Cubic-in-magnetization contributions to the magneto-optic Kerr effect investigated for Ni(001) and Ni(111) thin films
VSB-Technical University of Ostrava（俄斯特拉发理工大学）；Bielefeld University（比勒费尔德大学）；Charles University（查理大学）；Czech Technical University（捷克理工大学）；Johannes Gutenberg University Mainz（美因茨约翰内斯古腾堡大学）
Robin Silber, Maik Gaerner, Kamil Postava, Jaroslav Hamrle, Timo Kuschel
*The abstract of this article is too long to be included in the arXiv metadata; please see the paper for the full abstract.* ...In this paper, we introduce the detailed theory of cubic-in-magnetization magneto-optic Kerr effect (CMOKE) by deriving the magneto-optic tensor of third order in magnetization, denoted as $\bm{H}$, and comparing the strength of CMOKE for different crystal orientations theoretically and experimentally. In crystals with cubic symmetry, the tensor $\bm{H}$ is described by two independent parameters $H_{123}$ and $H_{125}$. Together with the linear magneto-optic tensor $\bm{K}$ and quadratic magento-optic tensor $\bm{G}$, the permittivity tensor is described up to third order in magnetization. We analytically describe equations of the MOKE including the contribution of QMOKE and CMOKE itself for (001)- and (111)-oriented cubic crystal structures. Those are compared to experimental measurements of two samples with an (001)- and (111)-oriented fcc Ni layer, respectively. Further, we use Yeh's 4$\times$4 transfer matrix calculus to simulate and describe the experimental measurements phenomenologically from the permittivity tensor up to third order in $\bm{M}$. We find that the MOKE anisotropy that stems from the magneto-optic tensor $\bm{H}$ described as $ΔH = H_{123}-3H_{125}$, is much more pronounced for the (111)-oriented cubic crystal structure, for which it manifests as three-fold in-plane angular dependencies of MOKE with longitudinal and also with transversal magnetization direction, respectively.
We demonstrate theoretically a large transverse magneto-optical Kerr effect (TMOKE) in subwavelength gratings consisting of alternating magneto-insulating and nonmagnetic dielectric nanostripes. The reflectivity of the grating reaches $96\%$ at the frequencies corresponding to the maximum of the TMOKE response. The combination of a large TMOKE response and high reflectivity is important for applications in $3$D imaging, magneto-optical data storage, and magnonics.
We propose a novel method to enhance the transverse magneto-optical Kerr effect (TMOKE) in the magneto-plasmonic (MP) nanostructures by means of the active dielectric layer. We report the theoretical analysis of the magnetoplasmonic structure with a ferromagnetic dielectric doped with rear-earth ions (Nd3+) as the example of a gain layer. The enhancement takes place near the surface plasmon polariton (SPP) resonances of the nanostructures. The stimulated emission of the dopants in the field of SPP wave partially compensates its losses. It is shown that due to a decrease of SPP damping a Q-fact…
It has been shown that a slab of a negative index material can behave as a superlens enhancing the imaging resolution beyond the wavelength limit. We show here that if such a slab possesses in addition some magneto-optical activity, it could act as an ideal optical filter and exhibit an extraordinary transverse magneto-optical Kerr effect. Moreover, we show that losses, which spoil the imaging resolution of these lenses, are a necessary ingredient to observe this effect.
In order to maximize the transversal magneto-optic Kerr effect (T-MOKE) of a Au/Co/Au structure, we propose a method to obtain the optimum thickness values. A criteria based on preserving good plasmonic properties has been included as part of this method. Using the theoretical prediction, we grew Au/Co/Au trilayers and perform optical andMO characterization using the Kretschmann configuration. The results admit very easy interpretation in terms of the interaction between the magneto-optical and plasmonic properties dictating the optimal thicknesses of the structure. Moreover, we have grown and…
In magnetoplasmonics, it is possible to tailor the magneto-optical properties of nanostructures by exciting surface plasmon polaritons (SPPs). Thus far, magnetoplasmonic effects have been considered static. Here, we describe ultrafast manifestations of magnetoplasmonics by observing the non-trivial evolution of the transverse magneto-optic Kerr effect within 45-fs pulses reflected from an iron-based magnetoplasmonic crystal. The effect occurs for resonant SPP excitations, displays opposite time derivative signs for different slopes of the resonance, and is explained with the magnetization-depe…
Large surface plasmon polariton assisted enhancement of the magneto-optical activity has been observed in the past, through spectral measurements of the polar Kerr rotation in Co hexagonal antidot arrays. Here, we report a strong thickness dependence, which is unexpected given that the Kerr effect is considered a surface sensitive phenomena. The maximum Kerr rotation was found to be -0.66 degrees for a 100 nm thick sample. This thickness is far above the typical optical penetration depth of a continuous Co film, demonstrating that in the presence of plasmons the critical lengthscales are drama…
The transverse magneto-optical Kerr effect (TMOKE) in magnetite-based magneto-plasmonic crystals is studied experimentally and theoretically. We analyze angle-resolved TMOKE spectra from two types of structures where noble metallic stripes are incorporated inside a thin magnetite film or located on top of a homogeneous film. A multiple wide band enhancement of the TMOKE signal in transmission is demonstrated. The complex dielectric permittivity and gyration are experimentally determined using the ellipsometry technique as well as Faraday rotation and ellipticity measurements. The obtained para…
Light polarization rotators and non-reciprocal optical isolators are essential building blocks in photonics technology. These macroscopic passive devices are commonly based on magneto-optical Faraday and Kerr polarization rotation. Magnetoplasmonics - the combination of magnetism and plasmonics - is a promising route to bring these devices to the nanoscale. We introduce design rules for highly tunable active magnetoplasmonic elements in which we can tailor the amplitude and sign of the Kerr response over a broad spectral range.
