The general behavior of magnetite (iron ferrite) at its low temperature transformation ($\mathrm{ca}$ 118°K) is reviewed. One of the properties which undergoes a large change is the magnetocrystalline anisotropy, which is larger in magnitude and has a lower symmetry below the transformation. The magnetic symmetry axis below the transition temperature can be predetermined by cooling a single crystal through the transition in a magnetic field, and can be changed from one cube edge to another below the transformation by means of a strong magnetic field.

Directional pressure also appears to be effective in establishing the axis. Hysteresis loop measurements show that if a compressive stress is applied along the length of a rod-shaped specimen cut parallel to [100] as it cools through the transition, the specimen is more easily magnetized in this direction. No such effect was observed along [110] or [111] directions.

Changes in dimension occurring at the transition have been measured by means of resistance strain gages cemented along the principal crystallographic directions. Data were obtained as the crystal warmed through the transition in the demagnetized state after having been cooled in various conditions of biasing magnetic field and pressure. It is concluded that the large changes in magnetic symmetry accompany small changes in crystal structure. The low temperature form appears to be orthorhombic, the maximum distortion from cubic symmetry, along [110], amounting to $\mathrm{ca}0.07\mathrm{}$ percent. All three orthorhombic axes can be established unambiguously by cooling the crystal through the transformation in a magnetic field along [100] with pressure applied simultaneously along [011]. The change in direction of easy magnetization above the transition from [111] to [100] is accompanied by a small dimension change ($\mathrm{ca}0.002\mathrm{}$ percent).

Similarities with the behavior of barium titanate at its ferroelectric Curie temperature are pointed out. Evidence for the existence of similar transformations in the other ferrites is discussed briefly.

The magnetic properties of mixed ferrites of iron and cobalt of the general class, [$x{\mathrm{Fe}}_2{\mathrm{O}}_3,(1-x)\mathrm{}\mathrm{CoO}$], where $x$ is the molar fraction, varying from 0.5 to 0.6, are studied. Depending on the conditions of preparation, a small amount of the trivalent iron may also transform into the bivalent form. These materials not only possess remarkable magnetic properties but are particularly amenable to a theoretical as well as experimental study of the fundamental mechanisms involved in orientation in a magnetic field, coercive force, remanence, initial susceptibility, law of approach to saturation, and the energies of magnetization. An attempt has been made to correlate all these factors for these materials.

An x-ray examination shows that these materials consist of only a single phase. Direct evidence concerning the mechanism of orientation by annealing in a magnetic field has been obtained. A study of the magnetostriction as a function of composition, density, and temperature—both on oriented and non-oriented materials—permits us to investigate the important factors affecting the fundamental mechanism of magnetization. These materials reveal an unusual characteristic in that the values for magnetostriction are very high ($\lambda \sim 3\times {10}^{-4\mathrm{}}$) and their dependence on temperature is very great ($\lambda \sim {10}^{-4\mathrm{}}$ at 20°C and 3×${10}^{-4\mathrm{}}$ at -196°C). The basic phenomena can thus be readily characterized.

As for the coercive force, we place emphasis on the fact that the value of $H_c$ depends on the density. When the density, $\delta$, of the materials is less than 2.9 (theoretical density is 5.1), the value of $H_c$ for a given temperature is independent of $\delta$ which strongly suggests rotations as the only elementary mechanism. Between -80°C and room temperature, we have shown that $H_c$ is effectively only a function of the magnetoelastic energy. At temperatures lower than this, the phenomena are more complicated and one must consider as well the magnetocrystalline energy in order to account for the values of $H_c$ encountered. If the density is between 2.9 and 5.1, $H_c$ depends on $\delta$ and, therefore, on the relative volume of voids. Accordingly, it is probable that, in this case, wall displacements also contribute to the properties and we have shown that $H_c$ is approximately proportional to the square of the volume of voids.

