Nonlinear magneto-optical Kerr effects

The polarization state of a second-harmonic wave after reflection from a semi-infinite, optically isotropic magnetic medium is considered for the three characteristic uniformmagnetization directions corresponding to the linear magneto-optical Kerr effects. Expressions for the complex amplitudes of the wave field which specify the nonlinear Kerr effects, viz., the polar, meridional, and equatorial effects, are obtained in a first approximation with respect to the magnetization. The dependences of these effects on the angle of incidence of the inducing wave obtained as a result of a numerical experiment are presented. Analytical formulas are found for them at small angles of incidence. A comparative analysis of the linear and nonlinear Kerr effects is made. Zh. éksp. Teor. Fiz. 116, 141–156 (July 1999)     

New nonlinear intensity Kerr effect in the polar geometry

The problem of the electromagnetic wave reflection on the second optical harmonic from a semi-infinite optically isotropic magnetic medium is considered for the uniform magnetization direction corresponding to the polar Kerr effect. In the first approximation in magnetization, the method of Green’s tensor functions is used to derive expressions for the complex amplitudes of the wave fields for the incidence of s-and p-polarized waves (as well as of their superposition) on the medium. It is shown that, in the latter case, the nonlinear polar Kerr effect is of the intensity type. The dependences of the intensity effect on the angle of incidence of the inducing wave and on the angle of its polarization, which were obtained in numerical experiments, are presented. A comparative analysis of the linear and nonlinear intensity Kerr effects is carried out.     

In situ investigations of magneto-optical properties of thin Fe layers

A thin polycrystalline Fe film on a single-crystal Si substrate with natural SiO₂ oxide is obtained by thermal evaporation in ultrahigh vacuum. The magneto-optical properties of the resultant structure are investigated in situ by the methods of spectral ellipsometry. The values of the coercive force for the Fe film are obtained, and the magnetization reversal loop and the energy dependence of the equatorial Kerr effect are constructed. The effectiveness of magnetoellipsometry for in situ analysis of the geometrical and magnetooptical properties of thin ferromagnetic layers is demonstrated.     

Magnetorefractive effect in granular films with tunneling magnetoresistance

The magnetorefractive effect, consisting in a change of reflectivity under magnetization, has been observed in granular Co-Al-O metal-insulator magnetic films with tunneling magnetoresistance in the IR region. It is shown that this effect manifests itself most clearly in interference conditions, is even in magnetization, and reaches as high as 0.8% at frequencies of about 1100 cm^?, which exceeds both the linear equatorial Kerr and the even orientational magneto-optic effects by an order of magnitude.     

Determination of the depth of formation of magnetooptical effects in CoNi films

The optical constants of CoNi films with magnetic properties that are nonuniform across their thickness are determined in reflected light by two methods, viz., optical and magnetooptical measurements. The values of the parameters L=λ/4πk and Z ₀=λ/8n, one of which (specifically, the one which has the smaller value at a given value of λ) determines the depth of formation of reflective magnetooptical effects (l _mo) according to the current theories, are calculated on the basis of the values obtained for the optical constants n and k of the films (λ is the wavelength of the light used, and n and k are the refractive index and the absorption coefficient of the magnet). It is established for the CoNi films investigated that l _mo is determined by L and varies from about 200 to 300 ? in the range 0.33 μm⩽λ⩽0.83 μm. In CoNi films, which are inhomogeneous across their thickness and are characterized by significant variation of the magnetic properties over distances ∼l _mo, variation of the form of the magnetization curves determined by measuring the equatorial Kerr effect is observed as λ increases. Zh. Tekh. Fiz. 68, 69–72 (February 1998)     

Magneto-optical effects upon reflection of light from a ferrodielectric with an arbitrary orientation of magnetization

The boundary problem for a semi-infinite magnetic medium with arbitrary orientation of the magnetization vector is solved and polarization-and intensity-related characteristics of the reflected light wave are analyzed. It is shown that variations of the angle of incidence and of the orientation of the magnetization and polarization plane substantially affect the polarization characteristics of the reflected wave and give rise to specific features of the dependences under study.     

Optical and magnetooptical properties of granular alloys with giant magnetoresistance in the IR region of the spectrum

The features of the optical and magnetooptical properties of granular alloys with giant magnetoresistance in the IR region are examined in reference to the magnetorefractive effect and the equatorial Kerr effect. Calculations are performed within the semiclassical approximation with consideration of spin-dependent scattering in the bulk of the granules and on their surfaces (interfaces). The expressions obtained for σ _xx(ω) and σ _xy(ω) are found to be sensitive to scattering on the surfaces and in the bulk of the granules, as well as to granule size, the type of impurities trapped on the interfaces, the frequency of the incident light, and the external magnetic field. For granular thin films exhibiting giant magnetoresistance, the theory predicts significant relative changes in the optical reflection and transmission coefficients when the sample is magnetized to saturation (0.02% and 20%, respectively, for giant magnetoresistance of the order of 20%), as well as Kerr and Faraday effects that are nonlinear with respect to magnetization. Zh. éksp. Teor. Fiz. 116, 1762–1769 (November 1999)     

