The primary goal of this paper is to evaluate the trans- verse complex magnetic susceptibility x ' ( v ) of a system of noninteracting single-domain **ferromagnetic** **particles** sub- jected to a constant magnetic field. We obtain ~ with the aid of linear-response theory ! the exact solutions for x ' ( v ) in terms of matrix continued fractions. In order to obtain these results we shall use the approach of Coffey, Kalmykov, and Waldron 12 for the solution of the infinite hierarchy of differential-recurrence relations which has already allowed us to obtain the exact solution for the longitudinal relaxation. 16 This approach is based on matrix continued fractions and essentially constitutes a further development of Risken’s method. 10 It has also been used in the theory of dielectric and Kerr effect relaxation. 24,25

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共 Received 26 March 2008; revised manuscript received 27 November 2008; published 2 February 2009 兲 The reversal time of the magnetization of single-domain **ferromagnetic** **particles** is estimated for mixed uniaxial and cubic anisotropy energies possessing nonparaboloidal saddles and well bottoms or either. The calculation generalizes the existing adaptation of the Kramers escape rate theory to fine **ferromagnetic** **particles** with nonaxially symmetric magnetocrystalline-Zeeman energies, originally based on the paraboloidal approxi- mation for the energy near its stationary points, yielding in addition a simple universal Kramers turnover formula 共 based on the Mel’nikov-Meshkov depopulation factor 兲 for the reversal time valid for all values of the damping. The asymptotic solution is compared with the appropriate numerically exact solution of the corre- sponding Fokker-Planck equation for the probability density function of magnetization orientations. The pre- dictions of the generalized nonparaboloidal stationary point turnover formula agree with the numerical solution for a wide range of damping and other parameters characterizing the mixed anisotropy.

It is known that micron-sized non-**ferromagnetic** **particles** dispersed in a ﬂuid medium generally possess an eﬃciency of magnetic alignment due to its diamagnetic or paramagnetic anisotropy . 1,2) The magnetically stable axis of a particle may align nearly parallel to the ﬁeld direction, when the ﬁeld- induced anisotropy energy exceed the energy of rotational Brownian motion supplied from thermal motions of the ﬂuid molecules. The process of the alignment depend on three parameters, namely the mol number of the particle N, magnetic anisotropy of the material per mol and temperature T . The eﬀect of these parameters has not been studied systematically as yet, in spite that the controlling of the alignment process by means of these parameters is an important basis to realize alignment at low ﬁeld intensity. The alignment at practical low ﬁeld-intensity may produce new types of applications based on the above-mentioned alignment. Up to now, alignment has been studied mainly on biological 3) and organic materials 4) in a strong magnetic ﬁeld above several Tesla.

Ellipsoids have the property that a uniform magnetization is an exact equilibrium of the micromagnetic equations. A large theoretical literature exists on rigorous results for the linear stability of this uniform state in prolate or oblate ellipsoids, and on the diﬀerent instability channels, see e.g. [1, 2, 8, 14, 17]. Switching is often associated with loss of linear stability. Even for ellipsoids, attention to the predictions of the SW model in cases without rotational symmetry is much more recent [7, 25], and a complete linear stability analysis is still missing. The question of the validity of the ellipsoidal approximation for non–ellipsoidal **particles** has attracted some attention [19, 23], but this issue is far from being fully understood. In Section 5 we present numerical results for **particles** of cubic or almost-cubic shape, within the single-domain regime, which illustrate the leading corrections to the SW model with increasing particle size. For small sizes our critical ﬁelds reproduce the SW results. Larger **particles** have shape-dependent critical ﬁelds with a non-monotone dependence on size and with a complex angular dependence, which cannot be reproduced assimilating the particle to an ellipsoid.

