Theory of first order magnetization processes: Uniaxial anisotropy

The first order magnetization process (FOMP) is associated with the irreversible rotation of the magnetization vector M_s between inequivalent states. The critical field H_cr and the amplitude ΔM of the jump observed in the direction parallel to the applied magnetic field are functions of the anisotropy constants of the crystal. A complete phenomenological analysis is given for the case of uniaxial anisotropy in terms of the first three anisotropy constants K₁, K₂ and K₃, as well as in terms of the anisotropy coefficients χ_2,0, χ_4,0, χ_6,0. Computer plots of the critical parameters and the magnetic phase diagram are given together with an analytical treatment of the problem. The results give a unified view of the FOMP in uniaxial crystals and provide a method for the accurate determination of the anisotropy constants at the temperatures where the phenomenon is present.     

Anisotropic contribution of magnetostriction to the elastic compliance constants in hexagonal materials: The Δs-effect

In this paper, we consider the single crystal analogue of the ΔE-effect in hexagonal materials with uniaxial magnetic anisotropy. We define Δs_ijld as the fractional change in the elastic compliance tensor s_ijkl in the demagnetized state relative to its value in the saturated state. The Δs-effect depends in general on the direction of the applied stress and the resulting magnetostrictive strain. We can show, however, that Δs_ijkl is always nonnegative when i=k and j=l. We then consider the measurements of the elastic constants in magnetic materials which have large magnetocrystalline anisotropy. The stresses applied in these measurements are not sufficient to rotate the magnetization away from the magnetically preferred direction, and hence cause no magnetostriction, and no Δs-effect. Therefore, it is not necessary to apply a saturating magnetic field along the easy axis in order to measure the true elastic constants in these materials.     

High-frequency properties of discontinuous FeCoSi/native-oxide multilayer films

Discontinuous [FeCoSi (d)/native-oxide]₅₀ multilayer films were fabricated by DC magnetron sputtering without any post-deposition treatment. The films exhibit good soft magnetic properties with initial permeability μ_i larger than 100, the saturation magnetization 4πM_s and the in-plane uniaxial anisotropy field H_k increase as the magnetic FeCoSi layer thickness d is increased from 5.5 to 20.5 Å. As a consequence, the ferromagnetic resonance frequencies f_r of the films increase from 2.0 to 3.9 GHz. The combination of high f_r and large μ_i makes these films potential candidates for magnetic devices applied in the high-frequency range. The origin of the excellent high-frequency properties in discontinuous FeCoSi/native-oxide multilayer films is discussed.     

Effect of thermal process on magnetic anisotropy in FeCoB soft underlayer

Relationship between magnetic anisotropy field H_k and thermal processes during the preparation has been studied for FeCoB thin films. The FeCoB films deposited on the glass substrates by facing targets sputtering successfully showed strong magnetic anisotropy when the substrate was heated at the substrate temperature T_s above 100 °C. Additionally, the lattice spacing of FeCo(1 1 0) in the perpendicular direction was found to decrease depending on the substrate temperature T_s. Among various temperature histories, the heating processes with a phase of increasing T_s revealed the further improvement of H_k. Meanwhile, high H_k in the films disappears after the post-deposition annealing at the temperature above 400 °C.     

Current induced domain wall motion in nanostripes with perpendicular magnetic anisotropy

We report micromagnetic modeling results of current induced domain wall (DW) motion in magnetic devices with perpendicular magnetic anisotropy by solving the Landau-Lifschitz-Gilbert equation including adiabatic and non-adiabatic terms. A nanostripe model system with dimensions of 500 nm (L)×25 nm (W)×5 nm (H) was selected for calculating the DW motion and its width, as a function of various parameters such as non-adiabatic contribution, anisotropy constant (K_u), saturation magnetization (M_s), and temperature (T). The DW velocity was found to increase when the values of K_u and T were increased and the M_s value decreased. In addition, a reduction of the domain wall width could be achieved by increasing K_u and lowering M_s values regardless of the non-adiabatic constant value.     

