Complex Kerr Angle Research Articles

Measurement of Kerr rotation and ellipticity in magnetic thin films by MOKE magnetometry

When polarized light is incident on a magnetic material, the magneto-optical Kerr effect (MOKE) rotates the polarization and induces ellipticity in the reflected light, which allows the magnetization direction to be probed optically. The Kerr rotation and ellipticity determine the magnitude of the effect and are usually measured using dedicated ellipsometers. Here, we demonstrate a simple method for extracting Kerr rotation and ellipticity in magnetic thin films using a conventional MOKE magnetometer consisting of two polarizers and a quarter waveplate. Using this technique, we report the longitudinal Kerr angle of BiYIG, GdCo, and TbCo. We additionally observe a linear decrease in polar complex Kerr angle magnitude in 3 nm GdCo films as the atomic fraction of Gd is increased.

High-sensitivity characterization of ultra-thin atomic layers using spin-Hall effect of light

The fast-emerging diverse applications using a variety of magnetic/non-magnetic heterostructure ultra-thin films warrant the sensitive characterization of the electrical, optical, and magnetic properties of the interface. As a practical alternate to the conventional magneto-optic Kerr effect (MOKE) method, we propose and demonstrate the spin-Hall effect of the light (SHEL)-based MOKE method with competitive sensitivity and scope for further improvement. The SHEL-MOKE technique is a versatile surface characterization tool for studying materials’ magnetic and dielectric ordering, which are extracted from the variations to the phase-polarization characteristics of a focused beam of light reflected at the interface, as a function of the applied magnetic field. Using this technique, we measure the magnetic field dependent complex Kerr angle and the coercivity in ultra-thin films of permalloy (Py) and at molybdenum disulfide (MoS2)—permalloy (MSPy) hetero-structure interfaces. A comprehensive theoretical model and simulation data are provided to strengthen the potential of this simple non-invasive optical method. The theoretical model is subsequently applied to extract the optical conductivity of non-magnetic ultra-thin layers of MoS2.

Magneto-optic Kerr effect in Gd20Co80 alloy

The magneto-optical Kerr effect in Gd20Co80 alloy and cobalt thin films has been studied in a broad spectral range applying spectral ellipsometry experimental technique. The results of the experiments showed the complex nature of the complex Kerr angle dispersion curves. A quantum mechanical formalism for degenerate and non-degenerate Landau levels for quasi-free electrons in ferromagnetic material has been developed in order to analyze the experimental data. The equivalence of relations for off-diagonal dielectric tensor elements for non-degenerate Landau levels to the classical case of the motion of quasi-free electrons along circular trajectories in a magnetic field has been theoretically shown. The degenerate Landau levels in this approach are the result of motion of electrons in small confined volumes near rare-earth alloy atoms. Rotation of light polarization occurs in this case due to transitions between subbands having different magnetic quantum numbers. This theoretical approach allowed us to interpret in detail shapes and sign of the complex Kerr angle dispersion curves, which actually include the contributions of optical transitions between degenerate and non-degenerate energy levels. The complex Kerr angle sign is determined by the magnetization magnetic field direction for non-degenerate Landau levels and the Hund rule for degenerate Landau levels.

