Static wall coercive force in ferromagnetic thin films

The static wall coercive force of thin ferromagnetic films has been calculated from a model of conservative wall energy. The spatial dependence of the wall energy γwis assumed to be given by the mean value of the local anisotropy energy, averaged over a coupling volume of the wall. The result of the calculation shows thatH_{w} propto frac{S}{M_{s}} (frac{D}{W})^{1/2} frac{1}{L}where the structure constantSincludes the local anisotropy,Dis the mean diameter of a region with constant anisotropy (for instance crystallites),Wis the wall width; andLis the coupling length parallel to the wall.     

A model of magnetostriction interaction in thin double-layer magnetic films of Ni-Fe alloy

Under the assumption that in a double-layer film both layers are equally deformed, the following formula for the magnetostriction energyE = K_{c} sin^{2} alphahas been derived whereK_{c} = (9/40)(2U'U"/U'_{0} + U_{0}")is the coupling constant and α is the angle between the magnetization vectors. This formula is valid if we can neglect interaction with the substrate. The sign of the coupling constant is discussed. It turns out that where the composition of the two layers are different, the value of Kccan be, in some special cases, negative.     

Two-Body Correlations and the Superfluid Fraction for Nonuniform Systems

We extend the one-body phase function upper bound on the superfluid fraction f _s in a periodic solid (a spatially ordered supersolid) to include two-body phase correlations. The one-body current density is no longer proportional to the gradient of the one-body phase times the one-body density, but rather it becomes $\vec{j}(\vec{r}_{1})=\rho_{1}(\vec{r}_{1})\frac{\hbar}{m}\vec{\nabla }_{1}\phi_{1}(\vec{r}_{1})+\frac{1}{N}\int d\vec{r}_{2}\rho_{2}(\vec{r}_{1},\vec{r}_{2})\frac{\hbar }{m}\vec{\nabla}_{1}\phi_{2}(\vec{r}_{1},\vec{r}_{2})$ . This expression therefore depends also on two-body correlation functions. The equations that simultaneously determine the one-body and two-body phase functions require a knowledge of one-, two-, and three-body correlation functions. The approach can also be extended to disordered solids. Fluids, with two-body densities and two-body phase functions that are translationally invariant, cannot take advantage of this additional degree of freedom to lower their energy.     

Models of elastic and inelastic flux switching

The totaldot{phi}(t)waveform of a square-loop magnetic core switched by MMFF(t)from negative remanencephi = -phi_{r}is composed of elasticdot{phi}_{epsilon}(t), decaying inelasticdot{phi}_{i}(t), and bell-shaped main inelasticdot{phi}_{ma}(t). The worst delta noise in a coincident-current memory core pair is essentiallydot{phi}_{i}(t). The sources of these components and the staticphi(F)curve are explained qualitatively by means of the random variations of the energy gradient vs. domain-wall position: elastic wall displacements and elastic rotation of magnetization inducedot{phi}_{epsilon}(t); minor inelastic wall displacements of essentially constant wall areas inducedot{phi}_{i}(t); and major inelastic wall displacements (involving domain collisions) of varying wall areas inducedot{phi}_{ma}(t). Semiempirical models for thedot{phi}components are based on the characteristics of these displacements. A satisfactory agreement is obtained between these models anddot{phi}(t)oscillograms of a thin ferrite core.     

Static and anhysteretic magnetic properties of tapes

The anhysteretic remanencebar{M}_{ar}(H_{o},T)of solidified suspensions of magnetic particles with predominant shape anisotropy is calculated from first principles for small dc fields Hoand arbitrary temperatureT < T_{B}(blocking temperature), describing the particle interactions by a mean field and assuming constant decrement of the ac field,2H_{d}per cycle. ForH_{d}< 2H_{o}, the anhysteretic distribution of particle magnetizations is found to be subject to the condition that the net internal dc fieldbar{H}_{i}is a minimum, and, for small Ho, to the condition,bar{H}_{i} = 0. The theory yieldsbar{M}_{ar}(H_{o},T)as a unique function of independently measurable static magnetic material properties, i.e., it contains no adjustable parameters and is hence quantitatively related to experimental data. Further, according to theory, ifbar{M}_{ar}(H_{o},T,T_{m})denotesbar{M}_{ar}as acquired in Hoat T and measured atT_{m}, bar{M}_{ar}(H_{o},T,T_{m} = T)is independent ofTforH_{d} ll 2H_{o}, andbar{M}_{ar}(H_{o},T,T_{m} neq T) = [M_{s}(T_{m})/M_{s}(T)] cdot bar{M}_{ar}(H_{o},T,T_{m} = T). The thermoremanent magnetization acquired in Hoand measured at a temperatureT_{m} ll T_{B},bar{M}_{thr}(H_{o},T_{m}), is related tobar{M}_{ar}(H_{o},T = T_{m}, T_{m})bybar{M}_{thr}(H_{o},T_{m}) = [M_{s}(T_{m})/M_{s}(T_{B})]bar{M}_{ar}(H_{o},T=T_{m},T_{m}), where TBis the blocking temperature below whichbar{M}_{thr}becomes thermally stable. Up to a constant factor of about 2, the theoretical results agree quantitatively with the experimental data on all materials that correspond to the premises of the theory, i.e., solidified suspensions, tapes in particular, of particles having predominant shape anisotropy.     

