Combined effect of demagnetizing field and induced magnetic anisotropy on the magnetic properties of manganese-zinc ferrite composites

This work is devoted to the analysis of factors responsible for the high-frequency shift of the complex permeability (μ^?) dispersion region in polymer composites of manganese-zinc (MnZn) ferrite, as well as to the increase in their thermomagnetic stability. The magnetic spectra of the ferrite and its composites with polyurethane (MnZn-PU) and polyaniline (MnZn-PANI) are measured in the frequency range from 1 MHz to 3 GHz in a longitudinal magnetization field of up to 700 Ое and in the temperature interval from −20 °С to +150 °С. The approximation of the magnetic spectra by a model, which takes into account the role of domain wall motion and magnetization rotation, allows one to determine the specific contribution of resonance processes associated with domain wall motion and the natural ferromagnetic resonance to the μ^?. It is established that, at high frequencies, the μ^? of the MnZn ferrite is determined solely by magnetization rotation, which occurs in the region of natural ferromagnetic resonance when the ferrite is in the “single domain” state. In the polymer composites of the MnZn ferrite, the high-frequency permeability is also determined mainly by the magnetization rotation; however, up to high values of magnetizing fields, there is a contribution of domain wall motion, thus the “single domain” state in ferrite is not reached. The frequency and temperature dependence of μ^? in polymer composites are governed by demagnetizing field and the induced magnetic anisotropy. The contribution of the induced magnetic anisotropy is crucial for MnZn-PANI. It is attributed to the elastic stresses that arise due to the domain wall pinning by a polyaniline film adsorbed on the surface of the ferrite during in-situ polymerization.     

Theoretical study of the temperature dependence of the width of magnetic domain walls

The temperature dependence of magnetic domain walls in ferromagnetic systems with strong exchange coupling and weak lattice anisotropy is studied assuming that the thermal influence results mainly from the temperature dependence of the magnetization. We obtain that in lattices with an uniaxial symmetry like Co the wall width increases with temperature, but stays finite up to the Curie temperature T_c. In contrary, for a cubic lattice like Fe the wall width diverges for T → T_c, if only the lattice anisotropy is taken into account. The shape of the domain walls is not conserved, since at T_c the wall is determined only by the lowest order of anisotropy. In addition, the temperature dependence of a domain wall width for a thin magnetic film is determined. Using a special symmetry, we obtain a diverging wall width at a temperature markedly lower than T_c. However, the consideration of additional domain wall modes should modify this result.     

Barkhausen effect in magnetic thin films: Experimental noise spectra

In this paper Barkhausen noise spectra are shown that were measured on thin uniaxial 83-17 Ni?Fe films and these spectra were compared with the known magnetic behaviour of these films. On these types of sample the Barkhausen effect had been investigated by Lambeck [1], but their Barkhausen noise spectra have not been investigated so far. The film thicknessd _m in our experiments ranged between 400 and 2400 Å. In this range a change occurs in the dynamics of the magnetization behaviour caused by transitions of the type of domain wall. The results presented here show the very strong dependence of the Barkhausen noise spectra on the type of domain wall. Films with Bloch walls always show a frequency dependence off ^?1.7 in the higher frequency range. Samples in the thickness range where the transition occurs from the Néel wall via the cross-tie wall to the Bloch wall, have exponents between ?1 and ?2. The frequencyf _c above which the measured noise intensity begins to decrease varies very much for the different films. The curve off _c versus film thicknessd _m has the same form as the curve of the domain wall mobilitym versusd _m.     

Low-temperature study of the magnetization reversal and magnetic anisotropy of Fe,Ni, and Co nanowires

We present an extensive study of the magnetic reversal mechanism of Fe and Ni nanowires with diameters down to 6 nm, i.e. smaller than the domain wall width. The coercive field at 5 K is a factor of 3 lower than the prediction for rotation in unison. We also observe that the activation energy associated with the reversal process is proportional to the cross-section of the wires and nearly independent of the wire length. From the temperature dependence of the coercive field and the magnetic viscosity we can conclude that magnetization reversal takes place via a nucleation of a small magnetic domain, probably at the end of the wire, followed by the movement of the domain wall. For Co wires, we observe a different behavior that is dominated by the competition between the shape anisotropy and the temperature-dependent magnetocrystalline anisotropy.     