Perturbative Generalized Magneto-optical Ellipsometry

We present a modified method of data collection and analysis for generalized Magneto-optical ellipsometry (GME) technique. By a perturbative analysis of the light intensity ( $I$ ) and Magneto-optically induced light intensity changes ( $\delta I$ ), as functions of the incident and reflected ray polarizer axis angles ( $\varphi _{1}$ and $\varphi _{2}$ ), we theoretically and experimentally demonstrate that in the proximity of the extinction of $I$ condition, $\varphi _{1}$ and $\varphi _{2}$ can be excellently modeled by a set of quadratic and linear polynomials of $\varphi _{1,2} $ with $R^{2}$ exceeding 0.9 999 in all cases. Compared with the previous conventional GME method (cGME), ours is at least $3.5\times $ more time efficient, the number of adjustable parameters is reduced from 7 to up to 3, and the fitting procedure properly isolates the GME signal from nonrelated effects on $I$ and $\delta I$ functions. Moreover, the routine incorporates the minimization of the offsets of $\varphi _{1}$ and $\varphi _{2}$ so that the extinction of $I$ coordinates can be determined with a precision better than $2\times 10^{-3} \text {deg.}$ The reliability of our method compared with cGME is tested by measuring the complex refractive index ( $N$ ) and Magneto-optical coupling constant ( $Q$ ) of NiFe and Fe films and the complex Kerr angle ( $\Phi $ ) and the ellipsometric parameters ( $\Psi $ and $\Delta $ ) on a series of ultrathin NiFe films.

Methods of Calculation of the Magneto-Optical Characteristics of Ferromagnetic Materials

We have calculated the optical and magneto-optical properties of ferromagnetics in a wide spectral range hv = 1.24–5.15 eV, by applying theoretical models which were reported earlier in the literature. This allowed us to find a connection between the conductivity and the measured values of the complex Kerr angle Θ in order to establish the most proper technique for processing the experimental data. The behavior of the dispersion curves of diagonal and non-diagonal components of the tensor of optical conductivity depends on the choice of signs of the imaginary parts of a complex Kerr angle and a refractive index, which should be taken into account in the data analysis. The differences between dispersion dependences are insignificant in the region of energies higher than 4.5 eV. In this paper, the classical theory of free electrons in metals has been applied to give more details about the magneto-optical Kerr effect in ferromagnetic samples.

Giant magneto-optical Kerr enhancement from films on SiC due to the optical properties of the substrate

We report a giant enhancement of the midinfrared magneto-optical complex Kerr angle (polarization change of reflected light) in a variety of materials grown on SiC. In epitaxially grown multilayer graphene, the Kerr angle is enhanced by a factor of 68, which is in good agreement with Kerr signal modeling. Strong Kerr enhancement is also observed in Fe films grown on SiC and Al-doped bulk SiC. Our experiments and modeling indicate that the enhancement occurs at the high-energy edge of the SiC reststrahlen band where the real component of the complex refractive index ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{n}}_{}$ passes through unity. Furthermore, since the signal is greatly enhanced when $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{n}=1$, the enhancement is predicted to exist over the entire visible and IR spectrum for a free-standing film. We also predict similar giant enhancement in both Faraday (transmission) and Kerr rotation for thin films on a metamaterial substrate with refractive index ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{n}}_{}=\ensuremath{-}1$. This paper demonstrates that the substrate used in magneto-optical Kerr effect (MOKE) measurements must be carefully chosen when investigating magneto-optical materials with weak MOKE signals or when designing MOKE-based optoelectronic devices.

Linear and quadratic magneto-optical Kerr effect investigation of Co2Mn1.30Si0.84 epitaxially grown on MgO

Abstract We investigated the magneto-optical properties of a L21 ordered nonstoichiometric Co2Mn1.30Si0.84 film epitaxially grown on a MgO-buffered MgO (001) single-crystal substrate. Longitudinal magneto-optical Kerr effects (LMOKE) and rotating magneto-optical Kerr effect (ROT-MOKE) measurements suggest that the film exhibits a cubic magnetic anisotropy with the extracted cubic anisotropy constant of K C = 6.7 × 10 4 e r g / c m 3 . Orientation-dependent ROT-MOKE suggest that the quadratic magneto-optical Kerr effects (QMOKE) components also show fourfold symmetry with a modest amplitude of 3 mdeg, which is in accordance with complex Kerr angle expression for cubic symmetry systems. Our results suggest that ROT-MOKE is not only an efficient method to determine magnetic anisotropy parameters but also a good method to extract QMOKE components.