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**Ferromagnetic** **particles** are a very promising tool in analytics, since they can be handled as a suspension by pipetting but can also be manipulated by magnetic force so that they temporarily become a solid phase. Depending on their surface coating, these **particles** can be used for i) the extraction of analytes, ii) the removal of disturbing substances from a sample or iii) to deliver a reagent. These **particles** are widely used in immunoanalysers and play an important role in (automatic) nucleic acid extraction [21]. Since the handling of these **particles** requires no centrifugation, vacuum or pressure, they could also be a valuable tool for the convenient automation of sample preparation prior to LC-MS/MS analysis [22].

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The magnetic relaxation of single-domain **ferromagnetic** **particles** with cubic magnetic anisotropy is treated by averaging the Gilbert-Langevin equation for an individual particle, so that the system of linear differential- recurrence relations for the appropriate equilibrium correlation functions is derived without recourse to the Fokker-Planck equation. The solution of this system ~ in terms of matrix continued fractions ! is determined and the longitudinal relaxation time and spectrum of the complex magnetic susceptibility are evaluated. It is shown that in contrast to **particles** with uniaxial anisotropy, there is an inherent geometric dependence of the complex susceptibility and the relaxation time on the damping parameter arising from coupling of longitudinal and transverse relaxation modes. @ S0163-1829 ~ 98 ! 06829-5 #

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were restricted by the Bitter magnet aperture. The mag- net with the 43 mm aperture was used to create a mag- netic field. The width-to-length ratio of 5:3 of a sample measuring approximately 35 by 21 mm, was assumed. The structure of the samples produced is presented in the cross-section in Figure 1 [5]. Prior to the sample produc- tion, the composites containing **ferromagnetic** **particles** of chemically pure iron, size 0.15-0.25 mm, as well as the **particles** of colloidal graphite of the size not exceeding 0.5 µm, were produced first. The pores in the samples were produced through resolving and rinsing sodium chloride grains of the size 0.15-0.25 mm. The **particles** of iron and sodium chloride of desirable sizes were obtained as a result of grinding and sieving.

The damping dependence of the thermally activated reversal time of the magnetization of noninteracting uniaxial single-domain **ferromagnetic** **particles** is determined using Langevin dynamics simulations and the analytic Néel-Brown theory with the latter given both in the form of the exact matrix-continued fraction solution of the governing Fokker-Planck equation and its accompanying asymptotes for the escape rate. The reversal time from Langevin dynamics simulations is extremely sensitive to the initial and switching conditions used. Thus if the latter are chosen inappropriately the simulation result may markedly disagree with the analytic one particularly for low damping, where the precessional effects dominate, so that complete agreement can only be obtained by correctly choosing these conditions.

properties of oxidized transition metal nanoparti- cles and ﬁlms have been extensively studied [4, 11–13]. In an MR head the output response is not linear. Therefore an exchange bias is required for linearization, which can be achieved by coupling FM to an AFM [14]. Research on exchange biasing effect in **ferromagnetic** wires is therefore of interest because of its potential application in the information storage. Earlier works on mag- netic wires were mostly concentrated on size dependence and orientation dependence on ﬁeld [2,15,16]. Fraune et al. [17] have investigated the size dependence of exchange bias in NiO/Ni nanostructures. They observed that for NiO/Ni wires narrower than 3 mm, the exchange bias ﬁeld signiﬁcantly depends on the wire width. In another experiment, Otani et al. [18] have investigated the magnetization reversal processes of the Fe 19 Ni 81 /

MacDonald et al. compared the FMwand to monopolar electrocautery and a pulsed radiofrequency device (PlasmaBlade, PEAK Surgical, Inc., Palo Alto, CA, USA) on rabbit liver. The study showed that both newer de- vices (FMwand, Plasma Device) had significant superior surgical tissue handling characteristics [6]. Bowers et al. had similar results with experiments on rabbit muscle comparing the FMwand with monopolar electrocautery showing a significantly less tissue drag with FMwand [7]. A recent controlled and systematic evaluation was done to show that the **ferromagnetic** device does not cause electromagnetic interference with cardiovascular implantable electronic devices (CIEDs) [8].

use the LLG equation to study the **ferromagnetic** resonance. The LLG equation is written in Eq. (1), where m is the unit vector of the macro magnetic moment, thus m 2 =1. In studying **ferromagnetic** resonance we assume that before applying alternating microwave field m 2 =1, after applying alternating microwave field m 2 ≠1.

