer samples, of the kind magnetic material/non-magnetic material, is discussed. In particular the fundamental influence of the interlayers is shown. Finally it is demonstrated that by measurement of saturation magnetostriction it is possible to have information on the interlayers thickness and average composition.     

FMR and SMFMR investigation of epitaxial Fe/GaAs(0 0 1) thin films with Si and Ge overlayer

The magnetic anisotropy and magnetoelastic properties of epitaxial iron films prepared by DC magnetron sputtering on single crystal GaAs(0 0 1) substrate and covered with a protective Si or Ge layer have been investigated by means of the ferromagnetic resonance and strain-modulated ferromagnetic resonance. It has been shown that the uniaxial and cubic anisotropy constants as well as two magnetoelastic constants strongly depend on the thickness of the film. The surface components of the cubic anisotropy and magnetoelastic constants have been determined.     

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.     

Magnetic Anisotropy and the Appearance of Stripe Magnetic Domains in Co/Fe Multilayers

Thin Co/Fe multilayers were e-beam evaporated in ultra-high vacuum, keeping constant the Co layer thickness and varying that of Fe in the 0.5÷15 nm range. By increasing the Fe layer thickness, a component of magnetization perpendicular to the film plane rises up, and long and parallel magnetic domains (stripe domains) appear. The phenomenon is explained on the basis of the competition between the magnetoelastic anisotropy induced by stresses at the interfaces, and the shape anisotropy constraining the magnetization in the film plane. This revised version was published online in August 2006 with corrections to the Cover Date.     

Effect of mechanical stresses on the magnetoelastic properties of TmVO4

In this paper the influence of mechanical stress on magnetoelastic properties, i.e., magnetostriction and thermal expansion in the neighborhood of a structural phase transition of the Jahn-Teller crystal TmVO₄ is investigated experimentally and theoretically. It is shown that the magnetoelastic properties of TmVO₄ for a magnetic field H∥[001] do not change the domain structure of the sample, which is rather well described when mechanical stresses in the crystal are taken into account using the parameter . Conversely, for magnetic fields along the direction of spontaneous strain [110] the magnetoelastic properties are primarily caused by reorientation of the Jahn-Teller domains and short-range order effects. It is shown that the “true” magnetostriction of a single-domain crystal for H∥[110] diverges at the phase transition point T _c=2.15 K in the absence of mechanical stresses and is strongly decreased by these stresses. Fiz. Tverd. Tela (St. Petersburg) 40, 701–705 (April 1998)