Engineering the polar magneto-optical Kerr effect in strongly strained L10–MnAl films

We report the engineering of the polar magnetooptical (MO) Kerr effect in perpendicularly magnetized L10–MnAl epitaxial films with remarkably tuned magnetization, strain, and structural disorder by varying substrate temperature (Ts) during molecular-beam epitaxy growth. The Kerr rotation was enhanced by a factor of up to 5 with Ts increasing from 150 to 350 °C as a direct consequence of the improvement of the magnetization. A similar remarkable tuning effect was also observed on the Kerr ellipticity and the magnitude of the complex Kerr angle, while the phase of the complex Kerr angle appears to be independent of the magnetization. The combination of the good semiconductor compatibility, the moderate coercivity of 0.3–8.2 kOe, the tunable polar MO Kerr effect of up to ~0.034°, and giant spin precession frequencies of up to ~180 GHz makes L10–MnAl films a very interesting MO material. Our results give insights into both the microscopic mechanisms of the MO Kerr effect in L10–MnAl alloys and their scientific and technological application potential in the emerging spintronics and ultrafast MO modulators.

Composition-tuned magneto-optical Kerr effect in L10-MnxGa films with giant perpendicular anisotropy

We report the large polar magnetooptical Kerr effect in L10-MnxGa (0.76 ⩽ x ⩽ 1.29) epitaxial films with giant perpendicular magnetic anisotropy. The Kerr rotation is enhanced by a factor of up to 2.5 by decreasing Mn atomic concentration, which most likely arises from the variation of the effective spin–orbit coupling strength, compensation effect of magnetic moments at different Mn atom sites, and overall strain. A significant tuning effect of composition is also observed on Kerr ellipticity and complex Kerr angle (including the magnitude and phase angle). The good epitaxial compatibility with semiconductors, moderate coercivity of 4.6–9.7 kOe, large Kerr rotation of up to 0.10°, high reflectivity of 35%–55% in a wide wavelength range of 400 ~ 850 nm, and giant magnetic anisotropic field of up to 140 kOe together make these L10-MnxGa films promising for scientific and technological applications in spintronics and terahertz-frequency magnetooptical modulators.

Resonant magneto-optic Kerr effect in the magnetic topological insulatorCr:(Sbx,Bi1−x)2Te3

We report measurements of the polar Kerr effect, proportional to the out-of-plane component of the magnetization, in thin films of the magnetically doped topological insulator $(\text{Cr}_{0.12}\text{Bi}_{0.26}\text{Sb}_{0.62})_2\text{Te}_3$. Measurements of the complex Kerr angle, $\Theta_K$, were performed as a function of photon energy in the range $0.8\text{ eV}<\hbar\omega<3.0\text{ eV}$. We observed a peak in the real part of $\Theta_K(\omega)$ and zero crossing in the imaginary part that we attribute to resonant interaction with a spin-orbit avoided crossing located $\approx$ 1.6 eV above the Fermi energy. The resonant enhancement allows measurement of the temperature and magnetic field dependence of $\Theta_K$ in the ultrathin film limit, $d\geq2$ quintuple layers. We find a sharp transition to zero remanent magnetization at 6 K for $d<8$~QL, consistent with theories of the dependence of impurity spin interactions on film thickness and their location relative to topological insulator surfaces.

Coherent ultrafast spin-dynamics probed in three dimensional topological insulators.

Topological insulators are candidates to open up a novel route in spin based electronics. Different to traditional ferromagnetic materials, where the carrier spin-polarization and magnetization are based on the exchange interaction, the spin properties in topological insulators are based on the coupling of spin- and orbit interaction connected to its momentum. Specific ways to control the spin-polarization with light have been demonstrated: the energy momentum landscape of the Dirac cone provides spin-momentum locking of the charge current and its spin. We investigate a spin-related signal present only during the laser excitation studying real and imaginary part of the complex Kerr angle by disentangling spin and lattice contributions. This coherent signal is only present at the time of the pump-pulses’ light field and can be described in terms of a Raman coherence time. The Raman transition involves states at the bottom edge of the conduction band. We demonstrate a coherent femtosecond control of spin-polarization for electronic states at around the Dirac cone.

