Magneto-optical Interaction Research Articles

Hydrodynamic Modeling of Spin-Polarized Edge Magnetoplasmons

A novel method, the so-called magneto-optical interaction, is gaining increasing interest for realizing the localization of the electromagnetic radiation to subwavelength scales and enhancement of the local electric fields. We investigate spin-polarized edge magnetoplasmons based on the spin-dependent quantum hydrodynamic model, in a bounded two-dimensional electron gas with perpendicular magnetic field and an electromagnetic wave. The effects of the Fermi pressure associated with Pauli exclusion principle and quantum force due to the Bohm potential, and the effect of the spin-induced ponderomotive force, are taken into consideration. Full spin-polarized edge state exists at the boundary of the two-dimensional electron gas. Spin rotation occurs due to the magneto-optical kerr effect. The existence of the electromagnetic field could reduce the spin amplitude and increase the spin rotation time, since their magnitude oscillates between positive and negative values and hinders the spin precession.

Design and fabrication of plasmonic cavities for magneto-optical sensing

The design and fabrication of a novel plasmonic cavity, intended to allow far-field recovery of signals arising from near field magneto-optical interactions, is presented. Finite element modeling is used to describe the interaction between a gold film, containing cross-shaped cavities, with a nearby magnetic under-layer. The modeling revealed strong electric field confinement near the center of the cross structure for certain optical wavelengths, which may be tuned by varying the length of the cross through a range that is compatible with available fabrication techniques. Furthermore, the magneto optical Kerr effect (MOKE) response of the composite structure can be enhanced with respect to that of the bare magnetic film. To confirm these findings, cavities were milled within gold films deposited upon a soluble film, allowing relocation to a ferromagnetic film using a float transfer technique. Cross cavity arrays were fabricated and characterized by optical transmission spectroscopy prior to floating, revealing resonances at optical wavelengths in good agreement with the finite element modeling. Following transfer to the magnetic film, circular test apertures within the gold film yielded clear magneto-optical signals even for diameters within the sub-wavelength regime. However, no magneto-optical signal was observed for the cross cavity arrays, since the FIB milling process was found to produce nanotube structures within the soluble under-layer that adhered to the gold. Further optimization of the fabrication process should allow recovery of magneto-optical signal from cross cavity structures.

Luminescent properties of Eu-doped magnetic Na3FeF6

Sodium iron fluoride (Na3FeF6) is a colorless ferromagnetic fluoride with a monoclinic crystal structure (space group P21/c), and it is expected to be an ideal platform for exploring magneto-optical interactions. In the present work, Eu3+ doped Na3FeF6 micro-powders were synthesized by a hydrothermal method, and the structures were examined by X-ray diffraction (XRD) and scanning electron microscopy (SEM). The optical properties were examined using UV-Vis spectra and fluorescence spectra, and the results show that the emission spectra can be finely tuned by the hydrothermal reaction temperature and doping concentration of Eu ions. We found that Na3FeF6 doped with 5% Eu3+ synthesized at 196 °C exhibited the optimal red emission under excitation at 395 nm. The magnetization of Na3FeF6:5% Eu3+ decreased rapidly from about 7.85 emu g−1 at 5 K to 0.4 emu g−1 at 60 K, then slowly decreased with temperature increase from 60 K to 300 K. This Eu3+ doped Na3FeF6 powder is expected to find potential applications in the field of magneto-optical modulation and relevant devices.

Correlation of light polarization in uncorrelated disordered magnetic media

Light scattering in a magnetic medium with uncorrelated inclusions is theoretically studied in the approximation of ladder diagram. Correlation between polarizations of electromagnetic waves that are produced by infinitely-distant dipole source is considered. Here white noise disorder model with Gaussian distribution is taken into account. In such a medium the magneto-optical interaction leads to correlation between perpendicular light polarizations. Spatial field correlation matrix with nonzero nondiagonal elements is obtained in the first order on gyration.