Domain walls confined in magnetic nanotubes with uniaxial anisotropy

We present calculations of the different domain wall structures confined in magnetic nanotubes, such as transverse wall, asymmetric vortex wall, branch fashion wall, and horse-saddle wall. The wall structures were calculated by micromagnetic simulations. The tube radii R=50 nm and 100 nm, and aspect ratios length/radius L/R≤15 were considered. The magnetic phase diagrams of the stability of different kinds of the domain walls were plotted as function of the tube aspect ratio L/R and the tube thickness (difference of the outer and inner tube radii).     

Measurement of the nucleation and domain depinning field in a single Co/Pt multilayer dot by Anomalous Hall effect

Co/Pt multilayer dots with perpendicular anisotropy and with diameters of 250 and 350 nm were fabricated on top of a Hall cross configuration. The angular dependence of the magnetic reversal of the individual dot was investigated by Anomalous Hall effect measurements. At near in-plane angles (85° with the magnetic easy axis) the dot switches partially into a stable two-domain state. This allows for separate analysis of the angular dependence of both the field required for nucleation of a reversed domain, and the field required for depinning of the domain wall. The angular dependence of the depinning field fits accurately to a 1/cos(θ) behavior, whereas the angular dependence of the nucleation field shows a minimum close to 45°. The latter dependency can be accurately fitted to the modified Kondorsky model proposed by Schumacher [1].     

Effect of a pulsed magnetic field on the nonlinear dynamics of vortexlike domain walls in magnetic films

The Landau-Lifshitz equation is numerically solved to study the nonlinear dynamic behavior of domain walls with the 2D vortexlike magnetization distribution in magnetically uniaxial films that have in-plane anisotropy and are exposed to a pulsed magnetic field. It is shown that a pulsed magnetic field H _p may induce transitions between various steady wall motions that differ in magnetization distribution. Solitary rectangular pulses, as well as a regular train of rectangular pulses, may be used to control the period of nonlinear dynamic transformations of the wall internal structure and the related period of variation of the wall velocity.     

Spin polarized current controlled dynamics of domain walls in magnetic films with in-plane anisotropy

We study the dynamic properties of asymmetric vortex Bloch walls and classical 1D Néel walls controlled by a spin-polarized current in magnetic films with in-plane anisotropy. It is shown that fairly high velocities of domain walls (up to 100 m/s) can be obtained for the current density in the range j = 10⁶–10⁸ A/cm². The nonlinear dependence of the wall velocity on the film thickness and the linear dependence of the velocity on the current density and inverse damping parameter are found.     

The defects influence on domain wall propagation in bistable glass-coated microwires

We studied the domain wall (DW) dynamics of magnetically bistable amorphous glass-coated Fe₇₄B₁₃Si₁₁C₂ microwires. In according to our experimental results magnetic field dependences of DW velocity of studied microwires can be divided into two groups: with uniform or uniformly accelerated DW propagation along the microwire. Strong correlation between the type of the magnetic field dependence of domain wall velocity, v(H), and the distribution of the local nucleation fields has been observed.Moreover, we observed abrupt increasing of DW velocity (jump) on the magnetic field dependences of the domain wall velocity, v(H), for the both types of the v(H) dependences. At the same time usual linear increasing of the domain wall velocity with magnetic field persists below these jumps. It was found that the jump height correlates with the location of nucleation place of the new domain wall. We have measured local nucleation field distribution in all the microwires. From local nucleation field distribution we have obtained the DW nucleation locations and estimated the jump height     

Theory of retardation of magnetic domain walls in rhombic magnetic materials

We calculate the retardation of a magnetic soliton describing a magnetic domain wall by using the generalized phenomenological theory of relaxation. We show that in this theory, based on the real dynamical symmetry of magnetic materials, the dissipation function has a different structure for high and low wall velocities. Finally, we calculate the viscous force of the wall in the Walker model and show that certain features, not discussed in the literature, emerge even when the generalized theory is applied to this simple model. In particular, the dependence of the viscous friction force on the wall velocity may be highly nonlinear and regions of unstable motion may appear. Zh. éksp. Teor. Fiz. 111, 158–173 (January 1997)     