Origin of the polar Kerr rotation in ordered and disordered FePt multilayers

The electronic structure and the magneto-optical properties of ordered and disordered FePt multilayers have been calculated by means of the spin-polarized relativistic linear muffin-tin orbital (SPR-LMTO) method within both the local spin-density approximation (LSDA) and generalized gradient approximation (GGA). Both approximations lead to the same magneto-optical results. The ordered FePt magneto-optical properties have also been calculated within the linear augmented plane wave method and the results are in good agreement with the SPR-LMTO calculations. The complex Kerr angle for ordered and disordered FePt has been calculated for photon energies of up to 6eV and is found to be in a good agreement with experiment. Different structures in the optical conductivity and Kerr rotation as a function of the photon energy are analyzed and discussed. To show the microscopic origin of the strong Kerr rotation at some particular photon energies the symmetry character of the bands contributing to interband transitions together with with the interband electric dipole momentum matrix elements are analyzed in the whole Brillouin zone (BZ). This analysis showed that the assignment of the peaks is complex and cannot only be attributed to interband transitions along high symmetry BZ directions.

Thickness independent magneto-optical coupling constant of nickel films in the visible spectral range

Magneto-optical properties of nominally 10, 20, and 30 nm thick ferromagnetic Ni films have been investigated at room temperature by vector-magneto-optical generalized ellipsometry under saturated magnetization conditions in the sample surface plane. The magneto-optical dielectric tensor of Ni has been determined by reflection Mueller matrix ellipsometry in the spectral range from 300 to 1100 nm. Different sets of magnetic field induced Mueller matrix elements enable us to identify the magnetization directions in the sample. The extracted magnetic field and thickness independent magneto-optical coupling constant is useful for modeling the Mueller matrix and complex Kerr angle of magnetized Ni thin films in layered sample systems in dependence of the incident angle of light, wavelength, and magnetization.

MOKE experiments and theory of uniform and nonuniform distribution of magnetic nanoscrystals: Mn5Ge3in Ge

We present a theoretical and experimental study of the magneto-optical (MO) Kerr effect (MOKE) on inhomogeneous systems. Starting from ab initio calculated band structures and using the effective medium approximation or the recently proposed alternating composition layers approximation [Phys. Rev. B 78, 134411 (2008)], we show that the complex Kerr angle can be reproduced also when a nonuniform distribution of the inhomogeneities is present. Applying our formalism to Mn-Ge--based systems, we find that a realistic account of the inhomogeneous concentration of Mn-rich precipitates in a Ge matrix is a necessary condition in order to describe, within the theoretical approach, the experimental Kerr spectra. The agreement between theoretical and measured MOKE spectra shows the validity of the model considered and establishes its predictive power also for a continuously varying concentration distribution of magnetic species in the system.

Threshold photoemission magnetic circular dichroism at the spin-reorientation transition of ultrathin epitaxial Pt/Co/Pt(111)/W(110) films

X-ray magnetic circular dichroism (MCD) is nowadays widely used for the investigation of magnetic properties of surfaces and thin films. Recently, similarly large effects have been observed for UV-VIS MCD effects both in single [1] and two-photon photoemission [2-3]. This threshold MCD effect is directly related to spin-orbit effects present at the Fermi edge. We report on the observation of threshold photoemission magnetic circular dichroism (TPMCD) in one-photon and two-photon photoemission (1PPE and 2PPE) at a Pt-capped ultrathin Co wedge grown on Pt(111)/W(110) using femtosecond laser light. TPMCD measurements result in asymmetries continuously increasing with the sample thickness. This indicates that the TPMCD asymmetry is dominantly influenced by the Co bulk properties. At 5 monolayers (ML) asymmetry values of 0.07 % for 1PPE and 0.11 % for 2PPE are derived. The spin reorientation transition is detected at a Co thickness of 5.5 ML. For the magnetically saturated sample the TPMCD does not depend on the orientation of the easy axis. Kerr ellipticities and rotations are measured and compared with the TPMCD data in the framework of optical transfer matrix calculations. The observed TPMCD asymmetry considerably deviates from the behaviour of the complex Kerr angle. Moreover, the TPMCD measurements are referred to Co bulk bandstructure calculations and the influence of a capping layer on the TPMCD asymmetry is discussed

