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The magnetic viscosity, S, of Mn-Ga and Mn-Al alloys with the L10 type crystal structure has been measured at temperatures in the range 2–300 K. The values of the fluctuation field, Sv, and the coercive field, Hc, of the two types of materials are comparable to each other. The observed dependence of Sv on the applied field, H, is not in accordance with the theory of magnetic viscosity of particulate recording media. The relationship between Hc and Sv, the latter measured at H = −Hc, fits the Barbier relationship, Sv ∼ H c α , rather well.

In this paper, an estimation method for the ageing factor of permanent magnets is proposed. It is based on a multi-scale model, which allows estimating the magnetic properties of permanent magnets, combined with the magnetic viscosity theory. Using this method, the necessary measurements can be drastically reduced. The results obtained are compared with measurements, with a satisfactory agreement.

The soft magnetic properties of the sintered Mn-Zn ferrites can be stabilized versus changing temperature by addition of CoO in suitable proportion. The material benefits in this case of anisotropy compensation brought about by the Co2+ cations. However, prolonged exposure of magnetic cores to high temperatures, as likely to occur in automotive applications, can be associated with local phenomena of induced anisotropy, resulting in magnetic viscosity and aging. We show in this paper that proper addition of TiO2 in optimally CoO-doped ferrites can restrain aging and the ensuing detrimental effects on loss and permeability. We find, in particular, that on passing from conventional doping with 1000 ppm to 5000 ppm of TiO2, the deterioration of the soft magnetic properties of the ferrite following an aging treatment of 100 h at 200 °C is in good part reduced below a few hundred kHz. It is concluded that this effect chiefly relates to a correspondingly reduced value of the magnetic anisotropy induced by directional ordering at 200 °C. This beneficial effect appears to descend from hindered diffusion of the Co2+ cations by the dissolved Ti4+ cations. The induced anisotropy, however, while leading to increased hysteresis and excess losses, brings about a decrease of the total energy loss at intermediate frequencies, by modifying the distribution of the resonance frequencies and the associated damping of the rotational processes. Little to negligible effects are observed beyond a few MHz.

The quasilogarithmic magnetic viscosity of the perpendicularly anisotropic Nd-Fe-B films is determined by measuring the time dependent magnetization in coercive fields at 300 K-4.2 K. The distribution of energy barrier heights in the films is believed to be the origin of this stretched exponential magnetic relaxation. Another feature exhibited in the anisotropic Nd-Fe-B films is the nonmonotonic temperature dependence of the magnetic viscosity coefficients, which are extracted by the decay slopes of the linear quasilogarithmic magnetic aftereffect curves. (C) 2012 Elsevier B.V. All rights reserved.

This work is an investigation of the experimental method used for measuring the magnetic viscosity in a hard ferromagnetic material, i.e. the recording of the magnetization under constant applied field and temperature, after the material has been magnetically saturated. It investigates how the experimental results are affected by the initial conditions of the method (saturation field, field change rate and field oscillation prior to its stabilization), and by minor variations of field and temperature during the recording. Based on the arising conclusions and the use of a more complex fitting function of measurements, the accuracy and repeatability of experimental results is improved.

Low-temperature viscous acquisition and decay measurements above and below the Verwey transition have been carried out for a selection of natural and synthetic multidomain magnetite samples. A strong correlation between the viscosity spectra and published disaccommodation spectra was found, where disaccommodation reflects electron mobility. Assuming the viscosity is controlled by identical mechanisms as disaccommodation, the reduction in electron mobility below the Verwey transition is found to significantly increase viscous acquisition and decay rates over the time scales measured (1–3000 s). Although strongly affecting the viscosity, disaccommodation processes do not appear to control the rate of change of viscosity with time, i.e. the viscosity curvature. It is suggested that the curvature is controlled by the shape of relaxation-time distributions, which is approximately the same for all the magnetite samples studied. In addition, the acquisition and decay curvature parameters mirror each other when plotted as a function of temperature, inferring that at any given temperature, the acquisition and decay processes are identical.

