arXiv subjects

Robin Silber

Publications and source records attributed to Robin Silber.

6 recordsLinked to original sources

arXiv2026

Cubic magneto-optic Kerr effect in Co(111) thin films

The magneto-optic Kerr effect (MOKE) is often applied as a tool for the magnetic characterization of thin films. Here, the change in polarization upon reflection from the magnetized sample is mainly regarded as being linearly proportional to the magnetization $\mathbf{M}$ (LinMOKE). MOKE contributions of second order in $\mathbf{M}$, also known as quadratic MOKE (QMOKE), which are proportional to $\mathbf{M}^2$, have also been studied in the past and used in thin film characterization. Recently, we reported on a systematic investigation of third-order MOKE contributions, named cubic MOKE (CMOKE) in Ni(111) thin films. This CMOKE manifests itself as an anisotropic contribution to the MOKE signal (with regard to the crystallographic orientation) measured in longitudinal or transversal configuration in full magnetic saturation. While LinMOKE (odd in $\mathbf{M}$) and QMOKE (even in $\mathbf{M}$) can easily be separated by methods based on magnetization parity, this no longer holds true for LinMOKE and CMOKE (odd in $\mathbf{M}$). It is therefore crucial to be aware of CMOKE contributions in order to correctly interpret MOKE data. Here, we report on the observation of CMOKE in thin film heterostructures with structurally twinned and untwinned Co(111) layers, demonstrating that a large CMOKE is not only present in Ni thin films. Additionally, we show that the observed anisotropic contributions cannot stem from LinMOKE by analyzing their dependence on the angle of incidence (AoI) of light. While the QMOKE is almost vanishing in Co(111) using light with wavelengths of 635\,nm and 406\,nm, the CMOKE contributions reach up to about 30\% of the LinMOKE contribution at an AoI of 45 degrees and become even more dominant towards normal AoI, which emphasizes the importance of higher-order MOKE effects in magneto-optic experiments.

physics.optics↗

arXiv2026

Cubic-in-magnetization contributions to the magneto-optic Kerr effect investigated for Ni(001) and Ni(111) thin films

*The abstract of this article is too long to be included in the arXiv metadata; please see the paper for the full abstract.* ...In this paper, we introduce the detailed theory of cubic-in-magnetization magneto-optic Kerr effect (CMOKE) by deriving the magneto-optic tensor of third order in magnetization, denoted as $\bm{H}$, and comparing the strength of CMOKE for different crystal orientations theoretically and experimentally. In crystals with cubic symmetry, the tensor $\bm{H}$ is described by two independent parameters $H_{123}$ and $H_{125}$. Together with the linear magneto-optic tensor $\bm{K}$ and quadratic magento-optic tensor $\bm{G}$, the permittivity tensor is described up to third order in magnetization. We analytically describe equations of the MOKE including the contribution of QMOKE and CMOKE itself for (001)- and (111)-oriented cubic crystal structures. Those are compared to experimental measurements of two samples with an (001)- and (111)-oriented fcc Ni layer, respectively. Further, we use Yeh's 4$\times$4 transfer matrix calculus to simulate and describe the experimental measurements phenomenologically from the permittivity tensor up to third order in $\bm{M}$. We find that the MOKE anisotropy that stems from the magneto-optic tensor $\bm{H}$ described as $\Delta H = H_{123}-3H_{125}$, is much more pronounced for the (111)-oriented cubic crystal structure, for which it manifests as three-fold in-plane angular dependencies of MOKE with longitudinal and also with transversal magnetization direction, respectively.

physics.optics↗

arXiv2022

Cubic magneto-optic Kerr effect in Ni(111) thin films with and without twinning

In most studies utilizing the magneto-optic Kerr effect (MOKE), the detected change of polarized light upon reflection from a magnetized sample is supposed to be proportional to the magnetization $\boldsymbol{M}$. However, MOKE signatures quadratic in $\boldsymbol{M}$ have also been identified and utilized, e.g., to sense the structural order in Heusler compounds, to detect spin-orbit torques or to image antiferromagnetic domains. In our study, we observe a strong anisotropic MOKE contribution of third order in $\boldsymbol{M}$ in Ni(111) thin films, attributed to a cubic magneto-optic tensor $\propto $ $\boldsymbol{M}^3$. We further show that the angular dependence of cubic MOKE (CMOKE) is affected by the amount of structural domain twinning in the sample. Our detailed study on CMOKE for two selected photon energies will open up new opportunities for CMOKE applications with sensitivity to twinning properties of thin films, e.g. CMOKE spectroscopy and microscopy or time-resolved CMOKE.