Dielectric behaviour of a ferrofluid subjected to a uniform magnetic field

The electric susceptibility of samples of ferrofluids subjected to a uniform magnetic fieldHwas measured. The electric susceptibilitychiis dependent on the magnitude of the magnetic field and on the relative direction between the electric fieldEand the magnetic fieldH. 1) WhenEis perpendicular toH, frac{partialchi_{perp}}{partialH} < 02) WhenEis parallel toH, frac{partialchi_{parellel}}{partialH} > 0These results have been interpreted as a magneto-electric directive effect. A model is proposed, based on the assumption that the magnetic particles are roughly ellipsoidal and conducting grains.     

Hyperfine Fields and Magnetic Structure in the B Phase of CeCoIn5

We re-analyze Nuclear Magnetic Resonance (NMR) spectra observed at low temperatures and high magnetic fields in the field-induced B phase of CeCoIn₅. The NMR spectra are consistent with incommensurate antiferromagnetic order of the Ce magnetic moments. However, we find that the spectra of the In(2) sites depend critically on the direction of the ordered moments, the ordering wavevector and the symmetry of the hyperfine coupling to the Ce spins. Assuming isotropic hyperfine coupling, the NMR spectra observed for H ∥[100] are consistent with magnetic order with wavevector $\mathbf{Q}=\pi(\frac{1+\delta}{a},\frac{1}{a},\frac{1}{c})$ and Ce moments ordered antiferromagnetically along the [100] direction in real space. If the hyperfine coupling has dipolar symmetry, then the NMR spectra require Ce moments along the [001] direction. The dipolar scenario is also consistent with recent neutron scattering measurements that find an ordered moment of 0.15μ _B along [001] and $\mathbf{Q_{n}}=\pi(\frac{1+\delta}{a},\frac{1+\delta}{a},\frac{1}{c})$ with incommensuration δ=0.12 for field $\mathbf{H}\parallel[1\bar{1}0]$ . Using these parameters, we find that a hyperfine field with dipolar contribution is consistent with findings from both experiments. We speculate that the B phase of CeCoIn₅ represents an intrinsic phase of modulated superconductivity and antiferromagnetism that can only emerge in a highly clean system.     

Limits of validity of the one-dimensional wall theory for bubble materials

It is shown that the one-dimensional studies of the wall surrounding a bubble domain do not violate some necessary self-consistency requirements. Moreover, it is shown that the ratio of the magnetostatic self energy (which is neglected in these studies) to the total one-dimensional wall energy isT/Q, whereTis of the order of 1 for typical film thickness of a typical bubble material. This justifies the use of the one-dimensional wall for these materials, as long as the quality factorQ = K/(2piMmin{s}max{2})is large.     

