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.

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.

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.

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 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.

Magneto-optical Kerr effect in Co_xAg_(1-x) nanostructured granular films

A series of CoxAg1-x nanostructured granular films have been prepared by ion beam sputtering and annealed at 100, 250, 400, 5001. The optical constants, the complex dielectric func-tion and magneto-optical Kerr parameters were measured at room temperature. For the samples hav-ing low Co compositions, the strong Kerr effect enhancement is observed around the Ag plasma edge. With an increase in annealing temperature, the resonance-like peaks appear in the Kerr rotation, and the peak positions are shifted toward the low photon energy region. From the analysis of the numerical calculations, it is concluded that the magneto-optical Kerr effect enhancement (MOKE) is due to the presence of the steep plasma edge.

Improving the sensitivity of DC magneto-optical Kerr effect measurement to 10^(-7)rad/√Hz

A high-sensitivity DC magneto-optical Kerr effect(MOKE)apparatus is described in this Letter.Via detailed analysis on several dominatingnoise sources,we have proposed solutions that significantly lower the MOKE noise,and a sensitivity of 1.5×10^(-7)rad/√Hz is achieved with long-term stability.The sensitivity of the apparatus is tested by measuring a wedgeshaped Ni thin film on SiO_(2)with Ni thickness varying from 0 to 3 nm.A noise floor of 1.5×10^(-8)rad is demonstrated.The possibility of further improving sensitivity to 10^(-9)rad via applying AC modulation is also discussed.

Frequency dependence of magnetization and giant magneto impedance effect of amorphous wires

The frequency dependence of magnetization process and giant magneto impedance （GMI） effect of Co-rich melt-extracted amorphous wires was studied by Kerr effect and impedance analyzer, respectively. It is demonstrated that the transverse Kerr intensity and the corresponding GMI response increase with increasing frequency, which contributes to the upgraded skin effect. However, the skin depth has a slothful trend with frequency when it is up to the megahertz range, which gives rise to the transformation of magnetization. The process is much more sensitive to the direct current magnetic field and the sensitive change of the circular permeability, and GMI response is observed as its consequence. This proves that the evolution of circumferential magnetization and the corresponding permeability with the direct current magnetic field is the essence of GMI response, and a much more sensitive magnetization promises a better GMI response.

Effects of Nd Doping on Magnetic-Optical Properties of GdFeCo Thin Films

The GdFeCo and NdGdFeCo thin films were prepared by sputtering, and their hysteresis loops, the temperature dependence of the saturation magnetization Ms and the magneto-optical Kerr spectrum in the visible light range were measured. By studying the effects of light rare earth element Nd doping on the magneto-optical Kerr rotation angle of GdFeCo thin films, it is found that proper Nd additives in GdFeCo films could enhance Kerr rotation at short wavelengths. So it could be better medium used as the readout layer of center aperture detection magnetically induced super resolution （CAD-MSR）.

Tuning the magnetic anisotropy of Co Fe B grown on flexible substrates

The magnetic properties of CoFeB thin films grown on flexible polyimide substrates were investigated using a magneto-optical Kerr effect magnetometer. In-plane uniaxial magnetic anisotropy was observed in the virgin state. The strain induced by bending the flexible substrate was applied on the sample to change the magnetic properties of CoFeB.The strain induced uniaxial magnetic anisotropy changed linearly with the deformation by about 8.41 × 10^4erg/cm^3 at 1%of deformation. Our results prove the magnetic properties of CoFeB grown on flexible polyimide substrate can be tuned effectively by bending, which could be important for future flexible spintronics.

Rapid screening of magnetic properties in several Fe-X-Ni systems via combinatorial materials chip method

Fe-X-Ni(X=Cr,W and V)combinatorial thin-film(∼100 nm thick)materials chips covering the full composition range of ternary systems were fabricated.The crystal structure distribution was mapped by micro-beam X-ray diffractometers(XRD)and the magnetic hysteresis loops over the chip were characterized by a high-throughput magneto-optical Kerr effect(HT-MOKE)system to establish the composition-phase-magnetic properties relationships.The results showed that saturation magnetization for all systems has a strong dependency on alloying composition,and decreases with increasing dopped elements content as a general trend.Although the trend of saturation magnetization in bulk is in good agreement with that from thin films,all bulk samples show almost no coercivity,attributable to the much smaller grain size,and stronger texture in thin-film samples.Comparing the Fe-X-Ni systems under a similar condition,in the out-of-plane,Cr alloying obtained the largest coercivity(∼400 mT)followed by W alloying(∼300 mT)and then V alloying(∼200 mT).We suggest that alloying with different elements leads to the diverse orientation and crystallinity of the fcc phase resulting in different magnetic properties.Meanwhile,the effect of heat treatment on magnetic properties indicates that saturation magnetization is more closely related to the duration of heat treatment.

Combining two-photon lithography with laser ablation of sacrificial layers:A route to isolated 3D magnetic nanostructures

Three-dimensional(3D)nanostructured functional materials are important systems allowing new means for intricate control of electromagnetic properties.A key problem is realising a 3D printing methodology on the nanoscale that can yield a range of functional materials.In this article,it is shown that two-photon lithography,when combined with laser ablation of sacrificial layers,can be used to realise such a vision and produce 3D functional nanomaterials of complex geometry.Proof-of-principle is first shown by fabricating planar magnetic nanowires raised above the substrate that exhibit controlled domain wall injection and propagation.Secondly,3D artificial spin-ice(3DASI)structures are fabricated,whose complex switching can be probed using optical magnetometry.We show that by careful analysis of the magneto-optical Kerr effect signal and by comparison with micromagnetic simulations,depth dependent switching information can be obtained from the 3DASI lattice.The work paves the way for new materials,which exploit additional physics provided by non-trivial 3D geometries.