DOI: 10.4236/oalib.1104461 8 Open Access Library Journal shields made of permalloy foil has been detected. Magnetic coils with partially shielding windings and placed in homogeneous magnetic fields were used. Dur- ing the first experiment, the coil moved relative to the Earth’s magnetic field, and during the second one, the magnetic field lines of the rotating disk magnet moved relative to the coil. The lack of voltage on the coils terminals indicates with a good accuracy the presence of motional EMF in the shielded parts of windings equal in magnitude to those ones in parts without a shield. This reveals the penetrating ability of the magnetic field through the **ferromagnetic** shield and shows the physical nature of the superposition principle. As a result, the universal method for calculating the induced EMF that occurs in the conductive body moving relative to magnetic field was represented. It withdraw the para- doxes in calculating induced EMF on the classical law [14] and shows the condi- tionality of dividing induced EMF into the usual and “motional” part. For the description of dynamic magnetic fields, it is necessary to introduce the kinematic parameters of the movement of their field lines, such as speed and acceleration. These parameters can be determined experimentally by introducing two closely spaced conductive probes into the region of the magnetic field under study. The tips of the probes should be placed with a slight shift in a direction perpendicu- lar to the magnetic power lines. The difference in motional EMF in the probes can be registered using a voltmeter with high input impedance. The dynamic magnetic field of permanent magnets rotating around their own magnetization axes was registered in [15] [16]. To do this, the authors used cylindrical capaci- tors arranged symmetrically to the axes. The potential difference that appears on the plates is explained by the action of uncompensated Lorentz forces in the lead wires. The advantage of this method for detecting a rotating magnetic field in comparison with the introduction of probes is the availability of essentially larg- er capacitance, which reduces the requirement for input impedance of the volt- meter. However, for characteristic of a moving magnetic field with complex con- figuration in a point, thin probes are required.

Whereas the framework phenomenologically quantifies certain accommodation processes, the exten- sion of the theory to incorporate energy mechanisms associated with magnetic accommodation has not been completed and is under present investigation. (v) Temperature and Stress-Dependencies: The kernel (29) incorporates certain temperature-dependencies as well as the transition between **ferromagnetic** and paramagnetic phases; however, its accuracy should be considered limited when quantifying changes over a broad temperature range. Certain extensions to the framework to provide more comprehensive characterization of temperature effects has been developed in [35] in the context of relaxor ferroelectric materials. The framework presented here focuses on constant stress condi- tions. Initial extensions of the theory to incorporate stress-dependencies in M due to magnetoelastic coupling are provide in [73]. (vi) Eddy Currents: The present framework does not incorporate eddy currents and hence should be employed in low frequency regimes or transducers constructed for mini- mal eddy losses (e.g., laminates). (vii) Anisotropy: The model is presently formulated for isotropic or weakly anisotropic materials and the extension of the framework to incorporate the energy associated with hexagonal and cubic crystalline anistropies is under investigation.

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Abstract—This article describes a method of guiding a moving **ferromagnetic** sphere. By using a magnetic field, it is possible to confine a moving object such as a steel sphere to motion along a curve. We have designed and built a device that uses the magnetic field in the gap of a steel tube to trap and guide a steel sphere along a circular path solely by a magnetic restoring force. A simple relationship between tangential velocity and magnetic field strength in the gap is developed. Excellent correlation between analytic, simulated, and measured results are shown.

