Internal Anisotropy Field Research Articles

THE EQUATION OF MOTION OF MAGNETIC DOMAIN WALLS IN A COMPOSED EXTERNAL FIELD AND ITS APPLICATION TO THE MAGNETOELA-STIC INTERNAL FRICTION

It has been found that the forces on the domain walls (DWs) in ferromagnetic material for measuring internal friction (IF) when the magnetic field (H) is increased at constant rate (a) are: (1) main driving force caused by the H, namely A00+A10at; (2) harmonic perturbation force A30sinωt; (3) interaction force which is proportional to A10at, A30sinωt and a resistant force depending on the internal stress field and anisotropy field A20sinωt. The equation of motion of DWs can be written as ρ(d2 x)/(dt2) + r(dx)/(dt)+κx = A00 + A10at + A20t sinωt + A30 sin ωt where A00,A10,A20,A30 are constants depending on material chosen and test condition; ρ is the mass density, γ is the viscous damping parameter and κ is the coefficient of restoring force. The IF caused by DWs motion can be obtained from the solution of the equation of motion as follows Qm-1=B1 (Eλsδ)/(Ms2Hm) (dM)/(dH)·α/ω (If for α≠0) Q0-1=B2 (γωE)/(κ2) (If for α=0) where E is the modulus, λs is the saturation magnetostriction,Ms is the saturation magnetization, Hm is a critical field at whichthe reversible motion of DWs becomes irreversible B1, B2 are dimensionless positive numbers. When α≠0, the visco-elastic IF may be initiated and the IF varies with α/ω; when α= 0, the low-frequency micro-eddy current IF may be initiated and the IF varies with ω. The calculated results are compared with experimental data and interface dynamics.

Electron spin resonance modes in a spin-glass

The microscopic Hamiltonian for a spin-glass is diagonalized using the Holstein-Primakoff and Bogoliubov transformations. Both an external, Zeeman, and internal anisotropy field are included. The Zeeman energy enters the resonance condition with an extra factor of one-half which is shown to be of geometrical origin. For single ion anisotropy the resonance condition is angular dependent. It is implied that single crystal ESR measurements will yield information about the nature of the anisotropy energy in a spin-glass.

Limiting viscosity of ferromagnetic suspensions in a strong magnetic field

The effective viscosity of a suspension of ferromagnetic particles with anisotropy of the “easy-axis” type is calculated. The case considered is that in which the magnetic field in which the suspension is flowing greatly exceeds the internal anisotropy field, and the concept of the “frozen” magnetic moments of the particles is inapplicable. The relationship between the viscosity and the anisotropy field is established. The question as to the magnitude of the viscosity for an arbitrary ratio of the internal and external fields is discussed.

Changes in Magnetization of Single-Crystal Dysprosium, Erbium, and Holmium in High Magnetic Fields

Measurements are reported on the behavior of magnetization with field of single-crystal dysprosium, erbium, and holmium in pulsed magnetic fields up to 165 kOe. These elements go progressively on decreasing temperature from a paramagnetic to antiferromagnetic to ferromagnetic state. Sufficiently high external fields applied along spin axes in single-crystal samples can cause spin realignment by overcoming the internal exchange and anisotropy fields. The strengths of the internal fields can be determined in this manner. Measurements with an external field H applied in the basal plane of Dy and of Ho, and with H parallel to the c axis in Er, confirm previous static field measurements of Hc for the AF/F transition. No change in spin alignment is seen in Dy with H parallel to c up to 165 kOe. In Ho below 80°K fields near 100 kOe produce strong changes in magnetization with H parallel to the c axis. Below 20°K fields up to 17 kOe in the basal plane in Er produce a sharp change in magnetization indicative of spin realignment. The magnetization of Er with H parallel to a is measured at 4.2°K in static fields up to 56 kOe. The magnetization increases sharply between 15 and 20 kOe, reaching 50 emu/g at 20 kOe. Little change is found above 40 kOe where M is 120 emu/g. These results are discussed with regard to the internal fields in Dy, Ho, and Er.

Hexagonal Ferrites for Use at X- to V-Band Frequencies

A series of uniaxial materials has been prepared and studied in which the effective anisotropy field can be controlled and varied over the range of 0 to 12 700 oe. The materials are solid solutions of the NiW and CoW compounds and have the chemical formula BaO·2[Ni1−xCoxO]·7.8Fe2O3 with x varying from zero, where the anisotropy field is 12 700 oe, to 0.5 where the anisotropy field is vanishingly small. The temperature dependence of the net resultant anisotropy field, linewidth, and g factor of these materials is discussed. By using oriented polycrystalline samples of these materials, the effective internal anisotropy field can be used to augument external applied fields. Different materials of this series have been used to construct resonance isolators at V- and K-band frequencies with bandwidths of the order of 20% and peak isolation ratios of greater than 30 to 1.

