Domain Wall Damping Research Articles

The influence of an electric current density on the complex permeability

In an attempt to influence the domain wall damping, an ac electric current was driven through contacted ferrite ring cores and parallelepipeds in different directions. The dependence of magnetic properties on current density, phase shift between the winding current and material current and current direction was measured. Changes in magnetic flux due to the additional magnetic field arising from the material current were considered. Variations of the complex permeability as a function of current phase shift and coaxial or radial direction were observed. Changes in damping and resonance frequency can be interpreted as due to the interaction of the electric current with domain walls. The observed effects can be explained by the domain drag effect.

An alternative approach to giant magnetoimpedance phenomena in amorphous ferromagnetic wires

Magnetoimpedance in as-cast, nonmagnetostrictive CoFeBSi amorphous ferromagnetic wires, submitted to an ac electric current of 5 mA in the frequency range 100 Hz–100 kHz, is analyzed in terms of equivalent circuits. It is shown that the equivalent circuit representing the wire frequency behavior can be approximated by a parallel LpRp arrangement with elements Rs and Ls in series; Lp and Rp are associated with circumferential domain wall permeability and wall damping, respectively; Ls is related to the circumferential rotational permeability of the wire, and Rs accounts for the dc resistance in the circuit. When the wire is submitted to a longitudinal dc field high enough to approach saturation (Hdc=3600 A/m), the circuit becomes simply a series RsLs circuit. The various contributions from basic magnetization processes to magnetoimpedance are discussed, as well as deviations from this idealized model.

Eddy current damping of thin film domain walls

A self-consistent two-dimensional numerical model, is developed to study eddy current damped domain wall motion in conductive, soft thin films. The micromagnetic Landau-Lifshitz equation and Maxwell's equation are solved simultaneously to provide a rigorous description of magnetization dynamics interacting with eddy current, which is relevant to the dynamic response of thin film inductive heads. Simulation results indicate that for Permalloy films thinner than 3000 AA, eddy current damping can be neglected in wall dynamics. For film thickness greater than 1 mu m this damping effect could be the dominating loss mechanism.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

On the phenomenological description of the damping of the domain walls in ferrite-garnets

The mechanisms of the domain wall relaxation in the ferromagnets have been analyzed in the frameworks of the phenomenological approach. It is shown that the mechanisms considered previously can not explain the experimental data entirely. The new diffusion mechanisms of the domain wall damping is discussed.

High-frequency domain wall motion and energy dissipation in soft ferromagnetic metallic glasses

High-frequency domain wall motion has been studied on two soft ferromagnetic metallic glasses, suitably stressed to deal with simple static domain patterns. Magnetization measurements were supported by direct observation of the magnetic domain configurations. Domain wall motion is dominated by energy dissipation effects. For small wall displacements, the measured coefficient of domain wall damping is very close to the eddy-current value. The power dissipated in the magnetization process decreases with increasing applied field, mainly owing to domain wall multiplication. A possible mechanism for such a multiplication is outlined.

Domain wall dynamics and relaxation through the frequency dependence of hysteresis loops

The frequency dependence of hysteresis loops of high purity yttrium iron garnet (YIG) polycrystals has been measured over the range of temperature and frequency where the permeability spectrum has evidenced significant dispersion. Very close to Tc, the effect of domain wall damping results in elliptical loops when the wall relaxation frequency is approached. The observed increase in losses with frequency implies values of the wall damping parameter β which agree with previous determinations from permeability data. In the 150 K range, migrating electrons due to the voluntary slight iron deficiency of the studied sample cannot follow fast wall motions and relax, which in turn produce more rectangular loops for frequencies above the diffusion relaxation frequency. The corresponding increase in hysteresis losses is due to an increase in the wall energy γ and possible dynamical changes of the domain wall configuration in the sample.

Temperature effect on domain-wall damping in an amorphous alloy

The temperature dependence of the viscous damping parameter $\ensuremath{\beta}$, restoring constant $\ensuremath{\alpha}$, and propagation field ${H}_{p}$ have been measured in ferromagnetic amorphous ribbons. We have observed that there is a linear dependence of $\ensuremath{\beta}$ on $\frac{{({\ensuremath{\mu}}_{0}{M}_{s})}^{2}}{\ensuremath{\rho}}$ up to $T=0.9{T}_{c}$ and that $\ensuremath{\alpha}$ is proportional to ${({\ensuremath{\mu}}_{0}{M}_{s})}^{2}$. From these data, it is possible to estimate the eddy-current (${\ensuremath{\beta}}_{E}$) and relaxation (${\ensuremath{\beta}}_{R}$) contributions to $\ensuremath{\beta}$ separately. It is further inferred that the number of domain walls and the magnetic pole distribution in the sample do not change up to $T\ensuremath{\simeq}0.9{T}_{c}$.

The correlation of ultrasonic attenuation, microstructure and ductile to brittle transition temperature in very low carbon steels

A study of the frequency dependence of the ultrasonic attenuation and the ductile to brittle transition temperature as a function of microstructure has been carried out for a very low carbon (0.02 wt%) steel. The ultrasonic attenuation was found to be anomalously high when compared to normal low carbon (0.2 wt%) steels and could not be interpreted in terms of simple scattering models. This is thought to be due partly to large hysteresis losses (dislocation and magnetic domain-wall damping) and partly to large grain-size distributions. An empirical correlation between the ductile to brittle transition temperature and an ultrasonic attenutation parameter has been found for this particular steel.