Electric Field Controlled Magneto-Optical Kerr Effect at Light Reflection From an Electro-Optic/Magneto-Optic Bilayer

The Kerr rotation for light reflection from a bilayered structure composed of an electro-optic semiconductor film and a slab with high values of magneto-optic and magneto-electric interactions is theoretically investigated. The influence of a dc external electric field on the optical plane rotation angles is analyzed. The influence of frequency dispersion of the system permittivities on the Kerr rotation is studied.

Electric field controlled Faraday rotation in an electro-optic/magneto-optic bilayer

The Faraday rotation for light transmission through a bilayered structure composed of an electro-optic semiconductor film and a slab with high values of magneto-optic and magnetoelectric interactions is theoretically investigated. The influence of dispersion as well as an external electric field on the Faraday rotation is studied.

Anomalies in the polariton dynamics of a one-dimensional magnetic photonic crystal with antiferromagnetic interlayer ordering in an external DC electric field

The effect of an external dc electric field on the electrodynamic properties of a one-dimensional magnetic photonic crystal (MPC) with antiferromagnetic interlayer ordering is analyzed within the effective-medium method with regard to the quadratic magneto-optical interaction. The magnetizations of adjacent tangentially magnetized ferromagnetic layers are antiparallel. In particular, the effect of a magnetic compensation point on the character of polariton dynamics in this type of MPCs is revealed.

Spin-wave modes in Ni nanorod arrays studied by Brillouin light scattering

Dynamic magnetic properties of arrays of Ni nanorods with a low aspect ratio have been investigated. It has been shown that the spectra of spin-wave resonances localized on nanorods with a low aspect ratio typically feature the presence of zones with high density of states resulting in a characteristic two-peak pattern of Stokes and anti-Stokes lines of magneto-optical (MO) Brillouin light scattering with pronounced Stokes--anti-Stokes (S-AS) asymmetry. A simple theoretical model based on the analysis of the elliptic character of the polarization of the optical wave interacting with a dipole magnetostatic wave has been proposed. It has been shown that the S-AS asymmetry is due entirely to the asymmetry of the MO interaction efficiency with respect to time reversal of the magnetic precession in a magnon.

Electric-field-induced features of propagation and localization of S-polaritons in a gyrotropic 1D magnetic photonic crystal

The effect of the quadratic magnetooptical interaction on the refraction of volume electromagnetic TE waves incident from outside onto the surface of a 1D photonic crystal of the easy-axis ferromagnet-nonmagnetic dielectric type in an external dc electric field.

Bragg diffraction of guided optical waves by spin dipole waves in a ferrimagnetic heterostructure

The peculiarities of the Bragg diffraction of guided optical waves (GOWs) by spin-dipole waves (SDWs) in a ferrite heterostructure, based on Bi3Fe5O12 (BIG) thin film deposited on a standard YIG/GGG sample, is presented. It is shown that the efficiency of waveguide magneto-optic interaction between GOWs and SDWs in BIG/YIG/GGG can be 4–14 times large compared to the standard YIG/GGG waveguide, even in the case when the interacting waves are localized in YIG waveguide layer.

Magnetooptical Kerr effect in the near field of a nanowire supporting surface plasmons

In terms of Green’s functions, a theory is developed describing the resonant magnetooptical Kerr effect in light scattering by a linear probe that is parallel to the surface of a magnet and placed at a subwavelength distance from it. The probe is supposed to be a metal nanowire supporting long-lived surface plasmons and forming the near field of the “probe + image” complex. The resonant interaction between the probe and the sample is taken into account within a self-consistent approximation of multiple-scattering theory, and the magnetooptical interaction is included in the linear approximation in magnetization. The problem of scanning near-field magnetooptical microscopy with a linear probe is solved analytically in the case where the magnetization is parallel to both the magnet surface and the plane of incidence of light (longitudinal magnetooptical Kerr effect). The polarization, spectral, and angular characteristics of scattered light modulated by magnetization are discussed. It is shown that the magnetooptical modulation of the scattered light intensity is significantly enhanced when surface plasmons are resonantly excited in the nanowire.

