Self-demagnetizing Field Research Articles

Domain wall displacements in amorphous films and multilayers studied with a magnetic force microscope

The magnetic force microscope (MFM) was used to study the displacement of domain walls (DW) in amorphous TbFe alloy films and Co/Pd multilayer films with high spatial resolution. The reversible bending of domain wall segments pinned to defects and irreversible, jumplike displacement of domain wall segments were imaged with the MFM in an applied magnetic field. The maximum reversible displacement of domain walls was 50–100 nm and the length of the segments which reversibly curved in the field was about 150 nm. Measurement of the change in radius of curvature of a DW segment in response to an applied field allowed estimation of the DW energy density and self-demagnetizing field of the film acting on the DW. The DW energy density for the TbFe films was about 1 erg/cm2. It was shown that the self-demagnetizing field acting on a domain wall depends on the domain structure surrounding the studied DW segment. For instance, for a film with saturation magnetization 100 G and thickness 80 nm, which exhibited a mazelike domain structure, the demagnetizing field varied from 100 G in the center of a mazelike domain to 400 G near the edge of a domain. The irreversible displacement of a DW was not a continuous process. The 200–400 nm long DW segments exhibited jumplike motion over distances of 100–150 nm.

Inferring domain state from magnetic hysteresis in high coercivity dolerites bearing magnetite with ilmenite lamellae

Hysteresis loops were measured for 16 dolerite samples from separate Precambrian dykes whose remanence is probably primary. Remanence is carried by grains of magnetite subdivided into fine particles, usually by ilmenite lamellae, as seems common in mafic igneous rocks of high coercivity. Coercive force H C ranges from 9 to 40 × 10 3A/m (110–500 Oe). The ratio J RS J S of saturation remanence to saturation magnetization ranges from 0.10 to 0.45. J RS J S varies in approximate proportion to H C with a constant of proportionality appropriate for pseudo-single-domain magnetite with one or two domain walls per particle. A cooling cycle to 77K causes large (40% on average) demagnetization of J RS in most samples, supporting the dominance of pseudo-single-domain magnetite. Most samples also show a large (29% on average) decrease in H C on cooling to 140K, suggesting magnetostrictive control of H C, perhaps through internal stresses opposing domain wall motion. Only the three dolerites with H C greater than 30 × 10 3 A/m (380 Oe) show little change in H C on cooling, suggesting dominance by single-domain particles with shape anisotropy. In magnetite grains subdivided into single-domain particles by ilmenite lamellae, magnetic interaction may lower J RS J S from the expected 0.5. Some theories [1,2] suggests that this is due to a self-demagnetizing field from magnetic poles on the surface of each grain of magnetite subdivided by ilmenite and should be corrected for. Another theory [3] suggests that this correction is not necessary because the self-demagnetizing field is already approximately cancelled, due to magnetic poles inside each subdivided grain, at the ends of magnetite particles. The latter suggestion is favoured by our three highest H C dolerites, whose J RS J S averages 0.42 ± 0.04 before and 0.66 ± 0.06 after correction for the self-demagnetizing field from poles on the surface of magnetite-ilmenite grains. Applying this correction to our other dolerites usually raises J RS J S significantly above 0.5, which is unreasonable for pseudo-single-domain magnetite. Hence, correcting for self-demagnetizing fields from poles on the surface of magnetite-ilmenite grains in rocks is not recommended, whatever the domain state.

Angular dependence of coercive field in (Sm,Zr) (Co,Cu,Fe)z alloys

The angular dependence of the coercive force, Hc(ψ), has been studied systematically for a variety of quasi-single-crystal spherical samples of non-stoichiometric Sm0.85Zr0.15(Co0.7Cu0.09Fe0.21)z alloys (z = 6.1, 6.4 and 6.7), for which possible effects of grain misalignment and nonuniform self-demagnetizing field are avoided. The observed Hc(ψ) variation agrees well with the model based on Néel's phase theory, which predicts a maximum in the Hc(ψ) curve followed by a decrease to zero for ψ = π/2, provided the samples have a narrow Hc distribution. Heat treatments resulting in a wide Hc distribution lead to a variety of rather exotic Hc(ψ) shapes which are explained by the appearance of cooperating low-anisotropy phases in these non-stoichiometric compounds.

Preisach diagrams and anhysteresis: do they measure interactions?