The effects of hydrostatic pressure on the ductility of metals and alloys

A law governing the change in the ductility of metals and alloys under pressure is given: $$\begin{gathered} \left( {\frac{P}{{\sigma _n }}} \right) = \tfrac{1}{2}\frac{1}{{\sigma _n }}\frac{{d\sigma }}{{d\varepsilon }}\{ \varepsilon _{local} (P)^{\tfrac{3}{2}} - \varepsilon _{local} (O)^{\tfrac{3}{2}} \} + \tfrac{1}{3}\frac{1}{{\sigma _n }}\frac{{d\sigma }}{{d\varepsilon }}\{ \varepsilon _{local} (P) - \varepsilon _{local} (O)\} + \hfill \\ {\text{ }} + \tfrac{1}{2}\{ \varepsilon _{local} (P)^{\tfrac{1}{2}} - \varepsilon _{local} (O)^{\tfrac{1}{2}} \} \hfill \\ \end{gathered}$$ where P is the hydrostatic pressure, ?_local is the strain accumulated from the start of necking to fracture, σ _n necking stress and (dσ/d?) the coefficient of linear work hardening. This relation is derived from a newly proposed criterion of ductile fracture, viz. “constancy of hydrostatic tensile stress”, which indicates that the change of ductility with pressure obeys a three halves power law. The observed increase in ductility of widely differing metals and alloys under pressure up to 10,000 kg/cm⁴ has confirmed that the proposed criterion is acceptable. It is further shown that the ductilities of some copper alloys with low stacking fault energy, such as Cu-Zn and Cu-Ge alloys, increases with pressure at the beginning but the increase stops at fairly low pressure, i.e. 3,500 ～ 4,000 kg/cm², and their ductilities become almost insensitive to the pressure applied. It is suggested that ductile fracture of metals with low stacking fault energy is dominated by a process which occurs not by the hydrostatic stress component but by shear stress only.     

Dependence of coercivity on driving field in multilayer films of nickel

The variation in the coercivity of magnetization loops of multilayer films of nickel was investigated as function of the rate of riserin the applied magnetic field. The films were prepared by deposition of nickel and copper alternately in a vacuum of2 times 10^{-6}mm of Hg on to substrates made of thin aluminium foils. The thickness of the nickel layersLvaried in the different films from 8 to 1000 angstroms. The loops were cycled with sinusoidal or triangular waveform driving fields, with a variety of amplitudes from 1 kOe to 4 kOe, with frequencies from 0.01 to 2 c/s. The measurements were performed from room down to liquid hydrogen temperatures. It was found that the coercive force could be expressed byH_{c} = H_{o} + Q(ln r - ln r_{o})/T^{1/2}for values ofrchanging from 1 to 5 Oe/ms, whereH_{o}, Aand rovaried slightly with temperatureT. The coercive force was a very sensitive function ofLand of the thickness δ of the copper layers, having the formH_{c} = A(L + delta) exp - BLwithBnearly constant in films deposited on a substrate at room temperature. The dependence of the coercivity onLwas displayed by a nonmonotonical function showing two peaks in Hccorresponding to values ofLof about 35 and 400 angstroms. The observed dependence of Hcon the rate of rise in the applied field, as well as on the thicknesses of the layers, can be discussed on the assumption of nonuniform magnetization within the thin layers as a result of their superparamagnetic properties and of the magneto-statical coupling between neighboring layers.     

Movement of an individual Bloch wall in a single-crystal picture frame of silicon iron at very low velocities

The movement of an individual Bloch wall in a single-crystal picture frame of silicon iron was studied. By using an electronic apparatus the wall velocity was held constant during the magnetization reversal. It was possible to control the wall velocity down to 10^-2mm/s. Even at these low velocities the relationship between the wall velocityvand the driving magnetic fieldHis precisely linear:v = const . (H-H_{0}). This is to be expected under the given experimental conditiondB/dt = const.     

Scaling of the Temperature Dependent Resistivity in 11 Iron-Pnictide Superconductors

In various $\mathrm{FeTe}_{1-x}\mathrm{Se}_{\mathrm{x}}$ (x=0?C1), members of the 11-iron-pnictide superconductor family, the temperature dependent resistivity ?? can be scaled into a universal curve. It?is found that the ??(T) dependences can be reproduced by the expressions $\rho(T) = \rho_{0} - (c/T)\exp( - \frac{2\varDelta }{T})$ and $\rho(T) =\rho_{0} + (c/T)\exp( - \frac{2\varDelta }{T})$ for x=0?C0.3 and 0.4?C1.0, respectively. The scaling was performed using the energy scale 2??, the parameter c, and the residual resistivity ?? ₀ as scaling parameters. The compositional variation of the scaling parameters 2?? and ?? ₀ has been determined. The existence of a universal metallic ??(T) curve is interpreted as an indication of a single mechanism which dominates the scattering of the charge carriers in FeTe_1?x Se _x (x=0?C1). Thus, the scaling of the normal-state properties seems to be a general feature not only for high-T _c cuprates but also for the iron-pnictides superconductor family.     

