Discovery of magnetic dichroism by P. Zeeman and H.A. Lorentz

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        The Figure (a) shows the classical electronic orbits of an electron bound to an unmovable mass center by an isotropic elastic force in the presence of a magnetic field, H. The orbits have been slightly displaced for reasons of presentation. The normal vibrations are labeled s, s’, p, where s stands for "senkrecht" = perpedicular and p for parallel. The oscillator p is not affected by the magnetic field; the oscillators s, s’ have frequencies that lie symmetrically below and above the unperturbed frequency of the p oscillator, Figure (c, f). This effect was observed by Zeeman in measurements of the emission spectra of sodium (the D1 and D2 bands) contained in a flame. The splitting amounts twice the Larmor angular frequency, which is linear in the field and proportional to the ratio of the charge and the mass of the electron:

The electron is in accelerated motion and therefore, radiates permanently at the expense of the amplitude of the oscillations (of course, this comment applies to the classical theory adopted here). The system emits radiation in all directions of which two have been indicated by green arrows (labeled by wave vectors k and k’ in Figure (a)). The polarization of the radiation is determined by the electronic motion, and depends on the direction of observation as defined with respect to the direction of the magnetic field (here, parallel or perpendicular to H). The polarization properties were evaluated and brought to the attention of Zeeman by Lorentz and established in subsequent polarization measurements conducted by the former investigator. The circular orbits s and s’ give rise to either circularly (Figure (b)) or linearly (Figure (e)) polarized light depending on the direction of observation (N.B. circular orbits look linear when considered from a direction perpendicular to H). The radiation generated by an electron in the p orbit has zero intensity in the direction of the magnetic field (Figure (b)). Hence, in parallel observation there is only radiation originating from the two s oscillators, that is, the line in the middle of the stick spectrum has zero intensity (Figure (c)). In perpendicular observation, the amplitudes of the s lines are half that of the p line (Figure (f)). The measurement of the size of the Zeeman splitting allowed the determination of the charge-to-mass ratio of the electron and of the sign of the electronic charge (see below).

        The magnetic spectra observed by Zeeman revealed an intensity difference in the emission of polarized light. Thus, the emitted light exhibits an effect called magnetic dichroism. Moreover, the dichroism was found to depend on the frequency of the light, a phenomenon called dispersion. Early in the 19th century it had been shown by Fraunhofer that absorption and emission phenomena observed for the same material give rise to spectra with identical line positions. Thus, the magnetic dichroism described above must also be observable in absorption spectra, and actually is. Figure (d) indicates that Magnetic Circular Dichroism (defined as the difference in absorption of Left and Right circularly polarized light) is observed in parallel observation. Figure (g) indicates that Magnetic Linear Dichroism (defined as the difference in the absorption of Parallel and Perpendicular linearly polarized light) is observed in perpendicular observation. The differential spectra are obtained from the Zeeman spectra by flipping the sign of one of the stick components (Figure (d, g)). Taking into account the bandwidth of the electronic transition (which, in the case of molecular systems is considerably larger than magnetic splitting due to coupling to nuclear vibrations), one obtains the 1st and 2nd derivative contours for MCD and MLD, respectively, shown in Figure (d, g). In the current literature, these spectra are designated A1 (MCD) and A2 (MLD). The A1 MCD spectrum is proportional to minus the derivative of the absorption band, the sign being for an elastically bound particle with a negative charge. In other words, the differential absorption spectrum, as deduced from the Zeeman spectrum, provides the sign of the electronic charge, a matter that remained unsettled till Zeeman’s work and Thompson’s discovery of the free electron in the same year.
        Noting that

(where f is the band shape function) it follows that the amplitude of MCD is proportional to H and MLD to H2.

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