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Magneto-optical (MO) effects, viz. magnetically induced changes in light intensity or polarization upon reflection from or transmission through a magnetic sample, were discovered over a century and a half ago. Initially they played a crucially relevant role in unveiling the fundamentals of electromagnetism and quantum mechanics. A more broad-based relevance and wide-spread use of MO methods, however, remained quite limited until the 1960s due to a lack of suitable, reliable and easy-to-operate light sources. The advent of Laser technology and the availability of other novel light sources led to an enormous expansion of MO measurement techniques and applications that continues to this day (see section 1). The here-assembled roadmap article is intended to provide a meaningful survey over many of the most relevant recent developments, advances, and emerging research directions in a rather condensed form, so that readers can easily access a significant overview about this very dynamic research field. While light source technology and other experimental developments were crucial in the establishment of today's magneto-optics, progress also relies on an ever-increasing theoretical understanding of MO effects from a quantum mechanical perspective (see section 2), as well as using electromagnetic theory and modelling approaches (see section 3) to enable quantitatively reliable predictions for ever more complex materials, metamaterials, and device geometries. The latest advances in established MO methodologies and especially the utilization of the MO Kerr effect (MOKE) are presented in sections 4 (MOKE spectroscopy), 5 (higher order MOKE effects), 6 (MOKE microscopy), 8 (high sensitivity MOKE), 9 (generalized MO ellipsometry), and 20 (Cotton-Mouton effect in two-dimensional materials). In addition, MO effects are now being investigated and utilized in spectral ranges, to which they originally seemed completely foreign, as those of synchrotron radiation x-rays (see section 14 on three-dimensional magnetic characterization and section 16 on light beams carrying orbital angular momentum) and, very recently, the terahertz (THz) regime (see section 18 on THz MOKE and section 19 on THz ellipsometry for electron paramagnetic resonance detection). Magneto-optics also demonstrates its strength in a unique way when combined with femtosecond laser pulses (see section 10 on ultrafast MOKE and section 15 on magneto-optics using x-ray free electron lasers), facilitating the very active field of time-resolved MO spectroscopy that enables investigations of phenomena like spin relaxation of non-equilibrium photoexcited carriers, transient modifications of ferromagnetic order, and photo-induced dynamic phase transitions, to name a few. Recent progress in nanoscience and nanotechnology, which is intimately linked to the achieved impressive ability to reliably fabricate materials and functional structures at the nanoscale, now enables the exploitation of strongly enhanced MO effects induced by light-matter interaction at the nanoscale (see section 12 on magnetoplasmonics and section 13 on MO metasurfaces). MO effects are also at the very heart of powerful magnetic characterization techniques like Brillouin light scattering and time-resolved pump-probe measurements for the study of spin waves (see section 7), their interactions with acoustic waves (see section 11), and ultra-sensitive magnetic field sensing applications based on nitrogen-vacancy centres in diamond (see section 17)., Despite our best attempt to represent the field of magneto-optics accurately and do justice to all its novel developments and its diversity, the research area is so extensive and active that there remains great latitude in deciding what to include in an article of this sort, which in turn means that some areas might not be adequately represented here. However, we feel that the 20 sections that form this 2022 magneto-optics roadmap article, each written by experts in the field and addressing a specific subject on only two pages, provide an accurate snapshot of where this research field stands today. Correspondingly, it should act as a valuable reference point and guideline for emerging research directions in modern magneto-optics, as well as illustrate the directions this research field might take in the foreseeable future., Journal of Physics D: Applied Physics, 55 (46), ISSN:0022-3727, ISSN:1361-6463

The concept of Berry phase and Berry curvature has become ubiquitous in solid state physics as it relates to variety of phenomena, such as topological insulators, polarization, and various Hall effects. It is well known that large Berry curvatures arise from close proximity of hybridiz-ing bands, however, the vectorial nature of the Berry curvature is not utilized in current research. On bulk bcc Fe, we demonstrate the flow of the Berry curvature vector field which features not only monopoles but also higher dimensional structures with its own topological features. They can provide a novel unique view on the electronic structure in all three dimensions. This knowledge is also used to quantify particular contributions to the intrinsic anomalous Hall effect in a simple analytical form.