Magnetooptical effects in bismuth-containing ferrite-garnet films

We present results of magnetooptical investigations of bismuth-containing ferrite-garnet films with the easy axis of magnetization parallel to the specimen surface. Measurements were conducted for incident light with energies in the range 1.5–3.2 eV for transverse [equatorial Kerr effect (EKE)] and for longitudinal [meridional intensity effect (MIE)] magnetizations of thin-layer specimens. It is shown that the EKE differs from zero when the films are opaque, and it is established that the EKE peak in the region 2.8 eV increases with increasing bismuth concentration. For longitudinal magnetization, conditions for observing magnetooptical interference were realized. The experimental curves agree well with the theoretical ones.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 10–14, November, 1989.     

Magnetic structure simulation of Fe/V superlattices with a variable thickness of iron layers

The model of the magnetic structure of Fe/V superlattices is discussed. The discrepancy in estimation of the critical temperature for the Fe₂/V _n /Fe₃/V _n superlattice obtained by neutron scattering and the magneto-optical Kerr effect is caused by inhomogeneity of the magnetization distribution in a finite superlattice.     

Magneto-optical and magnetic properties of (YBiSmTm)3(FeGa)5O12 ion-implanted films

A strong dependence of the meridional Kerr effect on the implantation regime that is different in different segments of the spectrum has been observed in He⁺-implanted (YBiSmTm)₃(FeGa)₅O₁₂ films. In addition to the Kerr effect, we have also investigated the dependence of the magnetization, the magnetic anisotropy, and the Néel temperature on the conditions of implantation. Correlations were noted in the behavior of the magnetic, magneto-optical, and electrical properties of the implanted layers. Fiz. Tverd. Tela (St. Petersburg) 39, 1267–1269 (July 1997)     

Magnetooptic setup for investigating the dynamic properties of domain walls in thin ferromagnetic films

A magnetooptic Kerr setup is designed for investigating the dynamic properties of domain walls in thin ferromagnetic films subjected to an external magnetic field in the temperature range 20–150°C. With this setup, the method of interrupted magnetization is implemented and the magnetic (domain) structure is visualized based on the meridional Kerr effect. The domain structure is displayed on a PC monitor using a Nikon DXM 1200 high-resolution digital video camera. A dedicated software makes it possible to automatize measurements and data processing.     

Observation and theory of strong stripe domains in amorphous sputtered FeB films

Domain structures in thin sputtered amorphous FeB films are studied by means of the longitudinal Kerr effect. In addition to the irregular domain structure characteristic of soft magnetic materials, we observe in certain regions a fine equilibrium domain structure with periodicity of a few micrometers. The Kerr contrast indicates that the magnetization at the surface of the film lies partially along the stripe direction. These characteristics and the behavior in applied fields suggests that the domains are similar to type II “strong stripe domains” observed earlier in permalloy films. Extending an earlier theory by Hara, we use a stray-field-free model with tilted orthorhombic anisotropy to show that there are at least two qualitatively different strong stripe structures: type IIa with surface magnetization perpendicular to the stripes and type IIb with surface magnetization at least partially parallel to the stripes. Type IIb is favored when K_p/K₀<cos 2θ ₀ where K₀ is the anisotropy component with axis tilted by θ₀ out of the film plane, and K_p is an in-plane anisotropy perpendicular to K₀. Strong stripes in amorphous FeB appear to be type IIb while those in permalloy are usually type IIa.     

Magneto-optical properties of metallic ferromagnetic materials

The authors have studied the magneto-optical Kerr rotation in more than 200 metallic systems comprising alloys as well as intermetallic compounds of 3d transition metals. For all these materials the crystal structure, the lattice constants, the room temperature magnetization and the room temperature Kerr rotation at two different wavelengths are specified. For several series of ternary compounds, comprising Heusler alloys Ni₂ In-type compounds and Cr₂₃C₆ type compounds, we determined the saturation moment at 4.2 K. For a number of representative alloys or compounds a study was also made of the wavelength dependence of the complex polar Kerr effect. The values of the Kerr rotation obtained at 633 nm were compared with the corresponding values of the measured magnetization. Systematic trends were observed and have been used to classify metallic systems into systems where the Kerr rotation will not reach values much in excess of 1° and systems where higher values are likely to be found.     