Five specially prepared elongated metal particle pigments have been analysed to determine the detailed switching behaviour and magnetic viscosity. The particles varied in length from about 130 nm down to 40 nm. Hysteresis loops and time dependence measurements were made which led to a calculation of the activation volume of reversal. The activation volumes reduce with the particle size and are comparable for the smallest pigments. Physical particle sizes were measured by TEM. The objective of the work is to find the limiting size of the current technology determined by superparamagnetic behaviour.

Magnetic activation volumes of obliquely evaporated Co–CoO tape were investigated. With introduction of oxygen, magnetic activation volume calculated from irreversible susceptibility and magnetic viscosity coefficient was saturated to almost 6.0×10−24 m3, which is due to the columnar structure caused from the oblique evaporation. Using this measurement, the carrier to noise ratio of Co–CoO tape can be estimated quantitatively.

PbFe12−xAlxO19 samples were obtained by the chemical coprecipitation method with compositions x=0.0, 3.0, 4.0, 6.0. As was expected, significant differences in magnetization reversal mechanisms were found at room temperature in these specimens. A magnetic viscosity study was carried out in the temperature range of 75–300 K in order to obtain information related to the mechanism of magnetization behavior. A logarithmic time dependence of the magnetization was observed during a period of 20–1200 s. The magnetic viscosity Sv and the activation volume Va increase as temperature is increased; the samples x=3.0 and 4.0 show the most rapid increase of the activation volume with temperature. Except for the samplesx=3.0 and 4.0, the experimental temperature dependencies of the coercive field are in agreement with a model due to Givord and co-workers in which the magnetization reversal occurs in a volume equal to the activation volume.

The interactions in ternary and quaternary Co-based alloy thin films for longitudinal recording media, with different thickness, are studied. The analysis is performed through the measurement of the initial magnetization and ordinary hysteresis curves. The interactions result stronger in quaternary than in ternary alloy films and when the film thickness is smaller. These findings are discussed in relationship with the evolution of the magnetization switching, characterized by a tendency towards a more coherent rotation of the magnetization in single-domain grains of thinnest and quaternary films, owing to the complex structure of these films. The impact of this evolution on the thermal stability of the magnetic properties is also discussed.

In this work we study the temperature dependence of coercivity and magnetic viscosity in mechanically alloyed magnets of composition (Nd1−xDyx)16Fe76B8 (0.1

Zero-field magnetic viscosity measurements at temperatures between 2 and 30 K were made on a sample of chemically disordered FePt nanoparticles prepared by solution phase chemical synthesis. The data have been used to calculate the apparent magnetic-moment-weighted energy barrier distribution for the FePt. This distribution is composed of a log–normal distribution plus a second distribution that is well described by an exponential decay of barrier frequency with increasing barrier height. The two distributions contribute approximately equally to the overall distribution.

Samples of Ba- and Sr-hexaferrite were prepared by mechanical alloying and subsequent heat treatment were found to consist of single domain particles of the single hexaferrite phase. The particles had a wide distribution of anisotropy fields. Study of irreversible magnetisation suggested, that the demagnetisation process is mainly controlled by the Wohlfarth rotation. It was deduced from the results of measurements of magnetic viscosity, that the activation volume was of same order of magnitude as the cube of the domain wall thickness.

A Stoner-Wohlfarth model has been used to simulate conventional magnetic viscosity experiments. The magnetic viscosity parameter Λ was found to vary depending on the method used for measurement of the irreversible magnetisation. The difference in Λ is found to be related to a parameter η which describes the dependence of reversible magnetisation on irreversible magnetisation. The correct value of Λ at any field has been related to the population of particles which reverse at that field and it is revealed that distributions of volume and orientation can obscure the interpretation of the measured Λ. Thus the measurement of Λ as an indicator of reversal mechanism is questioned.

Mechanically alloyed SmCo 5 materials with coercivities in the range of 50–75 kOe were studied in this work. Irreversible magnetisation processes were investigated by measuring remanences after initial magnetisation and after demagnetisation. A large deviation of the demagnetisation remanence from the Wohlfarth relationship indicated that interactions between grains play an important role in the irreversible magnetisation process. Viscosity tests showed nearly linear relationship between the magnetic field and the viscosity parameter for the initial magnetisation, while the viscosity was not strongly dependent on the field for the demagnetisation. High values of the viscosity parameter, Λ, between 120 to 220 Oe were measured at fields near coercivity.

