Unusual sign-changing Faraday effect in nanometer-thick magnetic films

Abstract

It is generally believed that the magneto-optical Faraday effect appears in the the bulk of a magnetic material and its sign is fully determined by the sign of the non-diagonal permittivity element. Here we reveal an additional contribution to the Faraday effect from the film interfaces. It becomes notable for films with a thickness of a few tens of nanometers. As a result, in the absorption band of the film a novel feature of the Faraday effect is experimentally observed and numerically confirmed: sign of the Faraday rotation at a fixed wavelength becomes dependent on the film thickness and therefore is ambiguously related to the sign of the gyration and magnetization of the film. We elaborated an analytical model taking into account an interplay between the bulk and surface contributions which nicely describes the experimental data. Moreover, the Faraday rotation coming purely from interfaces without any bulk contribution is demonstrated. Possible applications of the observed unusual Faraday rotation behavior include hardware data encryption and other devices performing polarization control at nanoscale.

Figures (3)

• Figure 1: (a) Scheme of the configuration with opposite FR for the two different thicknesses of magnetic film illuminated by light at a fixed wavelength. (b) The experimentally obtained FR spectra for three films of thicknesses $d$=5 nm, $d=$10 nm, and $d=65$ nm (open circles) compared with calculated spectra (solid curves). (c) Dependencies of the FR angle on the film thickness at light wavelength of 465 nm (first panel), 478 nm (second panel), 490 nm (third panel) and 510 nm (fourth panel), experimentally measured (orange circles) and calculated (dashed lines).
• Figure 2: Physical origin of the sign-changing FR. (a) Interface and bulk contributions (see legends below the graphs) to the FR as a function of the film thickness for the wavelengths $\lambda=465$ nm, $\lambda=478$ nm, $\lambda=490$ nm, $\lambda=510$ nm. (b) The FR dependence on the film thickness $d$ and ratio of imaginary and real parts of the gyration $g"_m/g'_m$. The real part of $g$ is $-0.013$, $\varepsilon = 7.16 + 0.65i$. Wavelength is $\lambda=480$ nm.
• Figure 3: Schematic example of data encryption showing 3 bits with 'up' magnetization read with different combinations of the wavelength keys.