Improvement of magnetic properties and read/write characteristics in SmCo5 perpendicular thin films

An SmCo₅ alloy is a promising candidate for ultra-high density magnetic recording media because of its strong uniaxial magnetocrystalline anisotropy, whose constant, K_u, is more than 1.1×10⁸ erg/cm³. Recently, we successfully obtained high perpendicular magnetic anisotropy for a sputter-deposited SmCo₅ thin film by introducing a Cu/Ti dual underlayer. However, it is necessary to improve magnetic properties and read/write (R/W) characteristics for applying SmCo₅ thin films to perpendicular magnetic recording media. In this study, we focused on reduction of magnetic domain size and change of a magnetization reversal process of SmCo₅ perpendicular magnetic thin films by introducing carbon (C) atoms into the constituent Cu underlayer. The magnetic domain size became small and the ratio of coercivity (H_c) against magnetic anisotropy (H_k) which is an index of the magnetization reversal process was increased by adding C atoms. We also evaluated the R/W characteristics of SmCo₅ double-layered media including C atoms. The medium noise was decreased and signal-to-noise ratio increased by introducing the C. The addition of C into the Cu underlayer is effective for changing the magnetization reversal process, reducing medium noise and increasing SNR.     

The tunable magnetic properties and microstructures of Co–Ni double-substituted M-type Casrla hexaferrites

M-type hexaferrites with Co²⁺ and Ni²⁺ions substituting for Fe³⁺ ions (Ca_0.30Sr_0.35La_0.35Fe_12.0−x(Co_0.5Ni_0.5)_xO₁₉, 0.0 ≤ x ≤ 1.0) were prepared by the traditional solid state method. X-ray diffractometer (XRD), field emission scanning electron microscopy (FE-SEM), physical property measurement system-vibrating sample magnetometer (PPMS-VSM) have been employed to study the microstructures and magnetic properties of hexaferrites. XRD patterns showed that the single magnetoplumbite phase is obtained if Co–Ni content (x) ≤ 0.4 and impurity phases are observed in the structure when Co–Ni content (x) ≥ 0.4. FE-SEM micrographs showed that the hexaferrites with hexagonal platelet-like grains is obtained. The saturation magnetization (M_s), remanent magnetization (M_r), M_r/M_s ratio, magneton number (n_B), coercivity (H_c), magnetic anisotropy field (H_a) and first anisotropy constant (K₁) decrease with increasing Co–Ni content (x) from 0.0 to 1.0. And our reported results with tunable H_c and M_r can be used for recording applications.     

(Ni, Zn, Sn) Ru and (Ni, Sn) Sn substituted barium ferrite prepared by mechanical alloying

NiRu, ZnRu, SnRu and SnSn mixtures considerably improved the saturation magnetization, M_s with low substitution values; diminishing quickly at the same times the coercivity, H _ci to suitable values for high-density magnetic recording applications. On the other hand, the NiSn mixture also decreased the coercivity rapidly however without enhancing the saturation magnetization. The shown differences on magnetic properties were mainly due both to magnetic nature of divalent ion and to secondary phase apparitions. The mixtures with Sn^2?+? as partner ion diminished markedly to T _c. The tetravalent Ru^4?+? ion has a special effect on magnetic properties of hexagonal ferrites (increases M_s and diminishes fast H _ci with low substitutions).     

Thermal stability and switching field of hard/soft-stacked perpendicular media

The time dependence of remanence coercivity and thermal stability were investigated for hard/soft-stacked media consisting of a magnetically hard granular layer underneath a very thin soft layer with a large saturation magnetization, M_s. The values of remanence coercivity at measurement times t′=10³ and 10⁻⁵ s (pulse field) were measured, and defined as H_r and H_r^P. The remanence coercivity on the recording time scale, H_r (1 ns), and the energy barrier, ΔE/kT, were evaluated by fitting H_r and H_r^P to Sharrock's equation taking into account the power law variation of the energy barrier, n. The value of H_r (1 ns) for a (Co–Pt)–SiO₂ (9 nm)/Co–SiO₂ (2 nm) stacked medium with an interfacial coupling control layer was about 9 kOe, which was less than half of that of a (Co–Pt)–SiO₂ (9 nm) conventional medium (=21.3 kOe). The value of ΔE/kT for the stacked medium was about 111 (n=0.7), and was not significantly different from the conventional medium. Moreover, no significant difference in the rate of decrease of H_r with increasing temperature was observed between media with and without interlayers. These results indicate that the use of a thin soft layer with high M_s was effective at significantly reducing H_r with no notable change in thermal stability.     

