Magneto-optical Kerr Effect of Mono-layer NiX_(2)(X=Cl,Br,I):A Density Functional Theory Study

The full-potential linearized augmented plane wave plus local orbital method is utilized for exploring the electronic,magnetic,and magneto-optical properties of the NiX_(2)(X=Cl,Br,and I)single layer.The first-principles calculation demonstrates that these compounds are ferromagnetic indirect semiconductors,and the energy band gaps of NiX_(2)for X=Cl,Br,and I are 3.888,3.134,and 2.157 eV,respectively.The magnetic moments of Ni atoms in NiX_(2)monolayer are 1.656,1.588,1.449μB,and their magneto-crystalline anisotropy energies are 0.167,0.029,0.090 meV,respectively.Based on the macro-linear response theory,we systematically studied the influences of the external magnetic field and out-of-plane strain on the magneto-optical Kerr effect(MOKE)spectrum of the NiX_(2)single layer.It is found that,when the external magnetic field is perpendicular to the sample plane,the value of the Kerr rotation angle reaches the maximum,and the single-layer NiI_(2)material has a Kerr rotation angle of 1.89°at the photon energy of 1.986 eV.Besides,the Kerr rotation spectrum of NiCl_(2)and NiBr_(2)monolayers redshift as the out-of-plane strain increases,while NiI_(2)monolayer blueshifts.Accurate computation of the MOKE spectrum of NiX_(2)materials provides an opportunity for applications of 2D magnetic material ranging from sensing to data storing.

Magneto-optical Kerr and Faraday effects in bilayer antiferromagnetic insulators

Control and detection of antiferromagnetic topological materials are challenging since the total magnetization vanishes.Here we investigate the magneto-optical Kerr and Faraday effects in bilayer antiferromagnetic insulator Mn Bi2Te4.We find that by breaking the combined mirror symmetries with either perpendicular electric field or external magnetic moment,Kerr and Faraday effects occur.Under perpendicular electric field,antiferromagnetic topological insulators(AFMTI)show sharp peaks at the interband transition threshold,whereas trivial insulators show small adjacent positive and negative peaks.Gate voltage and Fermi energy can be tuned to reveal the differences between AFMTI and trivial insulators.We find that AFMTI with large antiferromagnetic order can be proposed as a pure magneto-optical rotator due to sizable Kerr(Faraday)angles and vanishing ellipticity.Under external magnetic moment,AFMTI and trivial insulators are significantly different in the magnitude of Kerr and Faraday angles and ellipticity.For the qualitative behaviors,AFMTI shows distinct features of Kerr and Faraday angles when the spin configurations of the system change.These phenomena provide new possibilities to optically detect and manipulate the layered topological antiferromagnets.

Low Gilbert damping in Bi/In-doped YIG thin films with giant Faraday effect

Magnetic films with low Gilbert damping are crucial for magnonic devices,which provide a promising platform forrealizing ultralow-energy devices.In this study,low Gilbert damping and coercive field were observed in Bi/In-dopedyttrium iron garnet(BiIn:YIG)thin films.The BiIn:YIG(444)films were deposited onto different substrates using pulsedlaser deposition.Low coercivity(<1 Oe)with saturation magnetization of 125.09 emu/cc was achieved along the in-planedirection of BiIn:YIG film.The values of Gilbert damping and inhomogeneous broadening of ferromagnetic resonance inBiIn:YIG films were obtained to be as low as 4.05×10^(-4)and 5.62 Oe,respectively.In addition to low damping,the giantFaraday rotation angles(up to 2.9×10^(4)deg/cm)were also observed in the BiIn:YIG film.By modifying the magneticstructure and coupling effect between Bi^(3+)and Fe^(3+)of Bi:YIG,doped In^(3+)plays a key role on variation of the magneticproperties.The low damping and giant Faraday effect made the BiIn:YIG film an appealing candidate for magnonic andmagneto-optical devices.

