Experimental observations are reported on the magnetic properties of thin evaporated films of nickel. The saturation magnetization follows the general prediction of Klein and Smith after somewhat arbitrary modifications on the basis of fitting the Weiss curve for bulk specimens, as suggested by Drigo. Qualitatively observed properties due to domain structure follow the predictions of Kittle. The surface roughness of the specimens has been carefully controlled. Measurements of temperature coefficient of resistance have led to modification of the theory of electron mean free path in thin films. The mean free path is found to vary at small thicknesses, rather than remaining constant as assumed by Fuchs and Sondheimer. The surface roughness has been estimated with the help of this theory. The films of nickel behave as if surface variations extend into the film approximately 3 angstroms from each surface.

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.

The value of the saturation magnetization at absolute zero of BaO·6${\mathrm{Fe}}_2$${\mathrm{O}}_3$ and related compounds can be explained as due to noncompensated antiferromagnetism.

The Bloch wall formation in small particles is discussed. One is led to the assumption that in these materials Bloch walls are nucleated at imperfections. In specimens containing randomly oriented large crystals, Bloch wall formation becomes appreciable at a positive field strength of the order of $4\pi I_s$.

By orienting the crystals in a magnetic field ${\mathrm{}\left(\mathrm{BH}\right)\mathrm{}}_{max}$-values of 3×${10}^6$ gauss oersted have been obtained.

The critical diameter for wall formation changes with temperature. An excess of walls formed at a different temperature from the temperature of measurement may persist in a metastable equilibrium.

This is a brief explanation of the magnetic properties of fine ferromagnetic grains of single elementary domains, especially in reference to the influence of time on the magnetization at a given temperature. Application is made to the interpretation of the thermoremanent magnetization of lavas and clays and to the determination of the direction and intensity of the terrestrial magnetic field in the past. It is shown that, when the substance contains two kinds of fine ferromagnetic grains with clearly different Curie points, it is possible, under certain conditions explained in the text, that the constituent having the lowest Curie point becomes magnetized in a direction opposite to the exterior field: there arise, by this phenomenon, interactions between the grains and the demagnetizing field created by the constituent having the highest Curie point. Also, in certain cases, the total thermoremanent magnetization is directed inversely to the acting field. Recently Nagata found samples of lava in which the thermo-remanent magnetization obeys the mechanism thus described. In the geophysical interpretation, there will be, then, reason to keep in mind the possibility of this curious phenomenon, in considering the possible inversions of the terrestrial magnetic field.

The frequencies at which electronic resonance will occur apparently lie beyond the region now available with conventional microwave equipment for those materials having Curie temperatures well above 0°K. ${\mathrm{Cr}}_2$${\mathrm{O}}_3$, MnO, MnTe, and MnSe show a large decrease in the amount of resonance absorption as the material (powdered) is lowered through its Curie temperature, with only a small residual absorption remaining in the antiferromagnetic region. MnSe has an absorption vs temperature hysteresis loop that is correlated with a magnetic susceptibility loop previously reported for this material. The $g$ values remain constant as the absorption decreases. Considerable absorption is found at zero static magnetic field for MnO, MnS, and MnTe. The line widths increase sharply as the temperature of the material approaches the Curie temperature. CoO and V${\mathrm{O}}_2$ give no detectable absorption either above or below their Curie temperatures. NiO and CuO show no absorption in the antiferromagnetic region.

Neél's phenomenological theory of antiferromagnetism at zero temperature has been worked out for a three-dimensional case. When the external magnetic field comes near to a certain hyperbola in the field space lying in the plane through the favored and the least favored direction of magnetization, an anomaly occurs. This anomaly consists of a rapid turn-over of the two opposed directions of magnetization into the direction perpendicular to the plane just mentioned. At much higher fields the two opposed directions of magnetization will deviate towards the field, and finally antiferromagnetism will go over into paramagnetic saturation.

Following the general method of Kittel, Ubbink has investigated antiferromagnetic resonance. At not too high frequencies two resonance fields will be flanking the hyperbola in field space. At higher frequencies one resonance field will decrease and vanish, while the other one will approach the field of paramagnetic resonance.

In this paper the problem of the line shape in paramagnetic resonance when large exchange interaction is present is discussed from the standpoint of a simplified mathematical model. The mathematical model can be called the model of "random frequency modulation": It is assumed that the atom absorbs a single frequency, which varies over a distribution determined by the dipolar local fields, but that this frequency varies randomly in time at a rate determined by the exchange interactions.

The predicted line shape in the case in which exchange is large is of resonance type in the observable center of the line, but falls off more rapidly in the wings. This line shape has been verified experimentally in a number of cases. This conclusion seems quite independent of any assumption about the type of random frequency modulation, etc. The quantitative conclusions are reached in the following way: It is suspected, since the exchange motion is the superposition of the effects of a number of neighbors which is not particularly small, that a good approximation to the modulation function is Gaussian noise with a Gaussian spectrum. This, of course, is what would result from the superposition of a large number of rather small effects. Under this assumption both the second moment (which is independent of exchange) and the fourth moment of the line shape can be calculated. This kind of modulation is the simplest one which does give a finite fourth moment; a Markoffian, or "jump," type of modulation, which might seem more reasonable at first, does not. These moments are then compared with the moments computed by Van Vleck [Phys. Rev. 74, 1168 (1948)] to fix the two adjustable parameters, mean square frequency, and average rate of change of frequency, of the theory.

The result as to line breadth, which is essentially $\Delta \cong \frac{{〈\left(\Delta {\omega }^2\right)〉}_{\mathrm{Av}} \mathrm{d}\mathrm{i}\mathrm{p}\mathrm{o}\mathrm{l}\mathrm{e}-\mathrm{d}\mathrm{i}\mathrm{p}\mathrm{o}\mathrm{l}\mathrm{e}}{\frac{J}{\hslash }},$ if $J$ is the exchange integral, can be compared with observed line breadths by estimating $J$ from Curie-Weiss constants for a number of materials. The results are quite satisfactory if the theory is extended in two ways: (a) When the exchange frequency is larger than the resonance frequency, it can be shown that the off-diagonal elements of the dipolar interaction must be included, leading to a line-width larger by a factor of roughly 10/3; (b) in a number of cases hyperfine and Stark splitting is contributing importantly to the width.

The good agreement with experiment in the cases we have investigated leads us to believe that a quantitative approach to the paramagnetic resonance line breadth problem, using only the already known concepts of dipolar interaction, exchange narrowing, and fine structure splitting, will probably explain all the observed phenomena.