Bias susceptibility measurements in thin permalloy films

Susceptibility measurements at 5000 Hz have been performed in the easy and hard directions on two 80-20 Permalloy films (1000 Å, 1 cm in diameter) cut from large samples. The experimental results agree with the predictions of the Hoffmann theory. The susceptibility parallel to the average direction ofMis found to be proportional to1/(H - H_{k})^{7/4}or1/(H_{k} - H)^{7/4}when the net field is large enough to prevent blocking.     

Uniaxial anisotropy by "radiomagnetic" treatment; controlling factors in a new process

A new process-an electron-"radiomagnetic" treatment-for obtaining high-remanence, low-coercive-force loops in magnetic alloys was recently announced. As an example, 2-MeV electron irradiation of 6-mil-thick ring laminations of polycrystalline 5-80 Mo Permalloy with 10¹⁷e/cm²in an applied circumferential magnetic field of 0.2 Oe atsim100degC produced record highs in remanence (∼6700 G) for this material. Additional studies of this process have been made to determine some of the controlling factors and the range of application. In particular, the effects of the dose (number of e/cm²) and of the preirradiation magnetic properties were examined. The results show that: 1) for a given dose of1.1 times 10^{17}2-MeV e/cm², the relative change in remanence (DeltaB_{r}/B_{r}) is always positive, ranging from 10 to 50 percent, but varies inversely with the preirradiation value of remanence (Br); 2) for the same dose, the relative change in coercive force (DeltaH_{c}/H_{c}) also depends upon the preirradiation value of remanence, but in a different way. ForB_{r} < 5000G,DeltaH_{c}/H_{c}is either negative or zero. ForB_{r} > 5000G,DeltaH_{c}/H_{c}is positive, ranging from 20 to 150 percent, and increases linearly withB_{r}; 3) if the dose is reduced tosim0.8 times 10^{17}e/cm², thenDeltaH_{c}/H_{c}is reduced to a tolerable level (∼10 percent) with no significant sacrifice in the positive gain in remanence and rectangularity. Hence, there are optimum dose ranges in the "radio-magnetic" treatments of alloys, where significant gains in remanence may be obtained without appreciable increases in coercive force.     

Monte Carlo Simulation of 2D Ising Spin Glass with Power Law Decaying Interactions

We study the distance dependent interaction coupling in 2D in order to show how a spin glass phase transition occurs when couplings between far away spins are permitted by considering the Edwards–Anderson Ising spin glass model. The interaction coupling is a quenched random variable whose probability of being non-zero decays with distance between two spin sites $(p(J_{ij})\propto r_{ij}^{-\rho })$ . We study the model by changing ρ in three different regimes (ρ>2D, $\frac{4}{3} D < \rho < 2D$ , $\rho <\frac{4}{3} D$ ). We obtain a phase transition temperature for ρ=2,3,4.     

Domain models of eddy current loss due to normal magnetization in slightly misoriented

In Goss-oriented SiFe laminations, regions exist with a significant normal magnetization component arising from dip misorientation of the crystallites. It has recently been suggested by Imamura and co-workers that this normal magnetization can make a major contributionP_{perp}to the eddy current losses incurred during cyclic magnetization along the texture axis.P_{perp}is calculated for three distinct domain models of the magnetization process in laminar crystallites with modest dip misorientation. Contrary to the Imamura work,P_{perp}is found to be practically negligible for a simple slab domain structure without closure domains. This is because the normal demagnetizing field restricts normal induction to the neighborhood of the domain walls and ensures that its volume average is practically zero. In a second model monotonic reversal of normal magnetization in closure domain structures is also shown to give rise to rather low normal lossP_{perp}. A third model concerns how closure domains may interact with the major boundaries between slab domains and be swept along with them. Quite substantial lossesP_{perp}are predicted if all closure domains in a zone extending a distance rather greater than the sheet thickness either side of the major domain wall are displaced in this way. However, even this mechanism can explain only a small part of the marked increase in eddy loss with dip misorientation reported, and it is concluded that normal flux is probably not primarily responsible.     

