Fine Particle Magnetism Research Articles

Preparation of cobalt-rare-earth alloys by electrolysis

High-purity alloys of cobalt and rare-earth metals were produced by electrodeposition of rare-earth metal on a consumable cobalt cathode. These alloys, rich in rare-earth metals, are suitable for the preparation of cobalt-rare-earth compounds with addition of more cobalt by melting. The compounds can then be made into fine-particle permanent magnets by pulverization and consolidation.

Permanent magnet materials

Permanent magnets are finding ever-increasing uses as magnet technology develops and materials improve. Permanent magnet materials are evaluated in terms of the geometry and configuration of the application for which they are intended. The origin of the properties of most modern permanent magnet materials is interpreted in terms of fine-particle theory. The fine-particle structures are produced either synthetically or by a solid-state precipitation reaction in an alloy. The preparation and properties of commercial magnets are described. The Alnico alloys are based on magnetically heat-treated iron-nickel-aluminum-cobalt alloys and account for the great majority of present-day production. Ferrites are finding increasing use. Elongated single-domain fine-particle magnets and other materials are used in smaller quantities. A number of interesting, not yet commercial, materials deriving their properties primarily from crystal anisotropy are described.

The Fundamental Theorem of Fine-Ferromagnetic-Particle Theory

The theory of fine-particle magnets is based on the theorem that the state of lowest free energy of a ferromagnetic particle is one of uniform magnetization for particles of less than a certain critical size and one of nonuniform magnetization for larger particles. The theorem is inferred from several approximate calculations and has not been proved rigorously. Rigorous statements can be made if one is content to replace equalities by inequalities and exact values of critical radii by upper and lower bounds. For a sphere of radius a with uniaxial anisotropy, it can be shown that the lowest-free-energy state is one of uniform magnetization if a<ac0 and one of nonuniform magnetization if a>ac1 (for low anisotropy) or ac2 (for high anisotropy), where ac0, ac1 (>ac0), and ac2(>ac0) are determined by the exchange and anisotropy constants and the spontaneous magnetization. These bounds locate the critical radius to within about 12% at low anisotropy but only to within an order of magnitude or more at high.

Studies of Magnetic Hardness in Vicalloy using the Mössbauer Effect

Mössbauer spectra were taken at room temperature on rolled Vicalloy samples in (i) a state obtained by quenching the sample from 950°C; (ii) a state obtained by annealing for optimum permanent magnet properties. Annealing results in a narrowing of the absorption peaks, an increase in hyperfine field, and the appearance of an additional absorption peak indicative of a paramagnetic phase. These results are interpreted in terms of the known phase diagram of Fe–Co–V, and lend support to the description of Vicalloy magnets as fine-particle magnets.

Thermal Agitation of Single Domain Particles

The direction of magnetization of fine single-domain particles is known to fluctuate because of thermal agitation. The relaxation time for these fluctuations is calculated here for the case of uniaxial anisotropy and zero magnetic field. It is found that the commonly used approximation for high-energy barrier is still a good approximation when the barrier is of the order of $\mathrm{kT}$. For lower barriers, the eigenvalue is expressed as a power series in the energy barrier in terms of $\mathrm{kT}$.

Anisotropic Behavior in Superparamagnetic Systems

The relative magnetization of an assembly of fine, ferromagnetic, single-domain particles which show uniaxial magnetic anisotropy has been formulated as a function of ρ and λ, the ratios of magnetic energy of particle moment in field and anisotropy energy to thermal energy, respectively, under various situations for particle orientation. Strict formulation for the system where the anisotropic symmetry axes of particles are distributed in thermal equilibrium gives the simple Langevin equation without any influence of anisotropy. In the case, however, of particles with fixed random orientation of symmetry axes the observed decrease of relative magnetization was deduced, while it was found that the Langevin equation is still valid as low and high field approximations. Several simpler cases where the symmetry axes of particles are constrained on a plane parallel or perpendicular to the applied field were also treated and the deviations from the Langevin equation were estimated. These results confirm Bean and Livingston's view about the behavior of the system in low and high field extremes, but show that Knappwost and Rust's formulation, which was developed to explain the anomaly in the magnetization of fine cobalt particles, is not reasonable, suggesting sources of anisotropy other than those of magnetocrystalline origin.

