Quadratic Magneto-optical Effects Research Articles

Laser-driven first-order spin reorientation and Verwey phase transitions in magnetite Fe3O4 beyond the range of thermodynamic equilibrium

Ultrafast photo-induced phase transitions occurring under the impact of femtosecond laser pulses provide versatile opportunities for switching solids between distinctly-different crystalline, electronic, and magnetic states and thus modify their functional properties in a significant way. In this paper, we report on the laser-induced spin reorientation and Verwey phase transitions in a single crystalline ferrimagnetic magnetite ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$. Using femtosecond optical and magneto-optical pump-probe techniques, we define the range of the initial sample temperatures and laser fluences when partial or complete photo-induced phase transitions occur from a monoclinic insulating to a cubic metallic state with concomitant switching of magnetic anisotropy from the uniaxial to the cubic one. We thus reveal a connection between these phase transitions when driven by femtosecond laser pulses. Using transient linear and quadratic magneto-optical effects, we examine magnetization dynamics launched the switching of the magnetic anisotropy axis. We unveil the presence of the domains undergoing the laser-induced phase transitions even below the established threshold fluence for the transitions, as well as when the material is initially in the cubic phase. This is the manifestation of the first order of these both laser-induced phase transitions beyond the range of thermodynamic equilibrium.

Giant quadratic magneto-optical response of thin Y3Fe5O12 films for sensitive magnetometry experiments

We report on observation of a magneto-optical effect quadratic in magnetization (Cotton-Mouton effect) in 50 nm thick layer of Yttrium-Iron Garnet (YIG). By a combined theoretical and experimental approach, we managed to quantify both linear and quadratic magneto-optical effects. We show that the quadratic magneto-optical signal in the thin YIG film can exceed the linear magneto-optical response, reaching values of 450 urad that are comparable with Heusler alloys or ferromagnetic semiconductors. Furthermore, we demonstrate that a proper choice of experimental conditions, particularly with respect to the wavelength, is crucial for optimization of the quadratic magneto-optical effect for magnetometry measurement.

Quadratic magneto-optical effect in hexagonal non-collinear antiferromagnets

Quadratic magneto-optical (MO) effects can be utilized to investigate the spin order in antiferromagnetic (AFM) materials; however, the previously reported studies were all limited in antiferromagnets with collinear AFM order. Here, we develop a phenomenological theory to investigate the quadratic MO effects in hexagonal non-collinear AFM crystals with triangular spin structures. Based on the permittivity tensor up to the second-order in magnetization, we derive the formula to describe the quadratic MO responses and perform numerical calculations to obtain the MO rotation angle for different AFM spin configurations and sample orientations. For the sample with its spin plane lying perpendicular to the surface plane, we have revealed the emergence of quadratic MO response, which exhibits a strong dependence on the light incident angle. The MO rotation angle shows an approximately sinusoidal variation with a periodicity of 180° when the sample is rotated around its surface normal. The size of the MO response and its deviation from the sinusoidal form are analyzed for different values of the second-order permittivity tensor elements. This study provides important insights into the non-collinear AFM spin-induced quadratic MO effect, which may be used as a guidance for optical detections of the non-collinear AFM order, and, in particular, the ultrafast spin dynamics using the optical pump–probe technique.

Magnetic linear birefringence of light in Tb3Ga5O12

The spectra of the magnetic linear birefringence (MLB) in the terbium-gallium garnet TbGG (Tb3Ga5O12) have been studied within the visible spectral range for temperature T = 90 K. Analysis of the temperature and spectral dependences of MLB has made it possible to determine the “effective” frequencies of the allowed f→d electric dipolar transitions in rare-earth (RE) ions of Tb3+ ions responsible for the formation of quadratic magneto-optical effect in this garnet. The results of the performed magneto-optical experiments in TbGG have confirmed the Akulov's relations (for the quadratic magnetic effects) arising from the phenomenological consideration of MLB for the values of Δn measured at the orientation of the external field in the plane (110) along the main crystallographic directions of the garnet crystal. From analysis of the experimental data on MLB was obtained that for the TbGG MLB changes quadratically with the field within the temperature range 90–300 K. At the same time with a decrease in temperature, its value grows inversely proportional to the square of temperature. A certain difference was also found in the “effective" frequencies of the allowed transitions in Tb3+ ions of the garnet, which is determined from the optical absorption spectra of TbGG on the one hand, and from the analysis of the spectral dependence of MLD on the other one. It has been assumed that this difference can be due to significant distortions of the TbGG crystal lattice caused by this significant magnetostriction at low temperatures, leading to the "mixing" of the 9D term states with the "optically resolved" states of the 7D term.