Ultrafast demagnetization in Ni: theory of magneto-optics for non-equilibrium electrondistributions

The sensitivity of the magneto-optical Kerr response to electronic thermalization processesin ultrafast pump–probe experiments is studied by evaluating the complex conductivitytensor of Ni for non-equilibrium electron distributions. The electronic structureand optical matrix elements are calculated within density functional theory. Toaccount for the electronic redistributions generated by the intense pump-laserpulse during the initial stages of electronic thermalization, two kinds of modelelectron distributions are considered which mimic the so-called dichroic bleaching orstate-blocking effect. Thus, certain optical transitions which are allowed underequilibrium conditions are not accessible to the probe laser. It is shown that theconductivity tensor and the complex Kerr angle can be modified substantially bythe non-equilibrium electron distributions. Moreover, in striking contrast to thecase for ordinary equilibrium conditions, the Kerr rotation and ellipticity are nolonger proportional to the magnetization of the sample. The Kerr response atultrashort times can therefore not be taken as a measure of demagnetization.

Magneto-optical properties of iron thin films on paramagnetic substrates

We present first principles calculations of the magnetic properties and the magneto-optical Kerr effect of iron thin films epitaxially grown on the [001] surface of two paramagnetic noble metals: Cu and Ag. We investigate the role of hybridization with the substrate and we show how the relaxation effects influence the complex Kerr angle. Our results are obtained using the relativistic full-potential linear muffin-tin method. The film is modeled using a slab geometry within a supercell technique.

Layer-Resolved Magneto-Optical Kerr Effect In Semi-Infinite Inhomogeneous Layered Systems

The contour integration technique applied to calculate the optical conductivity tensor at finite temperatures in the case of inhomogeneous surface layered systems within the framework of the spin-polarized relativistic screened Korringa-Kohn-Rostoker band structure method is extended to arbitrary polarizations of the electric field. It is shown that besides the inter-band contribution, the contour integration technique also accounts for the intra-band contribution. Introducing a layer-resolved complex Kerr angle, the importance of the first, non-magnetic buffer layer below the ferromagnetic surface on the magneto-optical Kerr effect in the Co | Pt m multilayer system is shown. Increasing the thickness of the buffer Pt, the layer-resolved complex Kerr angles follow a linear dependence with respect to m only after nine Pt mono-layers.

Magneto-optical Faraday and Kerr effect of orthoferrite thin films at high temperatures

Orthoferrites present, as bulk materials, reorientation transitions of their magnetic moment alignment at temperatures depending on the rare-earth (RE) ion. In particular, orthoferrites (REFeO3) with RE = Sm, Dy, present this transition at T SRT = 443 K and 36 K, respectively. The spectra of the complex Kerr and Faraday angle have been measured on orthoferrite thin films (RE = Sm, Dy, Y), which were prepared by pulsed laser deposition on amorphous quartz substrates. The obtained spectra exhibit contributions of both surfaces and interfaces. Propagation effects of the polarized light in the magneto-optical medium which is interpreted in terms of a simplified theoretical formalism, is also observed. For selected photon energies, temperature dependent Faraday rotation measurements, , on orthoferrite thin films (RE = Sm, Dy, Y) have been performed. A quite different thermal variation compared to the bulk magnetization has been observed. Curie temperatures are found to be close to the bulk values or slightly larger by 10 K to 20 K as in the case of DyFeO3 and YFeO3. For RE = Sm and Dy, increases with increasing temperature contrary to the saturation magnetization, passes through a maximum at about 460 K and vanishes with a T C of 647±18 K, 695 K for RE = Sm and Dy respectively.