Simulation of magnetization process and Faraday effect of magnetic bilayer films

We described ferromagnetic film and bilayer films composed of two ferromagnetic layers coupled through antiferromagnetic interfacial interaction by classical Heisenberg model and simulated their magnetization state,magnetic permeability,and Faraday effect at zero and finite temperature by using the Landau–Lifshitz–Gilbert(LLG)equation.The results indicate that in a microwave field with positive circular polarization,the ferromagnetic film has one resonance peak while the bilayer film has two resonance peaks.However,the resonance peak disappears in ferromagnetic film,and only one resonance peak emerges in bilayer film in the negative circularly polarized microwave field.When the microwave field’s frequency exceeds the film’s resonance frequency,the Faraday rotation angle of the ferromagnetic film is the greatest,and it decreases when the thickness of the two halves of the bilayer is reduced.When the microwave field’s frequency remains constant,the Faraday rotation angle fluctuates with temperature in the same manner as spontaneous magnetization does.When a DC magnetic field is applied in the direction of the anisotropic axis of the film,the Faraday rotation angle varies with the DC magnetic field and shows a similar shape of the hysteresis loop.

Classic analogue of Autler–Townes-splitting transparency using a single magneto-optical ring resonator

We show that an optical transparency can be obtained by using only one single magneto-optical ring resonator. This effect is based on the splitting of counterclockwise and clockwise modes in the ring resonator. Within a proposed resonator-waveguide configuration the superposition between the two degeneracy broken modes produces a transparency window,which can be closed, open, and modified by tuning the applied magnetic field. This phenomenon is an analogue of Autler–Townes splitting, and the magnetic field is equivalent to the strong external pump field. We provide a theoretic analysis on the induced transparency, and numerically demonstrate the effect using full-wave simulation. Feasible implication of this effect and its potential applications are also discussed.

Determination of the magnetic anisotropy constant of Cu/Fe/SiO_2/Si by a magneto-optical Kerr effect susceptometer

The magneto-optical Kerr effect susceptometry technique is proposed to determine the uniaxial magnetic anisotropy （UMA） constant Ku. The magnetic properties of Cu/Fe/SiO2/Si grown by dc magnetron sputtering were investigated. The in-plane uniaxial magnetic anisotropy was probed by the magneto-optical Kerr effect （MOKE）. The value of UMA, Ku = 2.5 x 103 J/m3, was simulated from the field dependence of ac susceptibility along the hard axis according to the Stoner-Wohlfarth （S-W） model, which is consistent with Ku = 2.7~ 103 J/m3 calculated from the magnetic hysteresis loops. Our results show that the magneto-optical Kerr effect susceptometry can be employed to determine the magnetic anisotropy constant owing to its high sensitivity.

Resonant magneto-optical Kerr effect induced by hybrid plasma modes in ferromagnetic nanovoids

With nanovoids buried in Co films, resonant structures were observed in spectra of polar magneto-optical Kerr effect（MOKE）, where both a narrow bandwidth and high intensity were acquired. Through changing the thickness of Co films and the lattice of voids, different optical modes were introduced. For a very shallow array of voids, the resonant MOKE was induced by Ag plasma edge resonance, for deeper ones, hybrid plasma modes, such as void plasmons in the voids, surface lattice plasmons between the voids, and the co-action of them, etc. resulted in resonant MOKE. We found that resonant MOKE resulted from the void plasmons resonance which possesses the narrowest bandwidth for the lowest absorption of voids. The simulated electromagnetic field（EF） distribution consolidated different effects of these three optical modes on resonant MOKE modulation. Such resonant polar MOKE possesses high sensitivity, which might pave the way to on-chip MO devices.

Improvement on the magneto-optical Kerr effect of cobalt film with a quadrilayer structure

The magneto-optical Kerr effect of the HfO2/Co/HfO2/A1 multilayer structure is investigated in this work, and an ob- vious cavity enhancement of the Kerr response for the HfO2 semiconductor is found both theoretically and experimentally. Surprisingly, a maximum value of about -3 of the polar Kerr rotation for s-polarized incident light is observed in our experiment. We propose that this improvement on the Kerr effect can be attributed to the multiple reflection and optical interference in the cavity, which can also be proved by simulation using the finite element method.