Dislocations in β-alumina electrolyte material

β-alumina obtained from a number of sources and manufactured by different techniques has been examined in the electron microscope. Dislocations have been observed on the basal plane and the Burgers vector determined as \(b = a/3< 11\bar 20 > \) . The presence of this type of dislocation has been explained on the basis of the crystallographic structure ofβ-alumina. It is also predicted that the unit dislocation dissociates into two and four partials according to the energetically favourable reactions: $$\begin{gathered} \frac{a}{3}< 11\bar 20 > \to \frac{a}{6}< 11\bar 20 > + \frac{a}{6}< 11\bar 20 > \hfill \\ \frac{a}{3}< 11\bar 20 > \to \frac{a}{6}< 1\bar 100 > + \frac{a}{6}< 0\bar 110 > + \frac{a}{6}< 0\bar 110 > + \frac{a}{6}< 0\bar 110 > \hfill \\ \end{gathered} $$ . Experimental evidence has been obtained which shows the presence of dislocations separated into two and four partials inβ-alumina. Microscopic deformation has been shown to occur in thin crystals ofβ-alumina in the electron microscope, by the passage of large numbers of dislocations along basal slip planes.     

Optimization of Spin-Valve Structure NiFe/Cu/NiFe/IrMn for Planar Hall Effect Based Biochips

This paper deals with the planar Hall effect (PHE) of Ta(5)/NiFe$(t_{rm F})$/Cu(1.2)/NiFe$(t_{rm P})$/IrMn(15)/Ta(5) (nm) spin-valve structures. Experimental investigations are performed for 50 $mu$m$times hbox{50} mu$m junctions with various thicknesses of free layer ( $t_{rm F} = 4, 8, 10, 12, 16, 26$ nm) and pinned layer ($t_{rm P} = 1, 2, 6, 8, 9, 12$ nm). The results show that the thicker free layers, the higher PHE signal is observed. In addition, the thicker pinned layers lower PHE signal. The highest PHE sensitivity $S$ of 196 $mu$V/(kA/m) is obtained in the spin-valve configuration with $t_{rm F} = 26$ nm and $t_{bf P} = 1$ nm. The results are discussed in terms of the spin twist as well as to the coherent rotation of the magnetization in the individual ferromagnetic layers. This optimization is rather promising for the spintronic biochip developments.      

Computer simulation of the operation of a magnetic bubble domain propagation circuit modeled after a current-access device

The operation of a bubble-domain straight-line propagation circuit has been simulated successfully. This simulation has been achieved by our approximating the motion of an s = 0 frozen-azimuth bubble placed under a drive fieldH_{Z}(X, Y, T)= -H_{p} cdot cos [2pi(X/R_{X} - n(T)/4)] cdot exp [-(Y/R_{Y})^{2}]. The simulation has been generated from a previously developed numerical scheme to simulate the motion of a bubble, whose domain shape and magnetization structure along its domain wall were variable. The drive field has been modeled after a dual conductor-sheet, current-access propagation structure, which has a bit period RXand a transverse width on the order of2R_{Y}. The entire field contour has been advanced stepwise in the positiveXdirection by an increase of the integern(T), which represents the drive-phase number. The bubble motion has been observed during the first six drive phases to produce operating margin diagrams for drive frequencies of 250 KHz, 796 KHz and 1 MHz. The method of calculation and the results of the simulation are given.     

Wide PRIME-current range for all-magnetic shift registers

In an all-magnetic resistance-type shift register, a PRIME current pulsei_{p}(t), of amplitude Ip, is applied to Npand Nbturns through the minor and major apertures, respectively. For given operation frequencyf, the ratioR = I_{p}^{max}/I_{p}^{min}, whereI_{p}^{min} < I_{p} < I_{p}^{max}is the PRIME range of bistable operation, is maximized by matchingN_{p}/N_{b}so thatI_{p}^{max}values determined by spurious ZERO buildup and ONE dropout are the same. For a rectangular (or dc)i_{p}(t), the matchedN_{p}/N_{b}is fixed by the core properties, and R^maxis limited (e.g., <7). However, ifi_{p}(t)rises gradually, the matchedN_{p}/N_{b}depends also on the rise time Trofi_{p}(t). The lowerfis, with corresponding larger Tr, the smaller is the matchedN_{p}/N_{b}, and the larger is R^max. Calculation ofRis carried for ramp and half-sinusoidali_{p}(t)waveforms. The latter, for instance, atT = 25degC yields R^maxvalues of 14.0 and 22.0 forfof 1.0 and 0.5 kc/s respectively. Such wide PRIME ranges permit reliable register operation in a wide temperature range without resorting to temperature compensation of Ip. Experimental results are in agreement with the calculation.