The permanent magnet systems generating strong stray fields with large localization region

Three systems of permanent magnets, which produce strong magnetic stray fields (SFs) with H>B_r=4πM_r were studied in this work. Remarkable feature of the developed systems is localization of the strong fields in large region with linear dimension Δr comparable to characteristic magnet dimension a. The first system composed of uniformly magnetized magnets generates sufficiently homogeneous strong SFs, which amounts up to 1.5 of magnets induction B_r. The second system with nonuniform magnetization is represented by cylindrical and hemispheric magnets their magnetization vector directed at every point along the radius. Such distribution of magnetization is assumed to be the consequence of magnet radial crystal texture resulting in a high uniaxial anisotropy field H_K. It is shown that maximal SFs can exist on the flat surface of cylindrical magnet at the distance r from its axis and their limiting value equals to 4πM_r ln(2a/r). Here, the localization region of the fields is comparable to diameter of cylindrical magnet Δr≈2R. As for the hemisphere its SFs are less than corresponding SFs for the cylinder. The third so-called quasi-nonuniform system consists of uniformly magnetized cylindrical sectors their magnetization vector is directed along the sector bisectrix. The strong SFs and their localization region are calculated in details for this case. The passage to radial magnetized cylinder is considered.     

Magnetic anisotropy of single-domain particles

The competition between uniaxial and cubic magnetic anisotropies of single-domain particles is analyzed theoretically. As long as K _1c /K _1u < 5 (K _1c and K _1u are the first constants of the crystallographic and uniaxial anisotropies), the value of K _1u noticeably affects coercive force H _c and relative residual magnetization j _r of particle ensembles. If the uniaxial anisotropy direction coincides with crystallographic axis 〈111〉 or 〈100〉, the dependences of H _c and j _r on ratio K _1c /K _1u have a minimum. The competition between the induced uniaxial anisotropy and cubic anisotropy was detected experimentally when the effect of temperature T on the H _c (T) and j _r (T) dependences for single-domain spherical particles of magnetic 3d alloys and γ-Fe₂O₃ oxide was investigated. For all single-domain particles studied here, the effect of crystallographic anisotropy on H _c and j _r is manifested at low temperatures, while uniaxial anisotropy plays a decisive role in the temperature range T > 250 K. The effect of second constant K ₂ on H _c and j _r of ensembles of single-domain particles with uniaxial and cubic anisotropies is investigated theoretically. It is shown that the value of K ₂ may substantially change the value of H _c for a particle ensemble, preserving the value of j _r unchanged.     

On the relation between the effective ferromagnetic resonance linewidth Δfeff and damping parameter αeff in ferromagnetic Fe-Co-Hf-N nanocomposite films

Ferromagnetic Fe-Co-Hf-N nanocomposite films were investigated concerning their microstructure-dependent frequency behaviour. To modify the composition, the films were deposited by reactive RF magnetron sputtering by using three different 6 in. targets with various Hf fractions. The films were post-annealed up to 600 °C in a static magnetic field to induce an in-plane uniaxial anisotropy and to obtain different crystal sizes. Depending on the annealing temperature, high-frequency losses were investigated by considering the full-width at half-maximum (FWHM) Δf_eff of the imaginary part of the frequency-dependent permeability which showed a resonance frequency f_FMR of 2.3 GHz for an in-plane uniaxial anisotropy field H_u of 4 mT. The FWHM in correlation with the damping parameter α_eff is discussed, e.g., in terms of two-magnon scattering. Damping occurs due to film inhomogeneity in magnetisation and uniaxial anisotropy caused by a magnetocrystalline anisotropy H_a and/or non-magnetic phases. This will result in homogenous or even inhomogeneous resonance line broadening if additional and resonance as well as precession frequencies of independent grains arise.     