In order to examine the long-term stability of novel NdDyFeCoMoAlB magnets with enhanced temperature stability, after-effect measurements have been carried out in an open circuit in the temperature range 20–230°C. In this temperature range the ln( t ) law for the irreversible polarization losses is confirmed and the after-effect constant S and the fluctuation field S v decrease monotonically with temperature for the sample annealed at an optimum. It can be proved that the open circuit measurements of S ′ and the irreversible susceptibility, χ ′ irr = χ ′ tot − χ ′ rev , should be corrected by the same the demagnetization coefficient N depending factor and thereafter that the S v values can be derived directly by S v = S ′ v = S ′ χ ′ irr . The determined room-temperature values of S v between 8 and 11 kA m −1 are related to the coercivity approximately within the limits of a Barbier plot (log( S v ) = a · log( H cJ ) with a ≈ 0.5−1) and do not diminish the advantages of the low-temperature coefficient of the coercivity of the NdDyFeCoMoAlB magnets. The experimentally determined ratio S v / T yields an activation volume V c for the magnetization reversal corresponding to a critical diameter d c ≈ 7–14 nm, which is 1.5–2.5 times the Bloch wall thickness δ.

Magnetic relaxation (magnetic viscosity) experiments were conducted in nanocrystalline single and two-phase NdFeB melt spun ribbons. On hysteresis loops, at applied demagnetizing fields at some degree lager than H c , an anomalous non-monotonic variation M ( t ) has been found for all investigated samples either with exchange coupled or decoupled grains. On recoil curves, the same non-monotonic variation of the magnetization has been found in the case of suppressed fields lower than H c .

In this work we examine the effect of magnetic viscosity on the determination of the switching field distribution (SFD) in hard magnetic materials. We find that measuring at a slower rate broadens the measured SFD and leads to larger values of the Neel fluctuation field. The effect of intergranular exchange coupling is also discussed.

Magnetization measurements of ∼150 A size Cr 2 O 3 particles prepared by chemical precipitation are reported. Zero-field-cooled (ZFC) susceptibility exhibits a peak characterizing a blocking behaviour at T B ≈40 K. Above the bifurcation point of ∼160 K the reversal magnetizations vary linearly with H , whereas below it both ZFC and field-cooled hysteresis loops exhibit large coercivities. Exchange fields of ∼2000 Oe are also observed at low temperatures. Magnetization relaxes according to the equation M ( t )= M ( t 0 )[1− S ( T )ln(( t + t 0 )/ τ 0 )]. Magnetic viscosity S ( T ) is found to be linear for T ⩽10 K.

The influence of texture on the time and field dependence of the magnetization, the magnetic viscosity, the irreversible susceptibility and the fluctuation field is calculated for two models of non-interacting uniaxial particles differing in the angular dependence of the switching field. The first model consists of single-domain particles reversing their magnetization by coherent rotation. In the second model the grains exhibit a 1/cos ϑ dependence of the switching field on the misalign angle. A detailed comparison of our results with the existing theory of the magnetic viscosity is given. For both cases it was shown, that texture alone cannot give a barrier distribution smooth enough to get the mostly measured ln t behaviour of the magnetization. The fluctuation field S v is found to be independent on the texture, in good agreement with the experimental situation, but in contrast to the theoretical considerations reported in the literature.

The fluctuation fields of magnetic viscosity and read and write characteristics are measured to investigate the origin of medium noise in obliquely evaporated cobalt films. Medium noise increases with increasing product of activation volume and saturation magnetization per unit volume. Therefore, medium noise is believed to depend on the size of the minimum unit of magnetic moment in reversal.