The subwavelength tuned magneto-optical Kerr effect in L1_0-FePt films with perpendicular magnetic anisotropy

For L10-FePt films with strong perpendicular anisotropy covered by arrays of hexagonal close-packed polystyrene spheres （PSSs）, fine structures are observed in magneto-optical Kerr rotation spectra in the visible spectral range. The reflection minima are found to be located at the same wavelengths as the Kerr rotation peaks. The Kerr rotation enhancement is attributed to the excitation of both the surface plasmon polariton in the dielectric PSS/metal interface and the guide waves （guide mode） in the PSS array. The two-dimensional PSSs/SiO2/FePt system exhibiting a tunable magneto-optical Kerr effect and a high perpendicular magnetic anisotropy will be helpful for designing and fabricating magneto-optics devices.

Study of magnetization reversal and anisotropy of single crystalline ultrathin Fe/MgO (001) film by magneto-optic Kerr effect

The magnetization reversal process of Fe/MgO （001） thin film is investigated by combining transverse and longi- tudinal 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.

Surface Plasmon and Fabry-Perot Enhanced Magneto-Optical Kerr Effect in Graphene Microribbons

A single sheet of graphene exhibits the ability to turn polarization of light by several degrees in modest magnetic fields. Here we demonstrate that giant angle rotation in graphene in the terahertz range can be realized and further increased by the introduction of surface plasmon and constructive Fabry Perot interference with the supporting substrate. The maximum Kerr rotation angle is up to 15° in a single layer of graphene ribbons at 6 TPIz for the applied magnetic field 4 T. Such a magnification in magneto-optical Kerr effect can be realized in a fairly large incident angle.

Study of magnetic and magneto-optical properties of heavily doped bismuth substitute yttrium iron garnet (Bi∶YIG) film

The magnetic and magneto-optical properties of heavily doped Bi∶YIG film were studied. The film was deposited by radio frequency magnetron sputtering method and crystallized by rapid recurrent thermal annealing (RRTA). The results show that the RRTA treated film has good properties both in microwave and optical wave band. The saturation magnetization of the film on different substrates varies from 135.7 to 138.6 kA·m-1. The coercive field of the film on GGG substrate is about 0.32 kA·m-1, while about 0.8-1.43 kA·m-1 on YAG substrate and 1.75 kA·m-1 on Al2O3 substrate. The Faraday angle is about 3-5 (°)·μm-1 when optical wavelength ranges at 450-600 nm. The transmission spectra of the Bi∶YIG films on three substrates has similar change as annealing temperature below 800 ℃. Specially, when annealing temperature is above 800 ℃ a step is observed between 550 and 650 nm wavelength for the film deposited on Al2O3 substrate.Three results are very useful in magneto-optical recording application and integrated microwave devices.

Influence of Magnetic Field Inhomogeneity on a Magneto-Optical Current Sensor

The growth in the capacity of electric power system creates a demand for the protection of relaying systems. Optical current transducers—OCT that are mainly made up of single mode optical fibers which are subjected to Faraday rotation are used as a replacement for electromagnetic transducers due to their immunity to electromagnetic interference. However, the principal parameter in this system, the sensitivity to magnetic fields or current, depends on the Verdet constant, which is low in the case of optical fibers. However, the optical path length can be increased to compensate for it by winding the fiber around a current carrying element a large number of turns. In this work, we study a current sensor, which is made up of a conductor coil with a fiber inside, thus increasing sensitivity. We study the effect of the inhomogeneity of the magnetic field induced by the current on the sensitivity of the optical fiber sensor.

Magneto-Optic Fiber Bragg Gratings with Application to High-Resolution Magnetic Field Sensors

Magneto-optic fiber Bragg gratings （MFBG） based on magneto-optic materials have a lot of potential applications for sensing and optical signal processing. The transmission and reflection spectra of guided optical waves in the MFBG are investigated. According to the sensitivity of MFBG spectral lines to the magneto-optic coupling intensity varying with applied magnetic field, a novel magnetic field sensor of high-resolution up to 0.01 nm/（kA/m） is predicted.