Anomalous magnetization processes and non-symmetrical domain wall displacements in L10 FePt particulate films

Anomalous magnetization processes and non-symmetrical domain wall displacements in the minor loop of L1₀ FePt particulate films were investigated by magnetization measurements and in situ magnetic force microscopy. Magnetization (M) decreases dramatically on increasing the magnetic field to ∼3 kOe after which M becomes small and constant in the range of 5–20 kOe as observed in the successive measurement of minor loops. The domain wall displacement is non-symmetrical with respect to the field direction. The anomalous magnetization behavior was attributed to the non-symmetrical domain wall displacement and large magnetic field required for domain wall nucleation. Energy calculations from modeling suggest that non-symmetrical domain wall displacement is caused by the existence of metastable domains in which the domain edges are stuck to the particle boundaries.     

Stress dependence of the domain wall dynamics in the adiabatic regime

In this work, we determine the domain wall velocity in the low field region and study the domain dynamics in as-cast and annealed bi-stable amorphous glass-covered Fe_77.5Si_7.5B₁₅ microwires. In particular, from the relation between the domain wall velocity and magnetic field in the adiabatic regime, the power-law critical exponent β, the critical field H₀ and the domain wall damping η were obtained. It has been verified that the main source of domain wall damping is the eddy current and spin relaxation, both with a strong relation with the magnetoelastic energy. This energy term is changed by the axial applied stress, which, by its time, modifies the damping mechanisms. It was also verified that the domain wall damping terms present different behavior at low (mainly eddy currents) and high applied stress (spin relaxation).     

Insight into the magnetic behavior of Sr2IrO4: A spontaneous magnetization study

Sr₂IrO₄ is a weak ferromagnet where the spin arrangement is canted anti-ferromagnetic (AF). Moreover, the spin-structure coupling plays an important role in magnetic behavior of Sr₂IrO₄. In this concern the magnetization under zero applied field i.e. spontaneous magnetization would be interesting to study and would give insight into the novel magnetic behavior of Sr₂IrO₄. Sophisticated techniques like neutron diffraction, μSR etc has been used to understand the magnetic behavior of Sr₂IrO₄ under zero applied field. To understand the magnetic behavior we have performed field and temperature dependent magnetization study. The measured field and temperature dependent magnetic data is analyzed rigorously. We have attempted to understand the temperature dependance of spontaneous magnetization, remanent magnetization and coercive force. We observe that the spontaneous magnetization extracted from Arrott plot shows that the Sr₂IrO₄ is not an ideal ferromagnet. The temperature dependent coercive field follows Guant's model of strong domain wall pinning. Our investigation explicit the temperature dependence of various magnetic properties shows the magnetic transitions from paramagnetic to ferromagnetic phase with $T_c$ around 225 K and a low temperature evolution of magnetic moment around $T_M～90$ K.     

Magnetic microstructure of candidates for epitaxial dual Heusler magnetic tunnel junctions

Heusler alloys are considered as interesting ferromagnetic electrode materials for magnetic tunnel junctions, because of their high spin polarization. We, therefore, investigated the micromagnetic properties in a prototypical thin film system comprising two different Heusler phases Co₂MnSi (CMS) and Co₂FeSi (CFS) separated by a MgO barrier. The magnetic microstructure was investigated by X-ray photoemission electron microscopy (XPEEM). We find a strong influence of the Heusler phase formation process on the magnetic domain patterns. SiO₂/V/CMS/MgO/CFS and SiO₂/V/CFS/MgO/CMS trilayer structures exhibit a strikingly different magnetic behavior, which is due to pinhole coupling through the MgO barrier and a strong thickness dependence of the magnetic ordering in Co₂MnSi.     