Careful measurements of the magnetic viscosity S = d M / d ln t of non-oriented nano-particles of Ba-ferrite (317 A as mean diameter) show a remarkable scaling plot vs. two variables: the usual T ln( t /τ 0 and the applied magnetic field H . This plot takes into account two distributions, the particle size ρ ( s ) and the switching field v ( H 0 ) distributions. This last plays a dominant role on the magnetic viscosity of Ba-ferrite particles at low temperature. Taking a Lorentzian distribution for v ( H 0 ), one derives from the measured magnetic viscosity a particles size distribution ρ ( s ) which is exactly the same as the distribution observed directly by transmission electron microscopy. The agreement, obtained without free fitting parameter, allows to reproduce all typical features of the S ( H , T ) showing that ρ ( s ) and v ( H 0 ) are the relevant distributions. This approach allows to avoid erroneous interpretations of S ( H, T ) at low temperatures. In particular bimodal distributions, sometimes derived from magnetic viscosity experiments might, in some cases, be attributed to a convolution of ρ ( s ) and v ( H 0 ).

An initially saturated array of uniaxial particles with log-normal distribution (parameter σ) of activation volumes V relaxes in reversing field h at temperature T. We find that the time tc at which its net magnetization vanishes is κ(〈V〉, h)·tc(h, σ) = In 2·exp[γ(σ)Q(h)/T] where κ(〈V〉) is decay rate associated with the most probable volume and Q(h) is barrier height. The function γ(α)>0 if the particle magnetic moment M is proportional to V and γ(σ)

The magnetic viscosity of unoriented and oriented barium ferrite media has been investigated in order to understand the mechanism of magnetic reversal. The activation volume of magnetic reversal for the unoriented medium gradually increases with increasing test field. In contrast, the activation volumes for the oriented media depend on their degree of orientation. In the media with relatively low orientation, the activation volumes increase sharply in narrow field regions. In the higly oriented media, however, the amount of demagnetization varies nonlinearly against ln( t ) and the activation volume cannot be obtained as a function of field. In these cases, Richter-type demagnetization curves are obtained. The influence of magnetic viscosity on magnetostatic properties is also described.

Thermally-activated time-decay studies have been made on a variety of BaFe and metal particle flexible media. Measurements have been made of magnetic viscosity, irreversible susceptibility and activation volumes. In oriented BaFe and MP systems the measurements have been made as a function of temperature with a view to assessing archivability.

The observation of the quantum tunneling of magnetization has been accomplished in different multilayer systems of transition and rare earth metals. We have measured the time dependence of the thermoremanence magnetization up to temperaturesof 1.7 K. The tendency of the magnetic viscosity to have finite intercept at T = 0 and/or the plateau in the S(T) values are the experimental manifestations of this new and fascinating effect.

Time dependence of the magnetisation, or ‘magnetic viscosity’ is a well established phenomenon in magnetic recording media. On a practical basis magnetic viscosity is related to the phenomenon of print-through and the frequency dependence of the coercivity. The latter factor has a bearing on the use of the coercivity in materials characterisation and also has implications for the ultimate minimum size of switching volume usable in recording media. The physical origin of magnetic viscosity is reviewed, along with the relationships to the above factors. Also, recent work on the determination of switching volumes is described.

Results are presented on magnetic viscosity measurements performed at room temperature on Ba-ferrite pressed powder samples of different particle sizes. Maximum values of viscosity coefficients ( S ) occur around coercive fields, except for a sample with an intrinsic coercive force of 4639 Oe, in which the maximum is at a much higher field (5706 Oe). Activation volumes are of the order of 10 −17 cm 3 and decrease along with particle size (except, again, for the high coercivity sample). Experimental values of coercive fields and viscosity parameters ( kT / q ), used in connection with Gaunt's theory, suggest that the viscosity mechanism in Ba-ferrite, for particle sizes from 7 to 0.7 > m is the strong pinning of domain walls.

Nd(Dy)FeB/W/Si(1 1 1) films were prepared by DC magnetron sputtering. Magnetization reversal process of the Nd(Dy)FeB films was found to be dominated by strong domain-wall pinning as elucidated using the Gaunt model. The maximum pinning energy (fb) of the film is equal to 2.57 × 10−11 erg. Thermal activation volume is 1.41 × 10−18 cm3 measured by magnetic viscosity. Random-inhomogeneous pinning sites is explained more explicitly by HRTEM microstructure observation.