克尔磁光效应的经典理论分析

本文引入与自旋-轨道相互作用等有关的有效场概念,运用经典电磁场理论,推导了磁光克尔旋转的明确表达式.证明了各种磁光介质的极向克尔旋转θ_k的实部θ′_k和虚部θ″_k均与有效场H_i成正比,在铁磁性介质中近似与vM成正比,M为磁化强度,在亚铁磁性等介质中近似与(?)v_iM_i成正比,M_i为i次点阵的磁化强度.同时还证明了近似的横向克尔旋转θ_k^t与H_i^2正比;θ_k和θ_k^t的温度特性取决于H_i的温度特性.

Relationship between microstructure and magnetic domain structure of Nd-Fe-B melt-spun ribbon magnets

The relation between the microstructure, observed using an electron probe microanalyzer, and the domain structure, observed using a Kerr microscope, was established to evaluate the effects of hot rolling and the addition of Ti-C on the c-axis orientation and the magnetization process of hot-rolled Nd-Fe-B-Ti-C melt-spun ribbons. The addition of Ti-C promotes the c-axis orientation and high coercivity in the ribbons. Elemental mapping suggests a uniform elemental distribution; however, an uneven distribution of Ti was observed in an enlarged grain with Ti-enriched points inside the grain. The reversal domains that nucleated at the Ti-enriched point inside the grain cause low coercivity.

Optical spectroscopy study of charge density wave orderOptical spectroscopy study of charge density wave order in Sr_3Rh_4Sn_(13) and (Sr_(0.5)Ca_(0.5))3_Rh_4Sn_(13)

The ultrafast laser-excited magnetization dynamics of ferromagnetic （FM） La0.67Sr0.33MnO3 （LSMO） thin films with BiFeO3 （BFO） coating layers grown by laser molecular beam epitaxy are investigated using the optical pump-probe technique. Uniform magnetization precessions are observed in the films under an applied external magnetic field by measuring the time-resolved magneto-optical Kerr effect. The magnetization precession frequencies of the LSMO thin films with the BFO coating layers are lower than those of uncoated LSMO films, which is attributed to the suppression of the anisotropy field induced by the exchange interaction at the interface between the antiferromagnetic order of BFO and the FM order of LSMO.

Vector analysis of electric-field-induced antiparallel magnetic domain evolution in ferromagnetic/ferroelectric heterostructures

Electric field(E-field)control of magnetism based on magnetoelectric coupling is one of the promising approaches for manipulating the magnetization with low power consumption.The evolution of magnetic domains under in-situ E-fields is significant for the practical applications in integrated micro/nano devices.Here,we report the vector analysis of the E-field-driven antiparallel magnetic domain evolution in FeCoSiB/PMN-PT(011)multiferroic heterostructures via in-situ quantitative magneto-optical Kerr microscope.It is demonstrated that the magnetic domains can be switched to both the 0°and 180°easy directions at the same time by E-fields,resulting in antiparallel magnetization distribution in ferromagnetic/ferroelectric heterostructures.This antiparallel magnetic domain evolution is attributed to energy minimization with the uniaxial strains by E-fields which can induce the rotation of domains no more than 90°.Moreover,domains can be driven along only one or both easy axis directions by reasonably selecting the initial magnetic domain distribution.The vector analysis of magnetic domain evolution can provide visual insights into the strain-mediated magnetoelectric effect,and promote the fundamental understanding of electrical regulation of magnetism.

Transmission characteristics of linearly polarized light in reflection-type one-dimensional magnetophotonic crystals

The propagation properties of linearly polarized light in reflection・type one-dimensional magnetoph tonic crystals are studied by using the 4×4 transmission matrix method.The structure models of reflectiotype one-dimensional magnetophotonic crystals are designed,the magnetic field direction control characteristics of reflection spectrum and Kerr rotation angle are discussed,and the effect of applied magnetic field direction and strength on reflection spectrum and Kerr rotation angle are analyzed.The results show that the non-diagonal elements in the dielectric constant of magneto optical materials change when the angle φ between applied magnetic field and optical path changes,the reflectivity and Kerr rotation angle decrease when the angle φ increases;when the applied magnetic field strength changes,the reflectivity and Kerr rotation angle increase when the applied magnetic field strength increases;by adjusting the angleφ and strength of the applied magnetic field,the rotation angle of Kerr can be adjusted to 45°,and a more flat reflection spectrum can be obtained by designing the appropriate structure.

Observation of magnetic domain evolution in constrained epitaxial Ni–Mn–Ga thin films on MgO(0 0 1) substrate

Epitaxial Ni–Mn–Ga thin films have promising application potential in micro-electro-mechanical sensing and actuation systems. To date, large abrupt magnetization changes have been observed in some epitaxial Ni–Mn–Ga thin films, but their origin-either from magnetically induced martensite variant reorientation(MIR) or magnetic domain evolution-has been discussed controversially. In the present work, we investigated the evolutions of the magnetic domain and microstructure of a typical epitaxial Ni–Mn–Ga thin film through wide-field magneto-optical Kerr-microscopy. It is demonstrated that the abrupt magnetization changes in the hysteresis loops should be attributed to the magnetic domain evolution instead of the MIR.