Application of the Stoner-Wohlfarth model with interaction for the determination of the saturation magnetisation, anisotropy field, and mean field interaction in bulk amorphous ferromagnets

Magnetic hysteresis curves of bulk amorphous ferromagnet alloys of composition Nd₆₀Fe₃₀Al₁₀, Nd₆₀Fe₂₀Co₁₀Al₁₀ and Pr₅₈Fe₂₄Al₁₈ have been measured in applied magnetic fields up to 9 T at temperatures in the range 10-350 K. The behaviour of the demagnetisation curve in the first quadrant is interpreted using a mean field interaction model as proposed by Callen et al. [Phys. Rev. B 16 (1977) 263], which extends the Stoner-Wohlfarth model [Philos. Trans. Roy. Soc. A 240 (1948) 599] for a random distribution of non-interacting uniaxial grains. Application of the mean field interaction model enables the determination of the saturation magnetisation M_s, anisotropy field H_a, and interaction parameter d, and from these other magnetic parameters, such as the anisotropy constant, K, are deduced. For the three alloys, the temperature dependent behaviour of M_s, H_a, d and K over the range 20-350 K are found to be qualitatively similar, though there are quantitative differences. In all cases M_s increases with decreasing temperature, both H_a and K increase with decreasing temperature, reaching a peak in the range 75-120 K, and then decreasing, and d decreases approximately linearly as the temperature decreases. The physical mechanisms responsible for coercivity in these materials are discussed in the context of random anisotropy and a strong pinning model of domain walls.     

3-D FEM analysis of thermal degradation in writing and reading characteristics of a perpendicular magnetic head

In order to achieve high-density recording, the detailed behavior of thermal degradation should be investigated. In this paper, the degradation of magnetization of high-density recording medium is examined using the 3-D finite element method (FEM) combined with the modeling of Stoner–Wohlfarth (SW) particles and Neel–Arrhenius switching probability. It is shown that the anisotropy field H_k suppressed the thermal degradation and the saturation magnetization M_s enhances it. The thermal degradation is also changed by the amplitude of magnetization.     

Synthesis, magnetic and dielectric properties of Er-Ni doped Sr-hexaferrite nanomaterials for applications in High density recording media and microwave devices

A sol-gel combustion method has been successfully employed for the synthesis of Sr-hexaferrite nanomaterials doped with Er³⁺ and Ni²⁺ at strontium and iron sites, respectively. The X-ray diffraction analysis confirmed the single magnetoplumbite phase and the crystallite size was found to be in the range of 14-16 nm, suitable for obtaining signal-to-noise ratio in the high density recording media. The magnetic properties such as saturation magnetization (M_s), remanence (M_r) and coercivity (H_c) were calculated from hysteresis loops. M_s, M_r and H_c are observed to increase with the Er-Ni content. The dielectric constant (ε´) and dielectric loss (tan δ) is found to decrease with the increase in frequency and is explained on the basis of Maxwell-Wagner and Koops theory. The decrease in dielectric constant and dielectric loss but increase in saturation magnetization and remanence with Er-Ni content suggests that the materials are suitable for applications in microwave devices and high density recording media .     

Optimization of perpendicular magnetic anisotropy tips for high resolution magnetic force microscopy by micromagnetic simulations

Magnetic Force Microscopy (MFM) tip coated with perpendicular magnetic anisotropy film (PMA tip) is one of the choices for high resolution imaging at low scan height (SH), since it has negligible tip–sample interaction related to its stable magnetic state, sharp, and small tip stray field. In this work, detailed micromagnetic studies are carried out to understand the effect of geometrical and magnetic parameters including the cone angle θ of the PMA tip, intergrain exchange constant $A_{2}^{*}$ , saturation magnetization M _s and uniaxial crystalline anisotropy constant K ₁ of the tip coating on the MFM tip resolution. To evaluate the resolution performance of the optimized PMA tip, MFM images of high-density granular recording media and patterned media are simulated. We find that, for the PMA tip and its coating, a cone angle in a range of 36.9^° to 53.1^°, a saturation M _s of 700 emu/cm³, a large uniaxial crystalline anisotropy constant K ₁ (>4.9×10⁶ erg/cm³) and a high intergrain exchange constant $A_{2}^{*}$ of (0.3–1.0)×10^?6 erg/cm are optimized conditions for high resolution imaging. The optimized PMA tip has an excellent performance on imaging of high-density thin film media (bit size of 8×16 nm²) at low SH of 2–8 nm and bit pattern media with a pitch of 50 nm, edge-edge spacing of 5–15 nm at SH of 8–15 nm.     

