658 MAGNETISM [FERROMAGNETISM right angles to the magnetic plane, about 150,000 gauss would be required. In whatever direction fields are applied, therefore, unless they are large, the direction of magnetization in the crystal will be approximately that of the axis of easy magnetization. The general effect of applying a field to a substance consisting of an aggregate of crystals of this type may readily be followed. In an unmagnetized state the crystals will be spontaneously magne Fig. ILLUSTRATING WEISS'S "DOMAIN" THEORY OF FERROMAGNETISM tized, but their magnetic axes will be distributed at random. Con sidering the crystals whose axes lie along the direction of an applied field, half will be magnetized in the field direction, and half in the opposite direction. When the magnitude of the field exceeds the coercive field, the magnetic moments of these "oppos ing" crystals will change their directions owing to an "irreversi ble" change in direction of the moments of the elementary car riers in them. For a crystal whose axis makes an angle 0 with the field, the irreversible change will occur when the resolved field exceeds that is, when H is greater than Hdcos0. As the field increases the first result will be that the magnetic moments of more and more crystals change sign, so that they have a com ponent in the field direction. The actual direction of the axis does not change. As the field increases to higher values, however, there will be a further reversible increase in the magnetization, due to the elementary magnets tending to turn in the field direc tion, and taking up an equilibrium position depending on both the external field, and the molecular field (which is responsible for the spontaneous magnetization). The successive states are rep resented diagrammatically in fig. 36, in which the arrows represent the direction of the magnetic moments of individual crystals. (It should be noted that change in the direction of the moment of a crystal does not imply change in the orientation of the crystal itself, but simply of the magnetic carriers in it.) By supposing that there are in an ordinary piece of iron small magnetic domains with properties of the same type as those found for the simple pyrrhotite crystals, the general character of the variation of the intensity of magnetization with the field, including hysteresis effects, which is observed in ferromagnetics can be accounted for. 'Weiss's theory of ferromagnetism is thus made up of two parts. In the first, the assumption of a molecular field, proportional to the intensity of magnetization, is shown to lead to the possibility of spontaneous magnetization. In the second, it is shown that the observed magnetic behaviour of ordinary ferro magnetic materials in external fields may be explained, in a gen eral manner, by supposing them to be built up of aggregates of domains in which there is spontaneous magnetization. The process of magnetization, by external fields, is to a large extent the ren dering apparent of the magnetization already existing, but more or less masked owing to the varying directions of the axes of the spontaneously magnetized domains.
Ferromagnetics Above and Below the Curie Tempera ture.—It is difficult to determine exactly the Curie temperature at which a substance ceases to be ferromagnetic, and there are considerable differences in the results of different observers. Some values which have been found are given in the following table, those for iron and nickel being probably correct to one or two degrees, the others less accurate : Curie Temperatures (Degrees Centigrade) The Curie temperatures may be markedly affected by the presence of impurities. Pure metals regain their ferromagnetism on cooling at the same temperature as that at which they lose it on heating. Some alloys, however, have to be cooled to a much lower temper ature. This temperature hysteresis is shown by iron-nickel alloys containing less than 3o% nickel, and by alloys of iron and man ganese. An alloy with 22% manganese, for example, loses its ferromagnetism, on heating, at 62o° C, but does not regain it on cooling until a temperature of —3o° is reached. Thus at ordi nary temperatures the alloy can exist in two states, in one of which it has no ferromagnetic properties, so that a "non-magnetic" manganese steel can be manufactured. At temperatures well below the Curie point the intensity of magnetization increases only very slowly in large fields. This is illustrated by some curves obtained for nickel, by P. Weiss and R. Forrer.
The extrapolated value of the intensity for zero applied field, may be taken, on the basis of the Weiss theory, as the value of the spontaneous magnetization at the temperature. The value of the spontaneous magnetization may also be deduced from a study of the magnetocaloric effect, which is considered later. It is ap parent from the magnetic isothermal curves for nickel that the spontaneous magnetization, except at high temperature, differs little from the ordinary so-called saturation intensity obtained in strong fields. By carrying out experiments in strong fields at dif ferent temperatures, the spontaneous magnetization may be found, and plotted as a function of the temperature. Such a curve for nickel is shown in fig. 37. Although of the same general shape as the 'theoretical' curve, it differs from it in that the decrease in the intensity as the temperature is increased at low temperatures is much more gradual. Somewhat similar results have been obtained for iron and cobalt.
At very low temperatures the saturation intensity corresponds to the complete alignment of the magnetic carriers, i.e., to satura tion in the Langevin sense. The gram atomic magnetic moment may be calculated directly from the results. For a substance of atomic weight A and density p, if is the saturation intensity