Traditionally, it is assumed that the off-diagonal distribution on the Preisach diagram and the inverse anhysteretic susceptibility as a function of DC field strength measure the spectrum of magnetostatic particle interactions in single-domain (SD) samples. To test this assumption, we have measured Preisach diagrams and anhysteretic remanence acquisition curves at a series of temperatures up to the Curie point for samples containing SD and small pseudo-single-domain (PSD) magnetites and maghemites. Preisach diagrams were also determined at room temperature only for a suite of PSD to multi-domain (MD) magnetites with mean sizes ranging from 2 to 100 μm. In the latter Preisach diagrams, the diagonal distributions, which are thought to represent microcoercivity spectra, changed from peaked, SD-like distributions for the smallest grains to typical quasi-exponential MD distributions for the largest grains. The transverse or off-diagonal distributions broadened enormously over the same grain-size range, probably indicating that self-demagnetizing fields become more influential in the larger grains. In the SD and small PSD samples, the diagonal and transverse Preisach distributions contracted about equal amounts at each high-temperature step. Both distributions changed approximately in proportion to bulk coercive force, HC(T), and not in proportion to saturation magnetization, Ms(T). Such a temperature dependence was expected for the diagonal distribution, which depends on crystalline and shape anisotropies. It was not anticipated for the transverse distribution, as magnetostatic interactions should vary with temperature as MS(T). Inverse anhysteretic susceptibilities at first changed like MS(T), but at the higher temperatures they also decreased in proportion to HC(T). Therefore the off-diagonal Preisach distribution seems to be affected more by microcoercivity than by magnetostatic phenomena such as particle interaction or self-demagnetization, at least in this suite of samples, and inverse anhysteretic susceptibility is also a dubious measure of interaction strength. A preliminary theoretical model is presented in which an interaction field acting perpendicular to the easy axis of anisotropy considerably reduces the particle coercivity. Thus the diagonal Preisach distribution is not independent of interactions. However, it remains unclear why the off-diagonal distribution is not independent of coercivity.

Evidence for magnetostrictive control of intrinsic susceptibility and coercive force of multidomain magnetite in rocks

It is shown that intrinsic susceptibility x i (susceptibility in the absence of self-demagnetizing fields) as well as coercive force H C of multidomain magnetite in rocks are likely to be commonly magnetostrictively controlled-presumably through internal stresses opposing domain wall motion. We use observations of the thermal variation of observed susceptibility x per cm 3 of magnetite in the sample and coercive force H C on cooling to ∼ 130 K for seven basaltic rocks and for 0.25–0.21 mm magnetite grains dispersed in cement. As expected theoretically with magnetostrictively controlled x i , a plot of 1 x versus λ J S 2 for each sample (where λ is the polycrystalline magnetostriction coefficient and J S is saturation magnetization) gives a reasonably straight line whose 1 x - intercept agrees with N (average self-demagnetizing factor of magnetite grains in the sample) given by H C J R ≥ N ≥ H C J R − H C J Ri where J R is saturation remanence and Ri is J R when N=0. As expected theoretically with magnetostrictively controlled H C, a plot of H C versus λ J S for each sample reveals an approximate proportionality. This also implies magnetostrictive control of x i because a plot of 1 x versus H C J S for each sample yields a straight line of 1 x - intercept agreeing with N from H C J R ⪖ N ⪖ H C J R − H C J Ri as expected if H C and x i are both magnetorestrictively controlled.

A model of anisotropic Alnico magnets for field computation

The modeling of an anistropic Alnico magnet for the purpose of field computation involves assigning a value for the material's permeability in the transverse direction. This is generally based upon the preferred direction properties, being all that are easily available. By analyzing the rotation of intrinsic magnetization due to the self-demagnetizing field, it is shown that the common assumptions relating the transverse to the preferred direction are not accurate. Transverse magnetization characteristics are needed, and these are given for Alnico 5, 5-7, and 8 magnets, yielding appropriate permeability values.

The effect of the magnetization distribution within anisotropic alnico magnets upon field calculation

Magnetization characteristics of an anisotropic alnico permanent magnet have been measured at 10° increments from the preferred to the transverse axes. These are shown to correspond to results obtained in a magnetometer. Although the magnetization varies in magnitude and direction throughout the volume of alnico magnets, the rotation of magnetization may therefore be modelled using J vs. H characteristics. In fact, it is found that only curves for mutually perpendicular directions should be used, and these are incorporated in a rapid method for modelling these magnets. This new technique allows a non-uniform magnetization distribution to be determined from self-demagnetizing fields that have been calculated using a uniform magnetization distribution, thus eliminating a lengthy iterative procedure.

Remanence changes of magnetic tapes and disks stressed in zero and reverse fields

To estimate the extent to which a recording tape signal can be reduced during replay we have devised a rapid, sensitive, and simple testing technique. The method uses a Hall probe to measure the field profile after applying a localized stress to the center of a uniformly magnetized sample. We believe that this loss occurs when the pigment anisotropy is lowered by stressing particles, which have nonzero magnetostriction, in the presence of a demagnetizing field. The latter originates from particle interaction fields (H I ), self-demagnetizing fields from short magnetized segments, and fields from oppositely magnetized adjacent regions. The first effect is observed by stressing a uniformly magnetized sample in its remanent state; the second two are associated with frequency-dependent losses and can be simulated by applying stress with the sample located in a reverse field after initial saturation. Results indicate that H I is anisotropic and depends on the average angle between the magnetizing field and the long particle axis. When a reverse field is applied during stress, the maximum loss occurs at the coercive field where the loss is greater than the interaction field loss. All stress-induced losses vary logarithmically with the number of stress cycles, and scale with the magnitude of the applied stress and the absolute value of the saturation magnetostriction.