Study of magnetization reversal and anisotropy of single crystalline ultrathin Fe/MgO (001) film by magneto-optic Kerr effect**Project supported by the National Natural Science Foundation of China (Grant Nos. 11274033, 11474015, and 61227902), the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20131102130005), and the Beijing Key Discipline Foundation of Condensed Matter Physics.

The magnetization reversal process of Fe/MgO (001) thin film is investigated by combining transverse and longitudinal hysteresis loops. Owing to the competition between domain wall pinning energy and weak uniaxial magnetic anisotropy, the typical magnetization reversal process of Fe ultrathin film can take place via either an “l-jump” process near the easy axis, or a “2-jump” process near the hard axis, depending on the applied field orientation. Besides, the hysteresis loop presents strong asymmetry resulting from the variation of the detected light intensity due to the quadratic magneto-optic effect. Furthermore, we modify the detectable light intensity formula and simulate the hysteresis loops of the Kerr signal. The results show that they are in good agreement with the experimental data.

Amplitude and phase-frequency characteristics of the magneto-optical modulator based on the bimorph element in the mode of magneto-mechanical oscillations

This article presents the theoretical calculations of spatial distribution of the amplitude and phase characteristics of the Stokes vector for a magneto-optical modulator based on the magneto-optical crystal in the framework of a bimorph plate of rectangular shape for the fundamental mode of magneto-mechanical oscillations. The geometry of the magnetic fields and the direction of light propagation relative to the crystallographic axes provide the occurrence of linear and quadratic magneto-optical effects with respect to the magnetic field. It has been shown that due to the phase delays of voltages, which are excited in the bimorph plate in the frequency range of fundamental acoustical mode, the elements of the Stokes vector of the output radiation obtain spatially dependent amplitude variations within 10% range and phase variations within the range of π.

Linear and quadratic magneto-optical effects observed in La0.7Sr0.3MnO3 thin films in transmitted light

Magnetic linear dichroism (MLD) is observed in polycrystalline La0.7Sr0.3MnO3 films in transmitted light. The spectral and temperature dependences of the MLD are determined for the energy E of the light wave ranging from 1.5 to 3.5 eV. The experimental spectra are fitted by a sum of Lorentzian curves. The MLD spectrum exhibits more features in comparison to the spectra of magnetic circular dichroism (MCD), which we measured earlier using the same film samples. Various temperature behaviors of the intensities of the Lorentzian components centered at different E values have been revealed. This can be related to the effect of the surface states on the magneto-optical characteristics of the samples.

The possibility of measuring linear and quadratic magnetooptical effects in magnetic field under conditions of magnetomechanical resonance

We have considered the possibility of measuring the linear and quadratic (in magnetic field) magnetooptical effects in magnetooptical crystals that are simultaneously exposed to a constant (polarizing) magnetic field and to an alternating magnetic field under conditions of magnetomechanical resonance. The use of a Mueller polarimeter in combination with spectral analysis of the intensity of the light wave at the output of the polarimeter makes it possible to selectively determine elements of the Mueller matrix and minimize the amount of measurements. We have shown that there is a possibility of solving the inverse problem on finding two components of the alternating magnetic field in which a magnetooptical crystal is placed.

A New Phenomenon on the Surface of FINEMET Alloy

This paper is devoted to the analysis of quadratic magneto-optical effects (QMOKE) newly observed at the surface of FINEMET-type Fe73.5Si13.5Nb3Cu1B9 ribbons annealed at temperatures of 733 K and 743 K. A strongly inhomogeneous surface microstructure detected by grazing incident X-ray diffraction (GIXRD), scanning (SEM) and transmission (TEM) electron microscopy is responsible for amplitude and sign changes of the QMOKE in different sample places. Signals in saturation determined by an 8-directional method confirm the prevailing influence of M L M T contributions at some places of a surface and of \(M_{\mathrm{L}}^{2}-M_{\mathrm{T}}^{2}\) at other ones, where M L and M T are in-plane longitudinal and transversal magnetization components. This behavior is explained by random orientation of nanocrystals and/or clusters of the nanometer size (typically units of nm) in the surface layers. The maximal QMOKE magnitude in saturation reaches at some places as much as 0.2 mrad, which is approximately three times lower than the highest contribution observed in Co2FeSi Heusler compounds.