Nobel Lecture: From spin waves to giant magnetoresistance and beyond

The “Institute for Magnetism” within the department for solid-state physics at the research center in Julich, Germany, which I joined in 1972, was founded in 1971 by Professor W. Zinn. The main research topic was the exploration of the model magnetic semiconductors EuO and EuS with Curie temperatures Tc=60 K and Tc =17 K, respectively. As I had been working with light scattering LS techniques before I came to Julich, I was very much interested in the observation of spin waves in magnetic materials by means of LS. LS can be performed with grating spectrometers, which is called Raman spectroscopy, and alternatively by Brillouin light scattering BLS spectroscopy. In the latter case, a Fabry-Perot FP interferometer is used for the frequency analysis of the scattered light see righthand side of Fig. 1 . The central part consists of two FP mirrors whose distance is scanned during operation. BLS spectroscopy is used when the frequency shift of the scattered light is small below 100 GHz , as expected for spin waves in ferromagnets. In the early 1970s, an interesting instrumental development took place in BLS, namely, the invention of the multipass operation, and later, the combination of two multipass interferometers in tandem. The inventor was Dr. J. A. Sandercock in Zurich. Since we had the opportunity to install a new laboratory, we decided in favor of BLS, initially using a single three-pass instrument as displayed on the righthand side of Fig. 1. With this, we started investigating spin waves in EuO. We indeed were able to find and identify the expected spin waves as shown by the peaks in Fig. 1 marked green . Different intensities on the Stokes S and antiStokes aS side were known from other work to be due to the magneto-optic interaction of light with the spin waves. The peaks marked red remained a puzzle for some time until good luck came to help us. Good luck in this case was a breakdown of the system, a repair and unintentional interchange of the leads when reconnecting the magnet to the power supply. To our surprise S and aS side were now reversed. To understand what this means, one has to know that classically S and aS scattering is related to the propagation direction of the observed mode, which is opposite for the two cases. This can be understood from the corresponding Doppler shift, which is to higher frequencies when the wave travels towards the observer and down when away from him. The position of the observer here would be the same as of the viewer in Fig. 1. The appearance of the red peak in the spectra on only either the S or the aS side can be explained by an unidirectional propagation of the corresponding spin wave along the surface of the sample. It can be reversed by reversing B0 and M. The unidirectional behavior of the wave can be understood on the basis of symmetry. For this, one has to know that axial vectors which appear in nature, such as B and M on the left-hand side of Fig. 1, reverse their sign under time inversion and so does the sense of the propagation of the surface wave as indicated. The upper and lower parts of Fig. 1, on the left-hand side therefore are linked by time inversion symmetry, which is valid without damping. Hence, the unidirectional behavior reflects the symmetry of the underlying system. Finally, the observed wave could be identified as the DamonEshbach DE surface mode known from theory and from microwave experiments. From the magnetic parameters of EuO, one predicts in the present case that the penetration depth of the DE mode will be a few 100 A. Sample thickness d is of the order of mm. Therefore, for the present purpose, EuO is opaque. In this case, the wave traveling on the backside of the sample in the opposite direction to the wave on the front side cannot be seen in this experiment. BLS is then either S or aS but not both at the same time. Due to all of these unique features, the results of Fig. 1 have also been chosen as examples for current research in magnetism in a textbook on “Solid State Physics” Ibach and Luth, 1995, p. 186 .

Polariton dynamics of one-dimensional gyrotropic magnetic photonic crystal in an external dc electric field. Effective medium approach

For the example of a semi-infinite thin-layer one-dimensional gyrotropic magnetic photonic crystal of the weak ferromagnet-nonmagnetic insulator type in an external electric field, we determine the conditions under which the quadratic magnetooptic interaction will lead to various anomalies in the reflection and localization of TM or TE waves incident on the surface of the photonic crystal from outside. The electric field is a uniform dc field collinear with the equilibrium antiferromagnetic vector.

Polariton dynamics of a bounded weak ferromagnet in an external dc electric field tangential to the interface

Using the example of a semibounded easy-plane weakly ferromagnetic crystal, magnetized tangentially to its surface, the conditions have been determined under which, with the application of an external dc electric field along the easy-magnetization axis, a number of anomalies arise at the transmission and localization of OA and TM electromagnetic waves through the interface between a nonmagnetic dielectric and a weak ferromagnet due to quadratic magneto-optical interaction.