physics.optics↗

arXiv2020

Scaling of quadratic and linear magnetooptic Kerr effect spectra with L2$_1$ ordering of Co$_2$MnSi Heusler compound

The Heusler compound Co$_2$MnSi provides a crystallographic transition from B2 to L2$_1$ structure with increasing annealing temperature $T_a$, being a model system for investigating the influence of crystallographic ordering on structural, magnetic, optic, and magnetooptic (MO) properties. Here, we present quadratic magnetooptic Kerr effect (QMOKE) spectra depending on $M^2$ in addition to the linear magnetooptic Kerr effect (LinMOKE) spectra being proportional to $M$, both in the extended visible spectral range of light from 0.8\,eV to 5.5\,eV. We investigated a set of Co$_2$MnSi thin films deposited on MgO(001) substrates and annealed from 300$^\circ$C to 500$^\circ$C. The amplitude of LinMOKE and QMOKE spectra scales linearly with $T_a$, and this effect is well pronounced at the resonant peaks below 2.0\,eV of the QMOKE spectra. Furthermore, the spectra of the MO parameters, which fully describe the MO response of Co$_2$MnSi up to the second order in $M$, are obtained dependend on $T_a$. Finally, the spectra are compared to ab-initio calculations of a purely L2$_1$ ordered Co$_2$MnSi Heusler compound.

physics.app-ph↗

arXiv2019

Quadratic magnetooptic Kerr effect spectroscopy of Fe epitaxial films on MgO(001) substrates

The magnetooptic Kerr effect (MOKE) is a well known and handy tool to characterize ferro-, ferri- and antiferromagnetic materials. Many of the MOKE techniques employ effects solely linear in magnetization $\bm{M}$. Nevertheless, a higher-order term being proportional to $\bm{M}^2$ and called quadratic MOKE (QMOKE) can additionally contribute to the experimental data. Here, we present detailed QMOKE spectroscopy measurements in the range of 0.8 -- 5.5\,eV based on a modified 8-directional method applied on ferromagnetic bcc Fe thin films grown on MgO substrates. From the measured QMOKE spectra, two further complex spectra of the QMOKE parameters $G_s$ and $2G_{44}$ are yielded. The difference between those two parameters, known as $\Delta G$, denotes the strength of the QMOKE anisotropy. Those QMOKE parameters give rise to the QMOKE tensor $\bm{G}$, fully describing the perturbation of the permittivity tensor in the second order in $\bm{M}$ for cubic crystal structures. We further present experimental measurements of ellipsometry and linear MOKE spectra, wherefrom permittivity in the zeroth and the first order in $\bm{M}$ are obtained, respectively. Finally, all those spectra are described by ab-initio calculations.

physics.optics↗

arXiv2018

Quadratic magnetooptic spectroscopy setup based on photoelastic light modulation

In most of the cases the magnetooptic Kerr effect (MOKE) techniques rely solely on the effects linear in magnetization ($\bm{M}$). Nevertheless, a higher-order term being proportional to $\bm{M}$$^2$ and called quadratic MOKE (QMOKE) can additionally contribute to experimental data. Handling and understanding the underlying origin of QMOKE could be the key to utilize this effect for investigation of antiferromagnetic materials in the future due to their vanishing first order MOKE contribution. Also, better understanding of QMOKE and hence better understanding of magnetooptic (MO) effects in general is very valuable, as the MO effect is very much employed in research of ferro- and ferrimagnetic materials. Therefore, we present our QMOKE and longitudinal MOKE spectroscopy setup with a spectral range of 0.8--5.5\,eV. The setup is based on light modulation through a photoelastic modulator and detection of second-harmonic intensity by a lock-in amplifier. To measure the Kerr ellipticity an achromatic compensator is used within the setup, whereas without it Kerr rotation is measured. The separation of QMOKE spectra directly from the measured data is based on measurements with multiple magnetization directions. So far the QMOKE separation algorithm is developed and tested for but not limited to cubic (001) oriented samples. The QMOKE spectra yielded by our setup arise from two quadratic MO parameters $G_s$ and $2G_{44}$, being elements of quadratic MO tensor $\bm{G}$, which describe perturbation of the permittivity tensor in the second order in $\bm{M}$.

physics.ins-det↗