Reaction of the muonium substituted cyclohexadienyl radical with 2,3-dimethyl-1,3,-butadiene

The rate constant for the title reaction is represented by log (k _M/M^–1s^–1)=6.9(4)–700(350)K/T between 279 and 343K, whereas the H analogous radical, C₆H₇, reacts at room temperature withk _H 12 M^–1s^–1 with dimethylbutadiene. The title reaction is proposed to be transfer of the light hydrogen isotope, Mu, and the large kinetic isotope effect is discussed.Support by the Swiss National Foundation for Scientific Research and by the Swiss Institute for Nuclear Research (SIN) are gratefully acknowledged.     

High-frequency FeCoNiNbB–SiO2 nano-granular films with high resistivity and adjustable resonance frequency from 1.3 to 7.8?GHz

A series of (FeCoNiNbB) _x –(SiO₂)_1−x nano-granular thin films were fabricated by magnetron sputtering with different oblique incidence angles θ. High-resolution transmission electron micrographs show that the films consist of amorphous CoFeM (M = Ni, Nb, B) alloy particles with diameter about 2 nm surrounded by amorphous SiO₂ matrix. Excellent soft magnetic properties have been achieved with a variable in-plane uniaxial magnetic anisotropy field H _k0, which increases monotonically with θ and x, and decreases with the composition of B in FeCoM. For one typical sample of x=0.63 with θ=30°, H _ch and H _ce are 4.2 Oe and 5.4 Oe, respectively, ρ reaches 12.5 mΩ cm and 4π M _s and H _k0 are 5.70 kG s and 92 Oe, respectively, which lead to a high ferromagnetic resonance frequency f _r of 2.2 GHz. Based on the analysis of experimental results, two sources for the origin of the magnetic anisotropy, namely anisotropic magnetic coupling and orientation order of atomic pairs, are suggested.     

Magnetic properties of barium ferrite nanoparticles: Quantitative test of the Stoner–Wohlfarth theory for uniaxial single-domain magnetic particles

We have successfully synthesized single-domain barium ferrite particles with uniaxial anisotropy. We have coated them with amorphous silica to reduce interparticle interactions so that the assembly of these particles behaves like a noninteracting randomly oriented uniaxial single-domain particle system, a prototype for the Stoner–Wohlfarth model. From the magnetic hysteresis loops of the particle system in a wide temperature range (10–700 K$10\text{–}700\text{K}$), we simultaneously determine the magnetic anisotropic field _HK$H_K$, the reduced remanence _Mr/_Ms$M_r/M_s$, and the coercive field _HC$H_C$ in the whole temperature range below the Curie temperature. These complete sets of data allow us to quantitatively test the Stoner–Wohlfarth theory and the agreement between experiment and theory is good.     

On the role of the higgs mechanism in present electroweak precision tests

Based on the observablesM _W, Γ _l ,s _W ^?2 (M _Z ² ), we evaluate the parameters Δx, Δy and ε at one-loop level within an electroweak massive vector-boson theory, which does not employ the Higgs mechanism. The theoretical results are consistent with the experimental ones on Δx, Δy, ε. The theoretical prediction for Δy coincides with the standard-model one (apart from numerically irrelevant terms which vanish forM _H→∞). Nonrenormalizability only affects Δx and ε, which differ from the standard-model results by the replacement logM _H→log Λ for a heavy Higgs mass,M _H (where Λ denotes an effective UV cut-off).