Internal Ferromagnetic Resonance and Magnetostatic Modes in Nickel-Iron Alloys

Experiments are described in which colloidal suspensions of nickel-iron alloys in paraffin-wax have been prepared for the purpose of measuring, by internal ferromagnetic resonance, the total internal magneto-crystalline anisotropy field as a function of alloy composition. Determination of the internal resonance frequency is by measurement of the complex permeability of the particles over a range of frequencies. The variation of internal field with composition is found to be in agreement with previous qualitative observations by Anderson and Donovan employing a different technique and the total anisotropy is found to pass through a minimum in the region of 65% nickel. Values for the anisotropy constants K1 and K2 are calculated from the results and are compared with published values.

Internal Ferromagnetic Resonance in Small Cobalt Particles

Experiments are described in which small particles of cubic cobalt have been obtained by precipitation from a 2% Co-Cu alloy for the purpose of measuring the total internal magneto-crystalline anisotropy field as a function of particle radius. Two methods have been used, namely static torque measurements of the principal anisotropy constants and dynamic measurements based on spin resonance in the anisotropy field. The two methods yield fair agreement in the values calculated for the anisotropy field in a range of particle sizes. The field is found to vary little with particle radius in a single crystal specimen and this is interpreted as evidence that internal resonance is independent of shape anisotropy.

A 5-MM Resonance Isolator (Correspondence)

The rectangular waveguide resonance isolator operating at frequencies from 3000 to 24,000 mc is a simple and compact device since the dc magnetic field requirements are relatively low. In the 5-mm range, however, resonance isolators are not practical if conventional ferrites are used because very high magnetic fields of about 20,000 oersteds are required to obtain resonance at these high frequencies. By using highly oriented Ferroxdure, resonance isolators in the millimeter range become feasible because of the high internal anisotropy field of 17,000 oersteds exhibited by this material. Thus, with Ferroxdure a magnetic fieId of a few thousand oersteds is sufficient for resonance in the 5-mm region.

Magnetic spectra

The various types of magnetic spectra are reviewed. In ferromagnetic metals, relaxations of various time-constants occur. Above 200 Mc/s, the magnetic dispersion is attributable to incomplete penetration of surface domains, due to skin effect, and internal phenomena are not observed. In low-conductivity paramagnetic materials, three types of relaxation have been found, namely spin-lattice, spin-spin, and a third, yet to be identified.The application of a static magnetic field normal to the h.f. field causes electron-spin resonance absorption at the Larmor precession frequency. This induced resonance, which has been observed in paramagnetic materials, in ferromagnetic metals and in ferrites, is broadened by relaxation effects. Similar induced nuclear magnetic resonance is found at lower frequencies.The magnetic spectra of the ferrites exhibit similar natural resonances in the absence of an applied static field. These resonances, which occur in both the microwave and r.f. regions, are due to domain spin rotations in the internal anisotropy field, and to domain wall displacements, and their identity is discussed. Magnetic dispersion due to relaxation of translational and other magnetization processes occurs at r.f. and lower frequencies. The relaxation of irreversible magnetization processes also occurs in the low-frequency region.

The low-frequency problem in the design of microwave gyrators and associated elements

The introduction of ferrite microwave circuit elements has allowed considerable simplification in the realization of many system functions. However, to date practical low loss ferrite devices have not been built to operate at frequencies below 3,000 mc. Many problems arise when one attempts to build devices to operate below this frequency. Some of these problems arise from the fact that mechanisms of loss occur in the ferrites at lower frequencies which are negligible at the higher microwave frequencies. In addition, at frequencies below 1,000 mc, one can seldom neglect the existence of internal anisotropy fields in the ferrite materials. The most fundamental limitation to the operation of ferrite devices at very low microwave frequencies, however, is that one is approaching the relaxation frequency for ferromagnetic resonance, and as a result the performance of all ferrite microwave devices must deteriorate at sufficiently low frequencies, regardless of whether one assumes a ferrite whose other properties are ideal. All these problems are discussed and quantitative expressions are obtained for the ultimate low-frequency limitation of ferrite isolators, circulators, and microwave gyrators.

The Properties of Ferromagnetic Compounds at Centimetre Wavelengths

The magnetic and dielectric properties of γ-ferric oxide, magnetite, Mn-Zn ferrite and Ni-Zn ferrite have been measured at wavelengths from 60 cm. to 1.23 cm. The pronounced magnetic dispersion and absorption which occur are attributed to the decay of the rotational magnetization, due to Larmor spin resonance in the internal anisotropy field HN. The theoretical relation HN = 2K/M, where K is the anisotropy coefficient, and M the saturation intensity, agrees satisfactorily with the observations, and|K| has been derived for each material. An inverse relationship between HN and the initial susceptibility is shown to account quantitatively for the magnetic resonance observed in high-permeability materials at much lower frequencies