We calculate theoretically the transverse magneto-optical Kerr effect (TMOKE) in the periodically patterned waveguide made from a diluted magnetic semiconductor. It is demonstrated that the TMOKE is resonantly enhanced when the incident wave is in resonance with the bound state in continuum, arising when the quality factor of the waveguide mode increases due to the far-field interference. Our results uncover the potential of all-dielectric and semiconductor nanostructures for resonant magneto-optics.
The magnetooptic Kerr effect (MOKE) is a well known and handy tool to characterize ferro-, ferri- and antiferromagnetic materials. Many of the MOKE techniques employ effects solely linear in magnetization $\bm{M}$. Nevertheless, a higher-order term being proportional to $\bm{M}^2$ and called quadratic MOKE (QMOKE) can additionally contribute to the experimental data. Here, we present detailed QMOKE spectroscopy measurements in the range of 0.8 -- 5.5\,eV based on a modified 8-directional method applied on ferromagnetic bcc Fe thin films grown on MgO substrates. From the measured QMOKE spectra,…
Giant enhancement of the transverse magneto-optical Kerr effect in etchless bismuth-substituted yttrium iron garnet empowered by quasi-bound states in the continuum
Magnetic and spintronic media have offered fundamental scientific subjects and technological applications. Magneto-optic Kerr effect (MOKE) microscopy provides the most accessible platform to study the dynamics of spins, magnetic quasi-particles, and domain walls. However, in the research of nanoscale spin textures and state-of-the-art spintronic devices, optical techniques are generally restricted by the extremely weak magneto-optical activity and diffraction limit. Highly sophisticated, expensive electron microscopy and scanning probe methods thus have come to the forefront. Here, we show th…
A high-sensitive DC Magneto-Optical Kerr Effect (MOKE) apparatus is described in this letter. Via detailed analysis on several dominating noise sources, we have proposed solutions that significantly lower the MOKE noise, and a sensitivity of $1.5\times10^{-7} \text{rad}/\sqrt{\text{Hz}}$ is achieved with long-term stability. The sensitivity of the apparatus is tested by measuring a wedge-shaped Ni thin film on $\text{SiO}_2$ with Ni thickness varying from 0 to 3 nm. A noise floor of $1.5\times10^{-8}$ rad is demonstrated. The possibility of further improving sensitivity to $10^{-9}$ rad via ap…
Temperature-invariant magneto-optical Kerr effect in a noncollinear antiferromagnet
University of California, Irvine（加州大学尔湾分校）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；Irvine Materials Research Institute, University of California, Irvine（加州大学尔湾分校欧文材料研究所）；Colorado State University（科罗拉多州立大学）
We performed non-degenerate pump-probe experiments on a GaAs/AlAs photonic structure. We switched the photonic properties using the optical Kerr effect and free carriers excited by three photon absorption. From these measurements we extracted the non-degenerate Kerr coefficients over a broad wavelength range and we extracted the three photon absorption coefficient for GaAs at three wavelengths in the near infrared. We show that the optical Kerr effect is large enough to switch a cavity resonance with a high \emph{Q} ($Q>1000$) photonic cavity.
We show that double-charged optical vortices can be generated with the help of Kerr electrooptic effect in either single crystals or isotropic media, including gaseous and liquid ones. We analyze possibilities for the vortex generation via the Kerr effect for different point group of symmetry and formulate the appropriate conditions. We prove that the crystals, textures and the isotropic media most suitable for the generation of double-charged optical vortices should belong to the symmetry groups 622, 6mm, 6/mmm, 6, 6/m, inf/m, inf, inf 2, inf mm, inf/mmm, inf/inf/mmm, and inf/inf2.