High precision magnetic linear dichroism measurements in (Ga,Mn)As

Investigation of magnetic materials using the first-order magneto-optical Kerr effects (MOKEs) is well established and is frequently used. On the other hand, the utilization of the second-order (or quadratic) magneto-optical (MO) effects for the material research is rather rare. This is due to the small magnitude of quadratic MO signals and the fact that the signals are even in magnetization (i.e., they do not change a sign when the magnetization orientation is reversed), which makes it difficult to separate second-order MO signals from various experimental artifacts. In 2005 a giant quadratic MO effect-magnetic linear dichroism (MLD)-was observed in the ferromagnetic semiconductor (Ga,Mn)As. This discovery not only provided a new experimental tool for the investigation of in-plane magnetization dynamics in (Ga,Mn)As using light at normal incidence, but it also motivated the development of experimental techniques for the measurement of second-order MO effects in general. In this paper we compare four different experimental techniques that can be used to measure MLD and to separate it from experimental artifacts. We show that the most reliable results are obtained when we monitor the polarization of reflected light while the magnetization of the sample is rotated by applying an external magnetic field. Using this technique we measure the MLD spectra of (Ga,Mn)As in a broad spectral range from 0.1 eV to 2.7 eV and we observe that MLD has a magnitude comparable to the polar MOKE signals in this material.

Quadratic magnetooptical effects in two-dimensional permalloy particles investigated by scanning X-ray microscopy

We have investigated the magnetization structure and magnetization curves of individual rectangularity shaped permalloy particles using scanning X-ray microscopy in the ultrasoft X-ray regime. Magnetic contrast originates from X-ray magnetic circular dichroism and from the transverse magnetooptical Kerr effect. We studied magnetization curves in dependence on the field direction for particles of different shapes and sizes. Adjacent particles cause a significant dipole interaction. Asymmetric magnetization loops indicate the presence of non-linear magnetooptical effects.

Influence of Annealing Temperature and Atmosphere on Surface Microstructure and Magnetism in FINEMET-Type FeSiNbCuB Ribbons

Paper is primarily devoted to the surface investigations of the FINEMET-type Fe73.5Si13.5Nb3Cu1B9 ribbons. As-quenched (AQ) samples were subsequently annealed at different temperatures from 733 K to 923 K in vacuum and hydrogen in order to follow the influence of both treatment parameters on microstructure and magnetic properties. Two-phase magneto-optical (MO) hysteresis loops observed at AQ ribbons correspond to an amorphous structure composed of clusters of the size in units of nm (calculated from XRD). The annealing temperatures are responsible for the origin of the α-Fe and/or α-Fe(Si) nanocrystals of various size formed at the surface and consequently penetrating into the ribbon volume while the atmospheres influence surface oxidation. An interesting occurrence of the asymmetric reversal of longitudinal magnetization, clearly observed after annealing at 733 K and 743 K, is discussed from the viewpoint of quadratic magneto-optical effects. The loop asymmetry decreases with increasing annealing temperature and disappears at 923 K.

Thickness dependence of linear and quadratic magneto-optical Kerr effects in ultrathin Fe(001) films

Magneto-optical (MO) Kerr effect (MOKE) magnetometry is one of the most widely employed techniques for the characterization of ferromagnetic thin-film samples. Some information, such as the magnitude of coercive fields or anisotropy strengths, can be readily obtained without any knowledge of the optical and MO properties of the material. On the other hand, a quantitative analysis, which requires precise knowledge of the material's index of refraction $n$ and the MO-coupling constants $K$ and $G$, is often desirable, for instance, for the comparison of samples which are different with respect to ferromagnetic layer thicknesses, substrates, or capping layers. While the values of the parameters $n$ and the linear MO-coupling parameter $K$ reported by different authors usually vary considerably, the relevant quadratic MO-coupling parameters $G$ even for Fe are completely unknown. Here, we report on measurements of the thickness dependence (0--60 nm) of the linear and quadratic magneto-optical effects in epitaxial bcc-Fe(001) wedge-type samples performed at a commonly used laser wavelength of 670 nm. By fitting the thickness dependence we are able to extract a complete set of parameters $n$, $K$, $({G}_{11}\ensuremath{-}{G}_{12})$, and ${G}_{44}$ for the quantitative description of the MOKE response of bcc-Fe(001). We find the parameters $n$, $K$, and $G$ to significantly differ for films thinner than about 10 nm as compared to those for thicker films, which is indicative of a thickness dependence of the electronic properties or of surface contributions to the MOKE. The magnitude of the quadratic magneto-optical effect is found to be about one-third of the record values reported recently for ${\text{Co}}_{2}\text{FeSi}$.

