The Magnitude of the Gyromagnetic RatioAuthor(s): O. W. RichardsonSource: Proceedings of the Royal Society of London. Series A, Containing Papers of aMathematical and Physical Character, Vol. 102, No. 718 (Feb. 1, 1923), pp. 538-540Published by: The Royal SocietyStable URL: http://www.jstor.org/stable/94028 .

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538

The Magnitude of the Gyrornagnetic Ratio. By 0. W. RICHARDSON, F.R.S., King's College, London.

(Received December 4, 1922.)

The accurate experiments of Chattock and Bates* prove that the angular momentum arising in a ferromagnetic substance from unit change in its magn etic moment is very nearly, if not exactly, one half the value 2n/e= 1 13 x 10-7, which seemed to me the most likely when I first dis- cussed this effect.t This conclusion is supported by the fact that the improvements which have been introduced into this subject by successive experimenterst in recent years hiave led to values showing a strong tendency to settle at the same limit n/e - 5 *65 x 10-8. This value is also in general agreen ent with that deduced by Barnett? from experiments on the converse effect. It seems desirable therefore to reconsider the interpretation of this ratio.

The higher value 2m/e is obtained by making rather definite assumptions, which evidently require modification, as to the nature of the phenomlena. These assumptions are that the process of magnetization involves the turning of electron orbits, and that nothing else which may occur has any important influence on the phenomena. The inertia of the electrons is assumed to be entirely of the type which controls the deflection of a beam of cathode rays by a magnetic field, and any change in the motion of the positively charged part of the atom is disregarded. These assumptions are essentially the same as those of the theories of Langevin alnd Weiss which have been successful in dealing with purely magnetic phenomena.

Onie way of escape is to suppose that the inertia of the electrons in these nagnetic phenomena is not of the usual type. As an illustration of such possibilities, I showed at the Solvay Conference at Brussels in 1921 that the spin imposed on an electron by placing it in a magnetic field gives rise to an angular nmomtentum and magnetic moment whose ratio depends on the consti- tution assumed for the electron. If the electron is assumed to be a chlarged

* Chattock and Bates, 'Phil. Trans.,' A, vol. 223, p. 257 (1922). t Richardson, 'Phys. Rev.' (1), vol. 26, p. 248 (1908). t Einstein and de Haas, 'Verh. d. Deutsch. Physik. Ges.,' vol. 17, p. 152 (1915). De

Haas, 'Verh. d. Deutseh. Physik. Ges.,' vol. 18, p. 423 (1916). J. Q. Stewart, ' Phys. R-%ev.' (2), vol. 11, p. 100 (1918). Beck, 'Ann. der Physik,' (4), vol. 60, p. 109 (1919). Arvidsson, 'Physik. Zeits.,' vol. 21, p. 88 (1920).

? Barnett, 'Phys. Rev.' (2), vol. 6, p. 239 (1915); vol. 10, p. 7 (1917).

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The Magnyritude of the Gyromagnetic Ratio. 539

sphere, the charges being held in position by a non-electromagnetic tension of the amount suggested by Poincare, the ratio of angular momentum to magnetic moment created is found to be n/e instead of 2m/e. This effect, however, is diamagnetic and very small, and, in fact, such ways of escape do not seem at all promising. The turning-orbit theory of the Langevin type goes so far in explaining magnetic phenomena that it is almost certain that it is true in its essentials.

We are now practically driven, I think, to the conclusion that the motions of the positively charged parts of the atoms cannot be disregarded in con- sidering these gyromagnetic phenomena. The formulhe relevant to their discussion are given in my paper in the 'Physical Review' in 1908. They are

U, -2 (NMA+nma) (1)

and Mz NEA-[ned, (2)

where Uz and M, are respectively angular momentum and magnetic moment per unit volume for any axis Oz, N, n numbers of electrons per unit volume,

M, m masses of electrons and A, a the respective mean areal velocities about the Oz axis: capital letters refer to positive and small letters to negative electrons. If we assume the effect of the areal velocity of the positive parts

to be negligible and put A - o in these formulw we clearly get the ratio of angular momentum to magnetic moment to be 2m/e, the value appropriate to turning orbits of negative electrons. If the areal velocity of the positive parts is not negligible it is clear that it will be much more important in the expression (1) for the angular momentum than it is in expression (2) for the magnetic moment. This follows because the numerical magnitude of NM/nm is much greater than that of NE/ne. In the unequivocal case of the hydrogen atomi NM/nm is about 1800 times NE/ne. With the ferromagnetic elements the values of these quantities depend on the precise allocation we give to the magnetically effective orbits, but a disparity of comparable magnitude will always be found to subsist. To obtain a value of the ratio UZ/MZ which is smaller than 2m/e it is necessary that the averaged contribution of the positive charges to the angular momentum established by magnetization should be oppositely directed to that of the negative charges.

This does not necessarily mean that the positive particles are revolving in the atom in an opposite sense to those of the negative electrons, both sets might be revolving in the same sense, but in the act of magnetization the normals to one set might tend to align with the direction of the applied

2 o 2

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540 The iMlagnitude of the Gyromagmiettc Ratio.

field and the other to move away from it. They would, in fact, so tend, owing? to the opposite magnetic polarity of orbits executed in the same sense by charged particles of opposite sign. For the ratio UZ/MZ to fall to the experi- mental value m/e it is necessary and sufficient, on this view of the phenomena, that in the establishment by magnetization of angular momentunm the contribution arising from the positively charged parts of the atom should always be one half of that from the negative electrons and oppositely directed to it. This statement is exact to the degree of accuracy which disregards the effect on the magnetic moment of the positively charged parts in comparison with that from the negatively charged parts of the atom.

It seems possible to proceed further with the help of Bohr's theory. According to Ewing* the saturation intensity of magnetization of iron is very inearly 2 x 10-20 c.g.s. units per atom of iron. The angular momentum corresponding to this agrees within a few per cent. with twice the fundamental quantum unit h/2w. This strongly suggests tha.t the magnetism of iron is due to a pair of parallel or coplanar orbits each having a single azimuthal quantum. I am not able to find that Bohr has published a detailed picture of the structure of the iron atom, but from the constitutions.proposed for argon and krypton it is clear that it will have a number of pairs of symmetrical orbits each with one azimuthal quantum. To account for the fact that the ratio Uz/MZI is mn/e instead of 2m/e it is only necessary to assign another azimuthal quantum to the nucleus. If this orbit turns with the field in the same sense as the two effective electron orbits, as the q-uantum conditions seem to require, its angular momentum will have to be oppositely directed to theirs. In this case, since qnia -2MNA, the A's now denoting the actual areal velocities to which the mean values have become proportional, we have NA/na -nm/2M and

Uz t/1 2 - M) . For the iron nucleus (atomic number 26) E =-26e and M 56 X 1835m. If these numbers are substituted in (3) it is found that the ratio is less than m/e by a little more than one part in 10,000. The denominator on the right- hand side of (3) represents the effect of the motion of the nucleus on the magnetic moment, and the fact that it differs so slighltly from unity justifies our neglect of this effect in discussing the broad features of the phenomena. There are a number of other possible arrangements on the quantum theory which would fit the facts, but this seems to be the simplest and most probable.

* 'Pro1. S. Edin.,' vol. 42, p. 124 (1922).

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