Mechanically milled Pr4.25Tb1Fe71Co2.5Cr3B18 has been annealed to produce a material comprising a (Pr,Tb)2(Fe,Co)14B hard phase intimately mixed with (Fe,Cr)2B and α-Fe soft phases. Susceptibility and magnetic viscosity measurements have been used to characterise the reversal process in the temperature range 20–300 K.

The time dependence of materials for magnetic recording media, both particles and thin films, is studied. The stability, as deduced from the magnetization decay, magnetic viscosity and fluctuation field, is greater in undoped materials with good morphological and structural order. The activation volume is smaller than the physical size in all the particulate materials, and related to the magnetization switching: it shows relative decrease when the reversal does not take place by coherent rotation, as it occurs in doped particles, or when the particles are composed of segregated sub-units.

Theoretical relationships between the coercive force H c and the magnetic viscosity parameter S v have been obtained which give a very good explanation to the well-known phenomenological Barbier plot. For the strong pinning model, the formula obtained is l g S v = l g H c − l g {( 75 4 )[( 4fb 75 kT ) 2 3 − 1]} , where f is maximum pinning force and b is the range of interaction between domain wall and pin. For the weak pinning model, the obtained theoretical formula is: l g S v = l g H c − l g {25[( 3 1rb 2 25kT ) − 1]} , where r is domain wall energy. For the unpinning (nucleation) process, the obtained formula is: l g S v = l g H c − l g {( 75 2 )[( 4fb 75kT ) − 1] 2 3 } . For uniaxial single-domain particles, the obt ained relationship between H c and S v is: l g S v = l g H c − l g [( 2KV 1 2 p kT )(V 1 2 − V 1 2 p )] , where V p is the critical volume for superparamagnetic behaviour and V is the particle volume. At a given temperature, all the relationships obtained above can be written as: l g S v = const . + l g H c .

Time dependence measurements have been made on two Tb/Fe multilayer films possessing square and rounded hysteresis loops. Both films exhibit a non-linear variation of M with ln t . Experimental curves of d M /d t against reduced magnetisation have been compared with curves derived from a 2D theoretical model. These curves indicate that a two coercivity model may be applied to reversal in these films, and the nature of domain growth during reversal. MFM images of domains have been obtained and show that domain size correlates with the nature of reversal.

The magnetic viscosity of the spinel system Li 0.5 + 0.5 t Fe 2.5 − 1.5 t Ti t O 4 ( t = 1.25) has been studied as function of temperature, applied field and waiting time before switching off the field, on samples with different local order. The magnetic viscosity depends strongly on the applied field but does not appear to be influenced by the waiting time. The temperature dependence of the viscosity has an unusual behavior and the properties are explained from a thermally activated model based on the relaxation time of the transverse spin component.

General expressions for the zero-field-cooled magnetization and the initial susceptibility (χ) of magnetic particle assemblies are set up. These equations are evaluated analytically by specifying the distribution of geometric and magnetic properties of the particles. We derive relations between χ and the magnetic viscosity. The influence of interaction effects is examined.

Exact analytical expression for the time-dependent magnetization of the system with known energy barrier distribution is obtained. The relation between the obtained result and usual definition of the magnetic viscosity is discussed. Corrections to the ‘critical volume approach’ are shown to be of order σ ΔE / T , where σ ΔE is the width of the energy barrier distribution density.

We propose a model of domain wall dynamics and Barkhausen effect (BE) under the influence of magnetic viscosity. The theory is based on a Langevin description of the stochastic motion of a domain wall in a perturbed medium. A set of three coupled, stochastic differential equations has been derived and studied both analytically and numerically. A first comparison between the theory and experimental data was performed by simulating literature data on the temperature dependence of the BE in 12% Al-Fe alloys.

The magnetic viscosity of FePt/C granular thin films was studied in the temperature range from 2 to 300 K in order to examine the thermal stability of the nanoparticles. The magnetic viscosity coefficient ( S max ) was found to decrease with temperature because of decreased thermal activation. At low temperatures, S max showed an almost linear dependence on temperature. However, S max does not extrapolate to zero but seems to have a finite value at cryogenic temperatures.