Energy relations in hard and soft magnetic materials

Koch has criticized the common assumption that the force exerted by a permanent magnet on a keeper can be calculated from the increase of the internal or external energy of the magnet, since both these quantities pass through a maximum as the keeper is removed. He introduces a new term the "Demagnetizing energy". The present paper shows that this term is equal to the total field energy inside and outside the magnet, the former being equal to the energy of the self-demagnetizing field with the magnet treated as free space. The energy transitions in a permanent magnet are more easily understood, if it is recognized that the energy at the remanence point on closed circuit is not zero. This energy appears to be used in D.C. pulse transformers and ferrite memory cores.

The replay signal from a tape with magnetization components parallel and normal to its plane

A simple formula is given which describes the magnetization distribution recorded in magnetic tapes. This is more realistic than the usual <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M = M_{o}\sin wx</tex> in that it contains both longitudinal and normal components of magnetization. The corresponding output voltages are shown to be higher while the self-demagnetizing fields are lower than in the usual case.

Permanent magnet utilization criteria in a DC motor

In a dc motor with permanent magnet stator, the mean no-load working point of the magnet material can, after stabilization by stall current, be represented by a point B_{m},H_{m} on a recoil line inside the demagnetization curve. The point results from the application during stall of an effective mean field H a due to armature reaction in addition to the self-demagnetizing field due to circuit reluctance. It is shown that the motor specification and sizes lead to a specific value for H_{m}/H_{a} . The limiting values of this ratio (H m zero or H a zero) imply that the corresponding optimum magnet designs for minimum magnet volume should be based either on maximum recoil energy or on (BH)_{max} . In practice, the best extreme working point during stall should lie between the points for these two criteria, dependent on the actual H_{m}/H_{a} . In some existing motors H_{m}/H_{a} has been found to be between 0.5 and 1.5. For such values of H_{m}/H_{a} , the variation of B m and of B_{m},H_{m} with working point is illustrated for high coercivity ferrite and for two grades of cast alnico alloy. A note on design methods is appended

Permanent magnet applications

The main uses of permanent magnets are covered either by the range of cast and magnetically treated alnico alloys or by the several grades of sintered barium/strontium hexaferrite, but minority materials have their special applications and continue to develop. Three different technical classes of permanent magnet applications can be distinguished. Firstly, magnets working in a magnetic circuit of static reluctance, e.g., speakers, moving-coil measuring instruments, microwave devices, separators, etc. Secondly, those working in a varying self-demagnetizing field due to change of circuit reluctance, such as clamping and holding magnets which range from planning-board indicators to large chucks for machine-tools. Thirdly, magnets which work in both a self-demagnetizing field and a varying externally produced field, as in motors, generators, the several types of magnetic couplings, and magnetic suspensions. For each of these three classes the basic design principles are indicated and typical applications are described. Additionally, there are uses for high-hysteresis permanent magnet materials without premagnetization, as in hysteresis motors.

Fast Nondestructive Read, Slow Write Memory Device Using Thick Magnetic Films

A device is proposed for providing an ultra high speed read, but comparatively slow write, memory device. The device has certain similarities to other proposed devices, but the mode of operation and performance is quite new and makes use of effects which are normally avoided or minimized in usual memory devices. The storage element is a thick-film bias magnet with a coercive force smaller than its self-demagnetizing field and is tightly coupled to a second anisotropic thick film which serves as the sensing or reading device. The array conductors are all external to the coupled structure (i.e., no conductors lie between the films) thereby simplifying fabrication. A modified coincident current technique is used to write the information into the bias film. A stored ``1'' is obtained by setting the bias film and hence the read film into a demagnetized state. A read current applied to the word line will cause rotation of the magnetic moments of the read film toward its hard axis, thus inducing a signal in the sense line. A stored ``0'' is obtained by saturating the bias film, which in turn saturates the read film in its hard direction and thus prevents any signal from being induced in the sense line during reading. The modes of operation and design parameters are presented as well as a number of measurements. The results thus far have shown that there are no fundamental barriers to overcome.

Thermo-remanent magnetization (TRM) of multidomain grains in igneous rocks

Abstract The magnetic moment of a multidomain grain at its blocking temperature is determined by the domain arrangement which gives the minimum magnetic energy; for a large grain the energy minimum is produced by a self-demagnetizing field equal and opposite to the external field. Below the blocking temperature the domain configuration is frozen in and the moment increases with the increasing spontaneous magnetization. This results in a TRM proportional to small inducing fields, as in the theory of single domain grains and as required for agreement with experimental observations. Artificial TRM's of 17 rocks for which analyses of magnetic minerals are available show good agreement with calculated values. The theory also gives a formula for the maximum possible initial susceptibility of rocks which agrees well with experimental observations.

The influence of some head and tape constants on the signal recorded on a magnetic tape

With recording heads of conventional design, the distribution of magnetization through the depth of a recorded tape may be markedly non-uniform to an extent depending upon the h.f. bias setting. An analysis of this effect is shown to be of value in explaining several aspects of recording performance, including the anomalous loss of high-frequency response commonly observed when using large values of h.f. bias. An analysis of the self-demagnetizing fields created within a recorded tape is also given, and an attempt is made to relate the losses these introduce into the high-frequency performance of the system to the dimensional and magnetic constants of the tape.