Università degli Studi di Salerno（萨莱诺大学）；CNR-SPIN, Unità di Salerno（意大利国家研究委员会自旋物理研究所萨莱诺分部）；CNISM, Unità di Salerno, Università degli Studi di Salerno（意大利纳米科学研究所萨莱诺分部，萨莱诺大学）
Magneto-optical spectroscopy based on the transverse magneto-optical Kerr effect (TMOKE) is a sensitive method for investigation of magnetically-ordered media. However, in magnetic materials the optical transitions are usually characterized by spectrally broad resonances with widths considerably exceeding the Zeeman splitting in the magnetic field. Here we investigate experimentally and theoretically the TMOKE in the vicinity of relatively narrow optical resonances provided by confined quantum systems. For experimental demonstration we use the exciton resonance in a (Cd,Mn)Te diluted magnetic …
Pulse laser deposited La2/3Sr1/3MnO3 ultrathin films on SrTiO3 substrates were characterized by polar and longitudinal Kerr magneto-optical spectroscopy. An agreement between experimental and theoretical spectra was achieved for a 10.7 nm thick film, while a distinction in the Kerr effect amplitudes was obtained for a 5 nm thick film. This points to the slight suppression of ferromagnetism by interface effects. Nevertheless, the room temperature ferromagnetism of the 5 nm thick film was clearly demonstrated. All the studied films exhibit magneto-optical properties similar to single crystals an…
We prove an instance of the Reciprocity Theorem that demonstrates that Kerr rotation, also known as the magneto-optical Kerr effect, may only arise in materials that break microscopic time reversal symmetry. This argument applies in the linear response regime, and only fails for nonlinear effects. Recent measurements with a modified Sagnac Interferometer have found finite Kerr rotation in a variety of superconductors. The Sagnac Interferometer is a probe for nonreciprocity, so it must be that time reversal symmetry is broken in these materials.
In conventional Kerr- and Faraday microscopy the sample is illuminated with plane-polarised light and a magnetic domain contrast is generated by an analyser making use of the Kerr- or Faraday rotation. In this paper we demonstrate possibilities of analyser-free magneto-optical microscopy based on magnetisation-dependent intensity modulations of the light: (i) The transverse Kerr effect can be applied for in-plane magnetised material, demonstrated for an FeSi sheet. (ii) Illuminating the same sample with circularly polarised light leads to a domain contrast with a different symmetry as the conv…
Plasmonics has been attracting considerable interest as it allows localization of light at nanoscale dimensions. A breakthrough in integrated nanophotonics can be obtained by fabricating plasmonic functional materials. Such systems may show a rich variety of novel phenomena and also have huge application potential. In particular magnetooptical materials are appealing as they may provide ultrafast control of laser light and surface plasmons via an external magnetic field. Here we demonstrate a new magnetooptical material: a one-dimensional plasmonic crystal formed by a periodically perforated n…
The concept of transformation optics is extended to nonlinear electrodynamics. It is shown that transformation optics favors implicit constitutive relations in terms of energy densities D.E and B.H rather than E^2 and H^2. The Kerr nonlinearity is studied in detail and the transformation optics based engineering of self-interaction effects is discussed. As a specific example we introduce transformation optics applied on a self-focusing field configuration.
We present here a generalization of the scattering-matrix approach for the description of the propagation of electromagnetic waves in nanostructured magneto-optical systems. Our formalism allows us to describe all the key magneto-optical effects in any configuration in periodically patterned multilayer structures. The method can also be applied to describe periodic multilayer systems comprising materials with any type of optical anisotropy. We illustrate the method with the analysis of a recent experiment in which the transverse magneto-optical Kerr effect was measured in a Fe film with a peri…
Advances in microresonator-based soliton generation promise chip-scale integration of optical frequency comb for applications spanning from time keeping to frequency synthesis. Miniaturized cavities harness Kerr nonlinearity and enable terahertz soliton repetition rates. However, such high repetition rates are not amenable to direct electronic detection. Here, we demonstrate hybrid Kerr and electro-optic microcombs using the lithium niobate thin film that exhibits both Kerr and Pockels nonlinearities. By interleaving the high-repetition-rate Kerr soliton comb with the low-repetition-rate elect…
Brée, Demircan, and Steinmeyer [Phys. Rev. Lett. 106, 183902 (2011)] recently calculated higher-order Kerr effect (HOKE) coefficients using the nonlinear Kramers-Kronig relations. We show that the saturated and negative nonlinear index of refraction obtained by Brée et al. is an artifact of their use of a perturbative theory of ionization in an intensity region where it breaks down.