Complex elastic, dielectric and piezoelectric constants by domain wall damping in ferroelectric ceramics

A model, describing losses in ferroelectric ceramics by the damped motion of 90° domain walls has been developed. The dependence of the complex dielectric, elastic and piezoelectric constants on the material properties P0 and S0 (spontaneous polarization and deformation), on the wall properties and on the directional distribution of the domains is derived. Measurements confirm this phenomenological, two dimensional theory, thus indicating the domain wall dampaing being the dominant loss mechanism in these ceramics.

Epitaxial small magnetic bubble La–Sm–Lu iron garnet films grown on NdGaG substrates oriented (100) and (111)

A Sm2.48Lu0.26(Pb,Pt)Fe5O12 garnet film composition grown earlier1 by LPE on NdGaG substrates oriented (100) and (111) is now diluted (in steps) to 56 mol% of a hypothetical La1.35Lu1.7Fe5O12 garnet. Most of the results reported are for films grown at 830 °C, but the effects of changing growth temperature for the compositions with the largest La–Lu substitutions are also discussed. La–Lu substitutions in fluxed melts significantly decrease film growth rates, and La must be present in melts in amounts in excess of those desired in the final crystal film. Both Pb from the fluxed melt and Pt from the crucible via the melt are incorporated into films in minor quantities. The ratio of rare earths and Pb to Fe and Pt in films is greater than the stoichiometric 0.6. The films support bubbles in the 0.5μm diameter range and have characteristic length l values of 0.037 to 0.062μm. Saturation magnetization values are 1700 to 2000 g (×10−4T). Domain wall damping coefficients are reduced in proportion to the amount of Sm replaced. The g factor is about 2 for all the films. The l, magnetic anisotropy Ku, and stability factor Q are decreased by La–Lu substitutions for (100) films, but they are first increased slightly then decreased for (111) films. With the largest La–Lu substitution, (100) films have zero Q. The highest l, Ku [3.6×105 erg/cm3 (×10−1 J/m3)] and Q (2.5) exist for (100) films with no La.

Spin-wave damping of domain walls in YFeO3

The mobility of domain walls in YFeO3 is determined by calculating the damping of the uniform precession or k=0 spin-wave mode. The presence of antisymmetric exchange is explicitly taken into account in obtaining the spin-wave modes. The dominant spin-wave damping mechanism is found to be a four-magnon scattering process. This process leads to a calculated wall mobility that has the same order of magnitude and temperature dependence as that observed.

Complex permeability variations of iron excess CoNiZn ferrites with annealing temperature

Induced anisotropy due to Co <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2+</sup> ions in excess iron ferrites is known to increase the magnetic Q, and the technologically important μQ product, by increasing the restoring force on domain walls. This anisotropy can be induced by slow cooling from below the Curie temperature. This paper studies the further increases in the magnetic Q that occur for slow cooling from above the Curie temperature. We show from measurements of the complex permeability spectrum between 1 and 1000 MHz that such improvements are due to a decrease in domain wall damping. Measurements of d.c. resistivity, an Auger spectroscopy analysis of grain boundary impurities and a thermogravimetric analysis indicate that oxidation of Fe <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2+</sup> ions in both grain boundaries and interiors is the origin of the decrease in the domain wall damping.

The shape, energy, eddy current loss, and relaxation damping of magnetic domain walls in glassy iron wire

A magnetostatic model is developed for extended domain boundaries of the type observed by O'Handley [1] separating opposed axially magnetized sections of glassy iron wire. The domains in any circular wire cross section are separated by a boundary that has the minimum length consistent with their areas, and the distribution of polarization over the wire length is such as to minimize the sum of the domain wall and magnetic divergence energies. The dependence of boundary length <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2L</tex> on the wire diameter <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2a</tex> , remanent polarization J <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</inf> , and domain wall energy per unit area γ, is evaluated so that γ may be obtained from measured values of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a, L</tex> , and J <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</inf> . For the glassy iron material [1] γ = 0.76 mJm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> . Eddy current loss and relaxation damping coefficients are calculated for a two-dimensional model with the same cross section and then appropriately averaged to obtain the mean coefficients for the three-dimensional model. It is shown that 55 percent of the losses observed by O'Handley are due to eddy currents, and attribution of the remainder to relaxation damping yields a value of 6.2 kgm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> s <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> for the relaxation damping coefficient indicating a Gilbert damping coefficient <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\alpha_{G}\simeq0.06</tex> if one assumes the exchange constant <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A = 10^{-11}</tex> Jm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> . De Blois' observations of domain wall motion in iron whiskers [9] are also briefly discussed.

``Elastic'' constants and wave phenomena in bubble lattices

The ``elastic'' properties of lattices of reversely magnetized perfectly cylindrical domains (bubbles) are studied. Expressions are presented for the ``elastic'' constants determining the forces resulting from displacements in a general bubble lattice. Numerical results are given for the hexagonal (triangular) lattice and for various bubble spacings. ``Elastic'' wave phenomena in these lattices are investigated and the velocities of propagation are determined under the assumptions that the domain-wall damping and the coercive field can be neglected. Finally, an estimate is made of the attenuation properties and of the quality factor of a resonating bubble lattice of finite dimensions.