Near-field magnetooptics in resonant light scattering by a linear nanoprobe

A theory of the magnetooptical scattering of light by a near-field linear probe parallel to the surface of a magnet is presented. The probe is modeled by a cylindrical nanowire supporting long-lived surface plasmons. The scattering of light is considered in the longitudinal magnetooptical Kerr effect geometry (with magnetization parallel to the sample surface and the plane of light incidence). The resonant interaction of the probe + image system is taken into account in the self-consistent approximation of the multiple scattering theory, while the magnetooptical interaction is described in the linear approximation with respect to magnetization. Polarization characteristics of the scattered light and the magnetooptical modulation of light intensity, which are resonantly enhanced by the surface plasmons, have been studied.

Magneto-optic behaviour in the presence of surface plasmons

Insight into the mechanism responsible for the enhanced level of magneto-optical (MO)activity observed from magnetic surfaces when supporting propagating surface plasmons(SPs) is provided by studies of ferromagnetic Ni and Co gratings where SPs are generatedand interact magneto-optically at the air/ferromagnetic interface. These ferromagneticgratings were subsequently coated with semi-transparent Ag layers. In these systems onlysome 30% of the light incident on the air/Ag interface is reflected; most is converted tosurface plasmons whilst the remainder propagates to reflect off the ferromagneticsurface where it undergoes a MO interaction before returning through the Ag. Theprecise nature of the beam returned from the ferromagnetic and the MO signatureimprinted on it depends on the relative magnitude of two driving sources: theE-field of the lightwave and the E-field associated with SPs penetrating through the Ag to the ferromagnetic. Evidence isobtained indicating that the degree of MO enhancement correlates strongly with themagnitude of the intense electric field associated with the presence of SPs at theferromagnetic surface, confirming previous experimental studies postulating that enhancedMO effects are not solely a consequence of the reduction in reflection that is experienced atsurface plasmon resonance.

Transformation of the spectrum of TM polaritons of a 1D magnetic photonic crystal under conditions of the quadratic electro-optic effect

Conditions under which quadratic magneto-optical interaction leads to a number of features in the conditions of localization and propagation of collective magnetic TM polaritons are determined by the example of a 1D magnetic superlattice of the easy-axis-antiferromagnet-nonmagnetic-insulator type, in which the easy magnetization axis is orthogonal to the applied external dc electric field.

Polariton dynamics of a one-dimensional magnetic photonic crystal in crossed magnetic and electric fields

By an example of a semibounded one-dimensional magnetic photonic crystal (MPC) of easy-axis antiferromagnet-nonmagnetic dielectric type placed in mutually orthogonal dc magnetic and electric fields, conditions are found under which the quadratic magneto-optic interaction leads to a number of anomalies in the reflection and propagation conditions for TM or TE waves incident from outside on the surface of the superlattice. It is assumed that the easy magnetic axis is collinear to the electric field.

Polariton dynamics of a bounded weak ferromagnetic in an external DC electric field normal to the interface

With a bounded easy-plane weakly ferromagnetic crystal magnetized tangentially to its surface taken as an example, it is shown that the external DC electric field (collinear simultaneously both with the easy magnetic axis and with the normal to the interface) can lead to the formation of multiple anomalies due to the quadratic magnetooptical interaction under the conditions of propagation of a volume TM or TE wave through the interface between magnetic and nonmagnetic media.

Over 40% transverse Kerr effect from Ni80Fe20

We show how mixed s- and p-polarized light incident on a ferromagnetic surface yields large transverse magneto-optical Kerr effect (MOKE) signals. Fractional MOKE signals of over 40% could be achieved from transverse magnetization changes in 35nm thick Ni80Fe20, an increase of over two orders of magnitude compared with the standard MOKE configuration. Transverse MOKE signals from patterned structures were also improved by an order of magnitude. Calculations of the magneto-optical interaction show how changing the incident polarization controls the Kerr rotation and reflected beam intensity for opposite magnetization orientations.