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Hybrid DFT calculations, with two trapped electrons and the spins in either vacancy in parallel or antiparallel configurations, showed an energy difference for these two states of just 1 meV, with the antiparallel configuration lower in energy. Thus there is very weak antiferromagnetic coupling between electrons with one electron per defect with a defect separation of over 11 ˚ A. This calculation illustrates the problem of explaining how **ferromagnetic** exchange between paramagnetic defects can arise over this range. However, similar calculations with three trapped electrons, with a total spin of zero or one-half, resulted in a total energy difference of 220 meV, even though the vacancy centers were separated by over 11 ˚ A. The spin one-half state was lower in energy. This energy difference is attributed to the difference in Coulomb repulsion energies for the trapped electrons in either state. In the spin-zero state the spin-up and down populations on either site were both 0.75, while in the spin one-half state the spin-up and down populations were 1.00 and 0.50 for either site. According to the Hubbard model in Eq. (1), the Coulomb energies of the two states are, respectively, 9U /8 and U . The total energy difference of 220 meV therefore corresponds to a U value of 1.7 eV for the on-site interaction of trapped electrons, which compares with the value of U = 1.2 eV from the differences in transition levels (Table III).

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The lower-temperature transition, at T = T c< , separates the **ferromagnetic** Coulomb phase from a conventional ferro- magnet. Because the magnetization is nonzero on both sides, the spin-inversion symmetry of the Hamiltonian is immaterial, and the transition is in the same universality class as the sat- uration transition in an applied field. 14,22 This is a Kasteleyn transition, which exhibits anisotropic scaling in the directions parallel and perpendicular to the magnetization, with relative scaling exponent z = 2. The transition is consequently at its upper critical dimension, and so shows mean-field exponents with logarithmic corrections. 19,22

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The measurements of the magnetoresistance as function of the external field were carried out with a low-frequency in-plane current density of 2.10 5 A/m 2 . The curves obtained, which are presented in Fig. 1, show a small effect of order 0.2%. As expected, because the atomic charge distributions of both Co and Ni are oblate, the resistance is higher when the current is parallel to the magnetization and lower in the transverse geometry. This reflects the effect of spin-orbit coupling and is consistent with measurements carried out on bulk **ferromagnetic** samples. 5 The minima obtained in the longitudinal geometry and the maxima in the transverse ge- ometry correspond to the maximum disorder of the distribu- 53

We performed studies of the temperature dependence of the magnetic susceptibility of CNT-containing NCM specimens synthesized using different transition metal (Fe, Co, Ni) oxides as catalysts. Our results demonstrated that magnetometry is an effective tool to control the content of **ferromagnetic** constituents. This method is capable to detect even low contents of metal catalyst. The proposed thermochemical treatment protocols result in effective cleaning of the source NCM from the refuses of ferro- magnetic phases. The efficiency of cleaning is determined by the sequence of thermochemical treatment steps as well as the type of the catalyst.

Figure 1.6. Schem atic bandstructure of different types o f half-m etallic ferromagnets. For T yp e lA , only spin-down electron are present at the Fermi level, the density of states for spin-up electron is zero. C r02 is an exam ple of this type half-m etal. M agnetite is an exam ple of a T ype IIB half-metallic **ferromagnetic**, where the carriers at the Fermi level are in a band sufficiently narrow for them to be localized. LSMO is o f type IIIA, with localized spin-up carriers and delocalized spin-down carriers. Classification after C oey et al. [31] grain boundaries or crystallite interfaces. Compared w ith single crystals and epitaxial films the polycrystalline sam ples have a higher resistivity, presumably caused by the presence of grain boundaries. Tw o groups [35] [36] devised an elegant experim ent to separate the intrinsic CMR effect from the extrinsic low field effect. W hereas the CM R effect decreases w ith lower tem peratures, the low field MR becomes larger for decreasing tem peratures.

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The control of perpendicular magnetocrystalline aniso- tropy (PMCA) at **ferromagnetic** transition – metal-insulator interfaces is of paramount importance in the manufacture of spintronic devices, such as perpendicular magnetic tunnel junctions [1 – 3] and tunneling anisotropic magnetoresistive systems [4]. Large PMCA can be achieved by fabricating heterostructures including heavy nonmagnetic elements with large spin-orbit coupling (SOC) [5], such as Co=Pt or Co=Au [6]. It has been shown that this out-of-plane