We next give a theoretical study of the remanent magnetization. The value of the ratio $\frac{I_r}{I_s}$, with a mechanism of orientation which places the magnetic vectors along cubic axes nearest the direction of the field, is in good agreement with our experimental results, at least to -80°C. Below this temperature, other phenomena intervene which we shall discuss.

A theoretical and experimental study of the initial susceptibility both on oriented and non-oriented materials has made it possible for us to discern the particular mechanisms which affect the orientation, the coercive force, and the remanence. The ratio $\frac{{\chi }_{\mathrm{oriented}}}{{\chi }_{\mathrm{n}\mathrm{o}\mathrm{n}-\mathrm{o}\mathrm{r}\mathrm{i}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{d}}}$ has been confirmed.

An investigation of the law of approach has proved that in all cases Weiss's law, ${\sigma }_H={\sigma }_{\infty }[1-(\frac{a}{H}\left)\right]$, is confirmed. The value of "$a$" depends on the relative volume of voids and on $\lambda$.

A study of the energy of magnetization as a function of temperature on both oriented and non-oriented materials has afforded a supplementary proof of the interconnection between the different mechanisms.

Finally, we give a résumé of the principal magnetic characteristics of these mixed oxides.

1. The study of the thermomagnetic properties of a natural single crystal of rhomobohedral iron sesquioxide, ${\mathrm{Fe}}_2$${\mathrm{O}}_3$, by Pauthenet, confirms the hypothesis of the superposition of a fundamental antiferromagnetism and a parasitic ferromagnetism. Below 260°K the direction of antiferromagnetism coincides with the ternary axis; above 260°K this direction is situated in the plane perpendicular to the ternary axis, with complete freedom of orientation in this plane. The parasitic ferromagnetism seems to be formed of two parts, one isotropic, the other anisotropic. The latter, tightly coupled with the direction of antiferromagnetism, can be observed only above 260°K and in a direction perpendicular to the ternary axis. The corresponding spontaneous magnetization may arise from the local imperfections in the compensation of the two constituent sublattices of the antiferromagnetism, and it is the freedom of orientation of the antiferromagnetism in the basic plane which permits observation of this spontaneous magnetization.

2. Pyrrhotite corresponds closely to the molecular formula ${\mathrm{Fe}}_7$${\mathrm{S}}_8$. The crystal structure contains holes: one of the eight sites which could be occupied by iron ions is vacant. Bertaut showed that at room temperature these holes form an ordered lattice such that the crystal unit of ${\mathrm{Fe}}_7$${\mathrm{S}}_8$ does not have the NiAs unit but one much more complicated, pseudohexagonal and slightly monoclinic, containing 8 ${\mathrm{Fe}}_7$${\mathrm{S}}_8$. This unit is such that the successive planes of iron perpendicular to the pseudo-hexagonal axis are not identical: only the odd-numbered planes contain holes. Because the two sublattices are crystallographically different, we have imperfect antiferromagnetism or ferrimagnetism, analogous to that of ferrites. A magnetic study by Benoit, at temperatures above the Curie point, seems to show that the ordered distribution of the holes disappears at 560°K. Finally, a thermomagnetic study by Pauthenet shows that the pseudo-hexagonal axis, which at ordinary temperature is a direction of very difficult magnetization, becomes progressively, at lower temperatures, a direction of easy magnetization.

If Permalloy (76 percent Ni-24 percent Fe) which has been previously quenched from 600°C is annealed at 490°C, its energy content decreases with time of annealing, not monotonically but in two steps. By direct measurement of the time-rate of energy decrease, it was concluded that the first step is connected with formation of short-range order and the second with that of longrange order.

