Theory of magnetic circular dichroism spectroscopy technique in reflected light using an additional mirror

TL;DR

This paper develops a theoretical framework for magnetic circular dichroism spectroscopy in reflected light using an additional mirror and phase modulation, simplifying the setup and enabling direct measurement of RMCD components.

Contribution

The paper introduces a simplified RMCD spectroscopy scheme with an additional mirror and phase modulation, allowing direct extraction of RMCD signals without an analyzer.

Findings

The method requires measuring three electrical signals: $V_{dc}$, $V_f$, and $V_{2f}$.

Ratios of these signals yield linear equations for RMCD components.

The approach simplifies the experimental setup and data analysis.

Abstract

The theory of the method of magnetic circular dichroism spectroscopy in reflected light (RMCD) has been developed using a simplified scheme without an analyzer, with the use of an additional mirror in the optical system and with the application of the method of phase modulation of the light wave using a photoelastic modulator. An additional mirror reflector, together with the mirror surface of the sample, forms a double mirror located between the pole pieces of a powerful laboratory electromagnet. The presence of an additional mirror leads to mixing of the amplitude ($\Delta R/R$) and phase ($\Delta \phi$) RMCD-components in the amplitudes of the signals at the first and second harmonics of the phase modulation. It is shown that the RMCD spectroscopy technique using a simplified scheme and an additional mirror requires the synchronous measurement of three electrical signals proportional to the amplitudes of the corresponding terms in the expression for the total intensity of monochromatic radiation detected by the photodetector: a constant signal $V_{dc}$ and high-frequency amplitudes $V_f$ and $V_{2f}$ at phase modulation frequencies $f$ and $2f$. The ratios $V_f/V_{dc}$ and $V_2f/Vdc$ determine a system of linear equations for $\Delta R/R$ and $\Delta \phi$ with known ellipsometric parameters $\tan\Psi$ and $\Delta$ of the additional mirror, which are found either from additional measurements using an ellipsometer or directly (in sity) using the RMCD spectrometer itself.