On the correlation between microstructure and magnetic losses in electrical steel

The magnetic properties of electrical steel such as magnetization curves, magnetization behavior and specific magnetic losses are related to the microstructure and the texture of the steel. A quantitative model, which describes the effect of microstructure and texture and their interplay on the magnetic losses P, is still missing. Based on experimental data for nonoriented electrical steels and FeSi-samples with high (Si, Al)-content, a more general formula is proposed for the dependence of P, at a given value of magnetic induction B, as a function of the mean value of the grain size d of the material and of the intensities of the relevant magnetic texture components.     

Spontaneous transformations of the magnetic structure of a film nanocontact

The magnetization distributions in a symmetric magnetic film nanocontact for oppositely magnetized ferromagnetic electrodes are analyzed based on numerically solving the Landau-Lifshitz and magnetostatic equations as a function of magnetic and geometrical factors. It is found that a symmetric magnetic configuration is unstable when the head-to-head domain wall dividing the regions with opposite orientations of magnetization is located at the center of the nanocontact. The instability arises when the uniaxial magnetic anisotropy constant reaches a certain critical value K _c below which it spontaneously leaves the center of the nanocontact. The transition from the symmetric state (wall at the center) to an asymmetric one can be continuous (second order) or discrete (first order), depending on the geometrical and physical parameters of the nanocontact (length to width ratio, anisotropy constant, and saturation magnetization). The phase diagram is constructed in terms of the variable’s nanocontact length vs. anisotropy constant. This diagram divides the symmetric and asymmetric magnetic configurations of the system. The occurrence of a tricritical point in the phase diagram is its characteristic feature.     

Behavior of higher harmonics of the granular HTSC response to a low-frequency magnetic field

A theoretical explanation is proposed for the experimental results on the behavior of higher harmonics of the granular HTSC response to a variable magnetic field of frequencies ～10² Hz. The theory explains the periodicity in the dependence of the harmonics amplitudes on a static external magnetic field; the dependence of the period on the harmonics number and on the amplitude of the variable magnetic field; the existence of the threshold in the dependence of the odd-harmonics amplitudes on the amplitude of the variable magnetic field; and the possible formation of pairs for these dependences for the neighboring odd harmonics. It is shown that the experimental dependences can be explained without a detailed analysis of microprocesses in individual Josephson loops only by treating HTSC as a macroscopic medium characterized by the dependence Φ(H) of the magnetic flux on the external magnetic field, which is typical of type II superconductors.     

The mobility of domain walls in magnetic films

The character of the dependence of domain wall velocityv on magnetic field intensityH varies with film thickness. Possible causes of the nonlinearity ofv(H) in films of some thickness are discussed. It has been shown how the mobility of domain walls varies over a wide range of thicknesses, from ultrathin films to bulk layers. The mobility measured for films up to 500 thick is consistent with the spin damping theory. For thicknesses greater than 1 the experimental data agree well with the eddy current damping theory. The mobility in thinner films is considerably lower than predicted by this theory. It greatly depends on the domain wall structure, magnetic ripple in domains as well as on the structural defects retarding the wall.     

Dynamics of domain walls in ultrathin magnetic films

The domain walls in ultrathin ferromagnetic films with uniaxial magnetic anisotropy are investigated theoretically. It is shown that taking account of the magnetodipole and magnetoelastic interactions leads to the appearance of an effective anisotropy with respect to the direction of the normal to the plane of the wall. The existence of a new type of domain walls—“corner” walls, at which the magnetization vector is rotated in the plane making a certain angle, which depends on the film parameters, with the plane of the domain wall and the static and dynamic properties of these walls are investigated. The dependence of the limiting velocity of the domain walls on the film thickness is found. Zh. éksp. Teor. Fiz. 112, 1476–1489 (October 1997)     

Nuclear spin-lattice relaxation due to non-linear excitations in magnetic chains

A simple classical model for nuclear spin-lattice relaxation due to solitons in XY one-dimensional magnetic chains in an external magnetic field is discussed. The results show that one should expect opposite behavior for the H/T dependence of T^-1₁ for the ferromagnetic and the antiferromagnetic case.