MOSSBAUER POLARIMETER AND MOSSBAUER FARADAY EFFECT

A Mossbauer polarimeter consists of a gamma ray source (polarizer), transmitter (sample to be analyzed), analyzer and automatic counting system. This equipment was used to observe the Mossbauer Faraday effect in non-stoichiometric Fe3O4. Experimental results demonstrated that electronic hopping above the Verwey temperature between Fe2+- Fe3+ ions on the octahedral sites is a only localized phenomenon and the recoilless fractions of 57Fe nuclei in Fe3-vO4 (v=0.02) are 0.71 for A sites and 0.62 for B sites, respectively.

Ramsey-CPT spectrum with the Faraday effect and its application to atomic clocks

A method that obtains the Ramsey-coherent population trapping （CPT） spectrum with the Faraday effect is investi- gated. An experiment is implemented to detect the light polarization components generated from the Faraday effect. The experimental results agree with the theoretical calculations based on the Liouville equation. By comparing with the method without using the Faraday effect, the potential of this method for a CPT-based atomic clock is assessed. The results indicate that this method should improve the short-term frequency stability by several times.

Microwave Magneto-Optic Bragg Modulators with Rectangular MSFVW Pulses

Microwave magneto-optic （MO） modulators can directly transform radio frequency （RF） signals into optical data through the Bragg diffraction of guided optical waves （GOWs） induced by microwave magneto-static waves （MSWs）. According to the MO coupled-mode theory, the modulation of continuous GOWs by a rectangular magneto-static-forwardvolume-wave （MSFVW） pulse in MO film waveguide is studied in the small signal case and the modulated optical pulse at the output is analyzed by means of an analytical form, which is dependent on the instantaneous diffraction intensity determined by the overlap of rectangular MSFVW pulse and light beam aperture. On the basis of it, the characteristics of MSFVW-based MO modulators can be explained well for the case of rectangular pulse modulation. It is also shown that the line codes of optical data generated by MO Bragg modulators can be controlled by adjusting the duty factor of modulating pulse signals.

Magneto-Optical Properties of Wider Gap Semiconductors ZnMnTe and ZnMnSe Films Prepared by MBE

TheⅡ-Ⅵbased magnetic semiconductors with a direct and wide optical bandgap are expected to show high potential for optical applications utilizing short wavelength laser diodes(LDs),such as 532-nm green and475-nm blue LDs.We have confirmed that the Faraday rotationθ_F in the ZnMnTe and ZnMnSe films deposited on quartz glass(QG)and sapphire(SA)substrates by using molecular beam epitaxy(MBE)is large near the absorption edge.This paper reports the magneto-optical properties of ZnMnTe and ZnMnSe films synthesized on the QG and SA substrates,and shows the result of a direct Faraday rotation observation successfully made for the ZnMnTe films under 1.28-kHz alternating magnetic fields.The optical absorption characteristics of the ZnMnTe films grown on the SA substrates by MBE are discussed by comparing them with the optical absorption properties and photoluminescence spectra of theⅡ-ⅥZnTe parent single crystals.

Study on Physical Process of Surface Oxidation of Rare Earth-Transition Metal Amorphous Magneto-Optical Thin Films

By using surface effects(Auger electron spectroscopy,X-ray photoelectron spectroscopy,polar Kerr effect)and volume effects(magnetization,torque curve)the physical process of surface oxidation of rare earth-transition metal amorphous magneto-optical thin films was studied in this paper.The rare earth elements oxidize preferentially and rich at the film surface,and the transition metals deplete in oxidation layer.Fe_2O_3 in the surface oxidation layer contributes to the planar magnetization,and thereby the anomalous peak appears near 180° on the torque curves and the amplitude of the peaks is related to the depth of surface oxidation layers.The iron bonds to oxygen easier than the cobolt.RE-Co magneto-optieal thin films have good properties of resistance to oxidation and humidity.

Gravitational Faraday effect in curved space-time induced by high-power lasers

Gravitational field produced by high-power laser is calculated according to the linearized Einstein field equation in weak field approximation. Gravitational Faraday effect of electromagnetic wave propagating in the above gravitational field is studied and the rotation angle of polarization plane of electromagnetic wave is derived. The result is discussed and estimated under the condition of present experiment facility.