Paramagnetism

The magnetic moment which would be acquired if all the mole cules were aligned parallel to the field is equal to nt; considering unit volume, if / is the intensity acquired, and I,, the saturation intensity, then The Langevin equation shows how the magnetization approaches a saturation value as H is increased; in general, however, with fields which are practically available, ,uH will be very small com pared with kT; the quantity a will then be small, and, to a suf ficient approximation, The magnetization then varies linearly with the field, at a rate indicated by the slope of the tangent at the origin to the Langevin curve (see fig. 27).

Let K be the volume susceptibility, x the specific susceptibility, XM the gram molecular susceptibility, the gas having molecular weight M; let T be the moment per gram molecule, the satura tion moment ; let n be the number of molecules per cu.cm. of a gas, N the number per gram molecule (Avogadro's number). Then constant per gram molecule. It indicates that, unless H can be made very large, or T very small, the susceptibility of a gas will be independent of the field; and that it will be inversely propor tional to the absolute temperature in accordance with Curie's law. Moreover, from the susceptibility, the saturation gram molecular magnetic moment, may be calculated, and, from this the molecular moment, by dividing a 0 by Avogadro's number, A = c The Langevin theory, then, leads to a satisfactory explanation of Curie's law; and for substances which obey it, such as gases and weak paramagnetic solutions, it enables estimates to be made of the magnetic moments of the molecules or ions responsible for the paramagnetism. The results of this application will be dis cussed in connection with those from a more extended form of the theory due to Weiss, which leads formally to the experi mentally observed variation with temperature of the susceptibility of a wider range of substances.

The Molecular Field Theory.

The effective field H, acting on a molecule may be regarded as a resultant of the external field H and that due to the other molecules. In the case of an ideal paramagnetic gas, the field due to the molecules may be neglected, but in general the "molecular field" will play a part in determining the orientation. Weiss supposed that the effect of the molecules was equivalent to that of a magnetic field, H1, proportional to the intensity of magnetization, so that, with N as a proportionality factor, If the inner field arose simply from the mutual magnetic action of the molecules, the constant N would depend on the arrangement of the molecules ; for special cases (e.g., random arrangement of

the molecules, or regular cubical arrangement) it may be shown that N would be equal to -Or (about 4.2), and this may be taken as indicating the order of magnitude to be expected generally. The value which may be calculated for N from the experimental results, however, is in some cases thousands of times greater than this, and in other cases it is negative. The consequences of sup posing that there is a field proportional to the magnetization will therefore be considered without any specific assumption as to its origin. It is necessary to substitute for H in Langevin's treatment. Considering a gram molecule, the Langevin result The Weiss equation indicates that a paramagnetic substance in which there is a molecular field will have a susceptibility varying inversely as the excess of the temperature above a certain critical temperature 0, which is named the Curie temperature. As will be discussed in the next section, ferromagnetic substances have a positive Curie temperature (e.g., that for iron is about 104o° A) below which they have ferromagnetic properties, and above, para magnetic. Among paramagnetics there are many which obey the Weiss law over wide ranges of temperature, 0 being usually rela tively small, sometimes positive and sometimes negative. The inverse of the susceptibility varies linearly with the temperature, so, from the slope of a graph, in which I is plotted against T, X and hence the molecular magnetic moment may be calculated, while the intercept on the temperature axis gives the value of 0, from which the molecular field constant may be found. The graphs sometimes show fairly abrupt changes of slope, indicating a change in the magnetic character of the molecules, so that it is not legitimate to conclude from the fact that 0 is positive over a certain range that a "real" Curie temperature exists below which the substance becomes ferromagnetic. In fact, investigations at very low temperatures have so far brought to light no instances of paramagnetic substances becoming ferromagnetic.