Exchange Anisotropy—A Review

Exchange anisotropy describes a magnetic interaction across the interface between two magnetic materials. A shifted hysteresis loop, sinθ torque curve, and rotational hysteresis in magnetic fields greater than 2K / Ms may result from this interaction if one of the materials is antiferromagnetic. This interaction has been found to exist between ferro-antiferromagnetic materials, ferri-antiferromagnetic materials, and ferri-ferromagnetic materials. The work of various people is discussed in terms of the expected behavior in these exchange coupled systems. Some interesting results of the exchange interaction are reviewed. These include improved properties of fine particle magnets, a memory effect in a mixed ferrimagnetic spinel, a rotatable anisotropy in thin films, and an explanation for the reverse magnetization of a deposit in the earth's crust. The interfacial conditions necessary to obtain the interaction between the two magnetic systems are discussed, and it is shown that they are met in several cases. Models are presented which yield rotational hysteresis in magnetic fields greater than 2K / Ms as has been found in all of the exchange coupled systems.

Development of Elongated Particle Magnets

The development of permanent magnet materials is briefly reviewed. The present status of fine particle magnets is discussed from the viewpoint of our present understanding and lack of understanding of their behavior. The present methods of preparation and the various theoretical descriptions of the properties of elongated particles are reviewed. New work is presented relating the parameters of preparation to the resulting diameter of the elongated particles prepared by electrolysis into mercury. Rotational hysteresis,coercive force, and coercive force as a function of orientation are reported for particle diameters from 130 A to 305 A. Their behavior is compared to various theoretical descriptions and found to correspond to a noncoherent magnetization reversal mechanism most similar to the chain-of-spheres fanning model rather than the curling, buckling or coherent rotation models. Iron and iron-cobalt alloy particle magnets are described with maximum energy products up to 4.3 and 6.5 million gauss-oe, respectively.

Experimental and Theoretical Investigation of the Magnetic Properties of Iron Oxide Recording Tape

Part A gives the results of remanent ,magnetization tests made under ordinary and anhysteretic conditions, and shows that the major anhysteretic properties of a recording tape can be expressed in terms of three easily measured constants. The design of the test equipment is discussed and test results are listed for thirteen representative types of tape. Part B reviews some of the theories of fine particle magnets that can be applied to recording tape, and gives an extensive treatment of remanent magnetization based upon the Preisach diagram. Some aspects of the Preisach diagram treatment may be of interest to workers outside the magnetic recording field. The anhysteretic properties are important in hf biased recording and a second paper describes how these properties can be used to predict certain recording performance characteristics.

PERMANENT MAGNETS FROM ELONGATED SINGLE-DOMAIN PARTICLES

A process is described for producing elongated single-domain (ESD) fine-particle magnets. The 150-A. ESD iron or iron–cobalt alloy particles are prepared by controlled electrodeposition into mercury, followed by thermal growth and treatment with a third metal to attain optimum particle shape and magnetic properties. The particles are then aligned by a magnetic field, compacted under pressure, freed of mercury by vacuum distillation, and embedded in a suitable matrix. This is ground to a coarse powder and fed into automatic presses for realigning and compacting to the final magnet shape. The factors controlling each step of the process are discussed, and the advantages of magnets with artificial microstructures synthesized by this approach are pointed out. The process described produces commercial ESD iron and iron–cobalt magnets with energy products of 2·2 and 3·5 million gauss-oersteds, and laboratory ESD iron and iron–cobalt magnets of 4·2 and 5·0 million gauss-oersteds.