Nongyrotropic magneto-optical effects in metal-insulator magnetic multilayer thin films

Nongyrotropic magneto-optical effects are investigated in metal-insulator magnetic multilayer thin films. These effects manifest themselves in changes in the coefficients of transmission and reflection of electromagnetic radiation from the surface of a multilayer film due to the crossover of the magnetic structure from an antiferromagnetic configuration to a ferromagnetic configuration. The nongyrotropic magneto-optical effect observed in reflected light is analyzed theoretically. It is assumed that the multilayer structure is exposed to radiation of a monochromatic plane wave polarized along the direction of magnetization of the film. The magneto-optical effect is described in terms of the permittivity tensor of the multilayer medium, which depends only on the light frequency. The Boltzmann kinetic equation is treated with allowance made for spin-dependent electron scattering both inside conducting layers and at rough interfaces. Using an Fe/C multilayer as an example, it is demonstrated that the nongyrotropic magneto-optical effect is equal in order of magnitude to the equatorial Kerr effect or other strong magneto-optical effects.     

The extended (G′/G)-expansion method and travelling wave solutions for the perturbed nonlinear Schrödinger’s equation with Kerr law nonlinearity

In this paper, we construct the travelling wave solutions to the perturbed nonlinear Schrödinger’s equation (NLSE) with Kerr law non-linearity by the extended (G′/G)-expansion method. Based on this method, we obtain abundant exact travelling wave solutions of NLSE with Kerr law nonlinearity with arbitrary parameters. The travelling wave solutions are expressed by the hyperbolic functions, trigonometric functions and rational functions.     

Qualitative analysis and traveling wave solutions for the perturbed nonlinear Schrödinger's equation with Kerr law nonlinearity

In this Letter, we investigate the perturbed nonlinear Schrödinger's equation (NLSE) with Kerr law nonlinearity. All explicit expressions of the bounded traveling wave solutions for the equation are obtained by using the bifurcation method and qualitative theory of dynamical systems. These solutions contain bell-shaped solitary wave solutions, kink-shaped solitary wave solutions and Jacobi elliptic function periodic solutions. Moreover, we point out the region which these periodic wave solutions lie in. We present the relation between the bounded traveling wave solution and the energy level h. We find that these periodic wave solutions tend to the corresponding solitary wave solutions as h increases or decreases. Finally, for some special selections of the energy level h, it is shown that the exact periodic solutions evolute into solitary wave solution.     

Room temperature ferromagnetism of a double-layer Dy1−x Ni x /Ni structure: in situ magneto-optical measurements

The double-layer Dy_1?x Ni _x /Ni structures have been studied in situ in an ultrahigh-vacuum chamber by the original technique using the surface meridional Kerr effect directly in the course of deposition. It has been shown that a layer of Dy_1?x Ni _x alloy is ferromagnetically ordered at room temperature.     

Gravitational radiation by a particle with nonzero orbital angular momentum falling into a Kerr black hole

We have computed the energy of the gravitational waves induced by a particle with nonzero orbital angular momentum μL_z plunging into a Kerr black hole in an equatorial plane. It is found that for the same |L_z| a corotating particle emits more energy than a counter-rotating one, which is due to the change of the frequency of the quasi-normal mode with the increase of the angular momentum of the black hole.     

Optical and magneto-optical spectroscopy of thin composite GaAs-MnAs layers

Ellipsometric and magneto-optical investigations of MnAs layers and GaAs-MnAs composites obtained by laser deposition have been performed in the energy range 1.0–4.5 eV. The spectra of the equatorial Kerr effect (EKE) and the refractive and absorption indices have been studied. Diagonal and off-diagonal components of the dielectric tensor have been calculated. It is established that the shape of the EKE spectra of MnAs layers depends on the crystallographic orientation of these layers. Features near 1.9, 3, and 4 eV are distinguished in the energy dependences of the interband density of states of the layers; these features correspond to the energies of interband d-p transitions, obtained from calculations of the MnAs band structure.     

Magnetic and magneto-optical properties of epitaxial cobalt films grown on a corrugated CaF<Subscript>2</Subscript>/Si surface

The magnetic properties of CaF₂/Co/CaF₂(110)/Si(001) heterostructures fabricated by molecular-beam epitaxy and having a corrugated CaF₂ buffer surface were studied. The optical and magneto-optical properties of these structures reflect the C _2v symmetry of the corrugated structure surface. The studies of hysteresis loops using the longitudinal and transverse magneto-optical Kerr effects under oblique light incidence and of magneto-optical phenomena under near-normal light incidence demonstrate that the corrugated structure surface leads to optical and magneto-optical anisotropies. The magnetization of such structures occurs via coherent magnetization rotation over a wide magnetic-field range. The magnetic anisotropy of these structures is described using a Gaussian distribution of easy axes of magnetization in cobalt granules about the direction parallel to the groove direction. The asymmetry of hysteresis loops of the rotation of the plane of polarization detected under oblique and normal light incidence is shown to be related to the contributions to the effective film permittivity that are quadratic in the magnetic moment.