The effect of a magnetic field applied during the course of cooling on the maximum permeability is associated mainly with formation of short-range order. Taking into consideration the fact that the saturation of the ordered state is about 4 percent higher than that of the disordered one, one would expect the short-range order to develop in the form of prolate ellipsoids elongated in the direction of spontaneous magnetization. Torque curves, measured on a disk cut from a Permalloy crystal parallel to the (110) plane and heat treated in a magnetic field showed uniaxial anisotropy, superposed on the ordinary cubic one. This uniaxial anisotropy increases with the formation of short-range order, but the formation of long-range order, followed after that of short-range one, has a tendency to annihilate it. The constricted hysteresis loop, which is characteristic of the Perminvar property, becomes most eminent at the end of short-range order formation.

If we assume two neighboring uniaxial domains, whose axes intersect perpendicularly with each other, and whose boundary bisects the angle between them, we can easily calculate the hysteresis loop of constricted form. The main characteristic of this model is that the displacement of the boundary cannot take place even in a strong field.

In attempting to explain the unusual magnetic properties of the iron-nickel alloys, single crystals of alloys containing 35 to 100 percent nickel were prepared, and measurements made of the magnetic crystal anisotropy and magnetostriction as dependent on cooling rate. It is confirmed that there is a large effect of cooling rate on the anisotropy in the region near Fe${\mathrm{Ni}}_3$, but the experiments show also a substantial effect between 50 and 85 percent nickel. Two magnetostriction constants, ${\lambda }_{100}$ and ${\lambda }_{111}$, were measured on the same crystals. The effect of cooling rate on magnetostriction was found to be substantial only in the composition range 70 to 80 percent nickel. When the specimens are quenched, ${\lambda }_{111}$ goes through zero for a nickel content just below 80 percent nickel, a composition very close to that for highest permeability. This is understandable because the magnetostrictive strain caused by movement of the boundary between two domains, each magnetized spontaneously in a [111] direction, depends on ${\lambda }_{111}$ alone. The same physical picture predicts that near 45 percent nickel, where [100] is the direction of easiest magnetization and ${\lambda }_{100}$ goes through zero, the permeability vs composition curve should again have a maximum. Such a maximum is known to exist, and initial permeabilities as high as 15 000 have been observed.

Although simple theory suggests that domain-rotation should occur in very weak fields when the crystal anisotropy is very small (75 percent nickel in quenched alloys), nevertheless, rotation involves magnetostrictive strains which prevent ${\mu }_0$ from becoming infinite. Internal poles are also likely to be formed. In slowly cooled alloys the anisotropy is zero at about 63 percent nickel; here there are random strains caused by magnetostriction and possibly also by atomic ordering.

The principal changes in magnetic properties with composition are explained in terms of the crystal anisotropy and magnetostriction, and their change with heat treatment.

The spin-wave theory in a modified form is applied to antiferromagnetism. The interaction between different modes of spin-waves, which is due to the higher order terms omitted in the customary spin-wave treatment, is taken into account in a self-consistent manner. It is shown that the interaction terms cause a change of the frequency spectrum of spin-waves which is equivalent to the existence of an anisotropic field. The upper limits of the ground levels are calculated. The variational method can also be applied to the discussions of the stable configurations of magnetization vectors in anisotropic and external fields, and it is consistent with the molecular field theory.

Measurements on the temperature variation of spontaneous magnetization by both the magnetothermal and magnetic methods have hitherto been confined to nickel; the extension of these measurements, calling for greater sensitivity, is discussed. To the direct method devised by Weiss and Forrer has been added a direct current amplifier, which allows a small magnetocaloric rise of temperature to be measured accurately. The original ferromagnetic balance devised by Sucksmith has been improved and now is capable of wider application to measurements of magnetic intensity in fields which are due to either air core coils or electromagnets. The method is not complicated by the presence of any image effect so that measurements of $\frac{d\sigma }{\mathrm{dH}}$ in high fields can be made with considerable precision.

Measurements on a copper-nickel alloy (27.5 percent Cu) have been made, and it is shown that the two methods give identical results except in the immediate neighborhood of the Curie temperature, where the thermal measurements give a steeper descent to the temperature axis with little "tail," while the magnetic data indicate a higher Curie temperature with a significant tail. Below the Curie temperature the linear relationship between the magnetocaloric rise of temperature and the square of the intensity magnetization is found as in nickel and iron; above this temperature there is pronounced curvature.