Remanent magnetization of fine particles

Remanent magnetization of fine particles

Magnetic Anisotropy and Rotational Hysteresis in Elongated Fine-Particle Magnets

Various aspects of the magnetic anisotropy of electrodeposited elongated single-domain Fe and FeCo alloy particles are examined with a view to better understanding their process of magnetization. The initial increase of coercivity with increase of the angle between alignment direction and measuring field is in qualitative accord with the prediction of the chain-of-spheres model with fanning, as previously proposed, and in contrast to coherent rotation models. Analyses of high-field torque curves and of the fields at which rotational hysteresis vanishes suggest that an anisotropy is present which is a little greater than predicted by the chain-of-spheres model but less than that predicted by the Stoner-Wohlfarth ellipsoid model, for the observed dimensional ratios. Calculations of the rotational hysteresis in single domain-particles are extended to the chain-of-spheres model. A study of the rotational hysteresis enables a relatively sensitive choice between several models of the magnetization process. Comparison of the observed and predicted values for the rotational hysteresis integral, ∫(Wr/Is)d(1/H), indicates strongly that a nonuniform rotation process, like fanning in a chain-of-spheres, is operative in electrodeposited elongated single-domain particles.

Reproducing the Properties of Alnico Permanent Magnet Alloys with Elongated Single-Domain Cobalt-Iron Particles

Single-domain particles of 40:60 cobalt-iron alloy have been prepared with a median diameter of 200 angstrom units, a median elongation of 5.4:1, and an intrinsic coercive force of 1950 oersteds. By compacting these particles to various packing densities and degrees of alignment, shape anisotropy fine-particle magnets have been made with magnetic properties duplicating those of each of the Alnico permanent magnet alloys, including maximum energy product values above five million gauss-oersteds. It is concluded that the Alnico alloys and the fine-particle magnets derive their properties from very similar, but not identical, shape anisotropy effects.

An Approach to Elongated Fine-Particle Magnets

The coercive force predicted by theory for single-domain particles with shape anisotropy frequently far exceeds the observed value. From an examination of the results of Paine, Mendelsohn, and Luborsky on elongated iron particles, several approximate models are suggested which may exist in certain experimental situations. Detailed calculations are presented for a model remagnetizing by several mechanisms. Comparison with experiment on certain single-domain particles of known elongation favors the chain-of-spheres model as a suitable description of their magnetic behavior. A successful calculation is made of the coercive force of material prepared by several earlier workers. A comparison of the new models with the older ones indicates a direction for experimental advance.

Permanent-Magnet Properties of Elongated Single-Domain Iron Particles

Previously described fine-particle magnets have been based upon crystal anisotropy; this paper reports permanent-magnet properties derived from the shape anisotropy of substantially elongated single-domain iron particles. The shape anisotropy of these particles overcomes the limitation imposed on the energy of previous fine-particle iron magnets by the low crystal anisotropy of iron. The predicted and observed properties of crystal anisotropy fine-particle magnets are reviewed and compared with an ideal fine-particle iron magnet based upon the shape-anisotropy model of Stoner and Wohlfarth. Experimental results are reported for magnets made by aligning and compacting single-domain iron particles 150 angstrom units in diameter, with a median length-to-diameter ratio of three to one, and an intrinsic coercive force before packing of 1600 oersteds. The effect of particle alignment and packing fraction on magnetic properties is described, and energy products above three million gauss-oersteds are reported. These results are compared with properties predicted from theoretical considerations, and with existing permanent-magnet materials.

Experimental Study of the Coercive Force of Fine Particles

The experiments described test the theory of fine-particle magnets. Particles of Fe, Co, and Ni, of size 100-2000A, were prepared by electrodeposition into a mercury cathode. Their sizes and shapes were determined with an electron microscope. Experiments on coercive force $\mathrm{vs}$ particle size show, in general agreement with theory, that the maximum coercive force of Fe particles occurs at about 150A and is about 1000 oersteds, for very small packing factors. The coercive force decreases rapidly for smaller particles, slowly for larger particles. The rapid decrease for particles smaller than 150A is attributed to thermal fluctuations; this is borne out by measurements at low temperatures.Addition of 25 percent by weight of 20-oersted Fe particles to 1250-oersted Fe particles decreases the coercive force to 500 oersteds: thus any experiment designed to check the predicted 10 000 oersteds for particles of 10-to-1 shape anisotropy requires an extremely high percentage of such particles. For both Fe and Co, the temperature variation of coercive force closely follows that of crystalline anisotropy and not that predicted for particles with shape anisotropy. Electron micrographs show that many of these particles are bean-shaped, with axis ratio 1.5. The extent of the present work is not sufficient for evaluation of the contribution of shape anisotropy to the coercive force of Fe.