The temperature dependence of the magnetic viscosity parameter Λ, also known as Sv, has been examined using two theories based on thermal energy barrier activation and thermally induced fluctuation fields. For aligned, non-interacting Stoner-Wohlfarth particle assemblies it is shown that both theories predict the same temperature dependence for Λ but that Λ ∞ T or T1/2 depending on how the field at which Λ is measured is varied with temperature. It is also shown that for other mechanisms other temperature variations are possible.

We have measured the magnetic viscosity in materials which undertake magnetisation reversal by two distinct processes. The materials examined were Pt/Co multilayer systems which have potential as magneto-optic recording materials. In these systems magnetisation reversal proceeds first by the nucleation of a reverse domain followed by the propagation of the domain wall. Thus, in materials where the domain wall pinning is strong two distinct regions of reversal occur. In consequence, we observe two different forms of variation of magnetisation with time and additionally different values for derived parameters such as the fluctuation field.

The magnetic viscosity parameter, S, within the recoil curves and on the major hysteresis loop of NiO/Ni nanocomposites were measured. On the major hysteresis loop S is negative and constant in time, while within the recoil curves S is initially positive before going through zero and becoming negative. This is modelled using a Markov chain which describes the occupation of the branches of a set of hysterons.

Magnetization reversal on recoil curves of a sintered SmCo 5 magnet is compared with that for a nanocrystalline SmFeCo alloy prepared by mechanical alloying. Recoil curves were found to be hysteretic and time-dependent in both cases, but magnetic viscosity was observed only for the nanocrystalline SmFeCo alloy. Magnetic interactions were studied via Henkel plots for different initial demagnetized states.

The magnetic relaxation in Ni wires has been investigated using a SQUID magnetometer. The magnetization M exhibited logarithmic dependence on time. The distribution of energy barriers was estimated from the temperature dependence of magnetic viscosity S = d M /d(log t ). Thermal excitation explains the field dependence of S - T curves except below 20 K. Below 20 K, macroscopic quantum tunneling and/or the interaction between Ni wires must be considered.

Magnetic viscosity has been measured in hard PrNdFeB samples prepared by crystallizing, at different heating rates, melt spun amorphous precursors. The temperature dependence of the coercive force of these samples was analyzed in terms of the temperature dependence of the activation volume.

We report here on low temperature magnetic relaxation in the erbium orthoferrite ErFeO 3 . The variation of magnetic viscosity, S ≡ ∂M / ∂ / ∂ ln t , with temperature shows three different regimes below 40 K. The most remarkable is that at T ≤ 3 K where S(T) remains constant suggesting the occurrence of macroscopic quantum tunneling of the magnetization.

We have made magnetic viscosity measurements S ( H , T ) in Ba-ferrite small particles. Both volume π ( V ) and switching field ν ( H 0 ) distributions were taken into account to understand the behaviour observed at low temperatures, S ( H , T ) α (T) 1 2 . We have found a scaling function for the relaxation measurements on field and temperature.

We present a computer simulation study of magnetic relaxation for a system of single-domain particles. We focus on the dependence of the magnetic viscosity coefficient with the shape of the distribution function of activation energies, and compare our computational results with known experimental results for a ferrofluid system.

It is shown that in Fe nanoparticles dispersed in SiO2 prepared by high energy ball milling the coefficient of magnetic viscosity depends weakly on the magnetization level. The dependence of this coefficient on the milling parameters and composition follows the behavior of the coercive force.

At room temperature the constant C in Barbier's relation lg [ S v | H = H c ]=- C + lg H c , S v is the magnetic viscosity parameter and H c the coercivity, is approximately the same for a wide range of systems. We take into account the frequency dependence of H c and derive an expression for C which is both system and measurement dependent. At low measurement frequencies and high temperatures, however, the system dependence of C is suppressed. A similar discussion is carried out for the activation volume v | H c .

A mathematical model of non-equilibrium thermomechanics of magnetic fluids is given as a logical generalization of the well-known Neuringer-Rosensweig model for equilibrium magnetization. Several phenomena are explained and predicted based on the proposed model: the effect of magnetic viscosity, the compensation of viscous stress in a shear flow, the presence of transverse stress and the magnetodynamic effects.