Measurements have also been carried out on a mixed ferrite (MgO ZnO 2${\mathrm{Fe}}_2$${\mathrm{O}}_3$). Satisfactory agreement between the results by the two methods are obtained, both curves differing markedly from the law of corresponding states for the ferromagnetic elements.

The magnetic anisotropy of single crystals of Fe${\mathrm{F}}_2$ and Co${\mathrm{F}}_2$ has been measured over the temperature range 11 to 340°K. Like Mn${\mathrm{F}}_2$, the anhydrous difluorides of iron and cobalt have the tetragonal rutile crystal structure, and the anisotropy results are compared with those found by Stout and Griffel for Mn${\mathrm{F}}_2$. In all three compounds the magnetic susceptibility parallel to the crystallographic $c$ axis is at room temperatures greater than that in a direction perpendicular to this axis. Because of the orbital magnetic moment the high temperature anisotropy is much greater for Fe${\mathrm{F}}_2$ and Co${\mathrm{F}}_2$ than for Mn${\mathrm{F}}_2$. As the temperature is lowered, the anisotropy changes sign and at 11°K has large negative values, indicating that the susceptibility parallel to the $c$ axis becomes small. This indicates that at low temperatures there is an ordered antiferromagnetic arrangement with the elementary magnetic moments aligned parallel and antiparallel to the $c$ axis. Such a magnetic structure has been found from neutron diffraction measurements by Shull and Erickson. The anomalous behavior of the magnetic anisotropy, associated with the antiferromagnetic ordering, is in the case of Co${\mathrm{F}}_2$ spread out over a much wider temperature range than in the case of Mn${\mathrm{F}}_2$ and Fe${\mathrm{F}}_2$. At the lowest temperatures the anisotropy of Mn${\mathrm{F}}_2$ varies as $T^2$, whereas those of Fe${\mathrm{F}}_2$ and Co${\mathrm{F}}_2$ vary as the fourth power of the temperature.

Four series of observations carried out in the Kamerlingh Onnes Laboratory on Cu${\mathrm{Cl}}_2$·2${\mathrm{H}}_2$O crystals are reviewed. The magnetization curves confirm the general picture given by the theoretical analysis of Gorter and Haantjes. At the lower temperature a sharp threshold field is found in the crystallographic $\mathrm{ac}$ plane with a minimum value of 6500 φ; at higher temperature its value increases somewhat.

Specific heat measurements reveal the existence of a short-range order tail above the sharp Néel temperature at which antiferromagnetism vanishes.

In the investigations on proton magnetic resonance a sharp transition is found between a nonsymmetrical paramagnetic resonance diagram and a symmetrical resonance diagram characteristic for antiferromagnetism. In this way it is found that the Néel temperature depends on the direction of the magnetizations.

It is possible to follow the turn-over of the magnetizations near the threshold field. The position of the protons and the nature of the sublattices have been determined. The sublattices do not exchange position within ${10}^{-4\mathrm{}}$ sec. Microwave resonances have been observed at 9400 and at 4000 megacycles/sec. The absorption bands are confined to the neighborhood of the turn-over fields. General agreement with Ubbink's theoretical treatment is found.

Cunico, Cunife, and the various types of Alnico are structurally analogous in that at the state of high coercive force the crystal structure of the precipitate is distorted from a cubic lattice to a tetragonal lattice. A single empirical relation has been derived from the data for these types of materials in which maximum coercive force is directly related to degree of tetragonality and saturation induction of the precipitate. On the basis of the fine particle theory this result suggests that not only shape anisotropy but also crystal anistropy, as affected by strain, contributes to the coercive force. This work represents the first successful attempt to correlate the coercive force of the various commercial permanent magnet alloys with more fundamental characteristics.