Magnetooptic effects in antiferromagnetic chromium

Transverse and polar Kerr effects and quadratic magnetooptical effect in reflected light have been discovered and studied in antiferromagnetic chromium. Measurements have been performed in IR, visible, and UV ranges of spectrum in a magnetic field H = 10 kOe. The frequency dispersion of the off-diagonal component of the dielectric constant tensor \(\hat \varepsilon \) of chromium has been determined for the first time. An analysis of the magnetooptical data obtained is carried out on the basis of available data on the electronic structure of chromium.

Anisotropy of quadratic magneto-optic effects in reflection

Quadratic or second-order magneto-optic effects in reflection significantly effect in-plane magnetization measurements. While the magneto-optic effects linear in magnetization are independent of orientation of cubic crystal axes, the amplitude and sign of the quadratic effects change significantly under crystal rotation. Theoretical formulas for the magneto-optic effects have been derived using a permittivity tensor including terms quadratic in magnetization. A method for separation of the diagonal and off-diagonal quadratic magneto-optic tensor components (G11−G12) and 2G44 is proposed. The theory was completed by an experimental observation of the quadratic effect anisotropy in an epitaxial Fe layer prepared on a MgO substrate. The influence of the magnetization components on the magneto-optic vector magnetometry is discussed for an interface, a single layer, and exchange coupled bilayer system for a general magnetization direction including the quadratic magneto-optic effect anisotropy.

Topographies of chiral and associated optical properties in FeBO3 using a novel polarimeter, the ‘tilter’

Topographies of the spontaneous Faraday effect and spontaneous rotation of the indicatrix are measured with a novel polarimetric device, the ‘tilter’. The contrast observed in the indicatrix rotation is interpreted with the quadratic magneto-optic effect. Additional measurements of the azimuth rotation of incident linear polarised light after passing the sample as a function of an external magnetic field and again tilting the sample confirmed the results obtained with the ‘tilter’ from the spontaneous effects.

Linear and quadratic magneto-optical measurements of the spin reorientation in epitaxial Fe films on MgO

We have undertaken a detailed study by magneto-optical techniques of in-plane magnetization reversal behaviour in epitaxial Fe films grown by MBE on (10 0) oriented MgO substrate. We measure M H loops for both orthogonal in-plane magnetization components M t (component parallel to the magnetic field) and M t (component perpendicular to the field) and for various orientations of the magnetic field with respect to the crystalline axis. These measurements show the classical four-fold cubic anisotropy for large Fe film thickness and confirm the appearance of weak uniaxial in-plane anisotropy superimposed for thinner films ( t = 20 A ̊ ). We have demonstrated the appearance of strong asymmetrical hysteresis loop for p-polarized incident light. We explain this behaviour as the mixing of transverse magnetization contribution to the longitudinal magnetization measurements on the basis of quadratic magneto-optical effects. The calculation of these effects based on eigenmode propagation in anisotropic layered media are developed by including the second-order magneto-optical terms in the permittivity tensor characteristic of a cubic crystal. The second-order reflection coefficients are discussed in the case of the normal incidence of the laser beam and for the magnetic field along the hard axis of the Fe film.

Waveguide interaction of light with spin waves in a ferromagnetic film

We discuss the results of a theoretical analysis of the waveguide interaction of light and spin waves. Both linear and quadratic magnetooptical effects are taken into account. The features of the interaction are considered for the three principal types of spin waves: waves in a normally magnetized ferromagnetic film, and longitudinal and transverse waves in a tangentially magnetized film. Isotropic and anisotropic diffraction processes are considered. Numerical estimates of the intensity and frequency properties of the diffraction scattering are given for a number of situations of practical interest. The effect of a strong constant magnetic field on the interaction of light and spin waves is considered.

EXCHANGE SPIN WAVES AND THEIR MANIFESTATION IN TWO-MAGNON ABSORPTION AND RAMAN SCATTERING

EXCHANGE SPIN WAVES AND THEIR MANIFESTATION IN TWO-MAGNON ABSORPTION AND RAMAN SCATTERING

Light diffraction by stripe domain structures in magnetic crystals

Light diffraction by stripe domain structures (SDS) in magnetic crystals is analyzed theoretically. The applicability of the Fresnel-Kirchhoff integral for description of magneto-optical diffraction is discussed. In this connection a criterion of an optically thin layer with SDS is proposed. The effects of symmetrical and unsymmetrical domain structure realignments on the intensity and polarization parameters of the light field diffracted by a binary magnetic grating are studied. Both linear and quadratic magneto-optical effects are taken into account to specify the diffraction spectrum. Peculiarities of phase and amplitude light modulation by a magnetic grating are revealed. [Russian Text Ignored].