Unlike ferromagnetic materials, ferrimagnetic metals have recently received considerable attention due to their bulk perpendicular magnetic anisotropy, low net magnetization and tunable magnetic properties. This makes them perfect candidates for the research of recently discovered spin-torque related phenomena. Among other ferrimagnetic metals, GdFe has an advantage in relatively large magnetic moments in both sublattices and tunability of compensation point above the room temperature by small changes in its composition. We present a systematic study of optical and magneto-optical properties of amorphous GdxFe(100-x) thin films of various compositions (x = 18.3, 20.0, 24.7, 26.7) prepared by DC sputtering on thermally oxidized SiO2 substrates. A combination of spectroscopic ellipsometry and magneto-optical spectroscopy in the photon energy range from 1.5 to 5.5 eV with advanced theoretical models allowed us to deduce the spectral dependence of complete permittivity tensors across the compensation point. Such information is important for further optical detection of spin related phenomena driven by vicinity of compensation point in nanostructures containing GdFe.

Homogeneous, smooth, and partially transparent nanocrystalline thin films of CoFe2O4 were fabricated using a chemical solution approach with additional annealing for 2 h in a temperature range of 300 °C to 600 °C. Structural properties investigated by X-ray diffraction showed a single-phase spinel structure with a random crystallographic orientation for samples annealed above 400 °C. The ferromagnetic nature of prepared films was established from combined substrate with film hysteresis loops measured using a vibrating sample magnetometer. Optical and magneto-optical spectroscopic measurements revealed an improvement in the structural quality of the films after annealing up to 600 °C.

Using the WIEN2k code, we perform ab-initio calculations of the electronic structure and the permittivity tensor of bcc Fe with magnetization along the [001] and [011] directions. The electronic structure is calculated with various numbers of k -points in the full Brillouin zone and the convergence of the calculated data is being studied. Two exchange-correlation potentials are employed, namely LDA and GGA, and their effect on the outcoming spectra is shown. The permittivity tensor is obtained from the electronic structure by the Kubo formula. From the permittivity tensor the complex spectra of linear ( K ) and quadratic ( G s , 2 G 44 ) magneto-optical parameters are extracted. The spectra are compared to the literature.

The Heusler compound ${\mathrm{Co}}_{2}{\mathrm{FeAl}}_{0.5}{\mathrm{Si}}_{0.5}$ is an interesting material for spintronic applications due to its predicted half-metal ferromagnetic character with a large band gap in the minority states. In this work, we present the optical and magneto-optical properties of a ${\mathrm{Co}}_{2}{\mathrm{FeAl}}_{0.5}{\mathrm{Si}}_{0.5}$ bulk sample at room temperature. The spectral permittivity is found to be dominated by an absorption peak at 1.4 eV, originating mostly from absorptions by minority electrons. The best agreement between the experimentally obtained spectral permittivity tensor and the ab initio calculated one is for the local density approximation potential, closely followed by the generalized gradient approximation potential. However, the half-metallic ferromagnet character with $100%$ spin polarization is preserved only in calculations employing the Coulomb interaction correction (+U). This suggests that ${\mathrm{Co}}_{2}{\mathrm{FeAl}}_{0.5}{\mathrm{Si}}_{0.5}$ is probably not a half metal as a single minority $d$-band dips below the Fermi level.

The in-plane current profile within multilayers of generic structure Ta/Pt/(CoNi)/Pt/Ta is investigated. A large set of samples where the thickness of each layer is systematically varied was grown, followed by the measurement of the sheet resistance of each sample. The data are analyzed by a series of increasingly elaborate models, from a macroscopic engineering approach to mesoscopic transport theory. Non-negligible variations of the estimated repartition of current between the layers are found. The importance of having additional structural data is highlighted., Comment: 10 pages, 7 figures

The Heusler compound Co$_2$MnSi provides a crystallographic transition from B2 to L2$_1$ structure with increasing annealing temperature $T_a$, being a model system for investigating the influence of crystallographic ordering on structural, magnetic, optic, and magnetooptic (MO) properties. Here, we present quadratic magnetooptic Kerr effect (QMOKE) spectra depending on $M^2$ in addition to the linear magnetooptic Kerr effect (LinMOKE) spectra being proportional to $M$, both in the extended visible spectral range of light from 0.8\,eV to 5.5\,eV. We investigated a set of Co$_2$MnSi thin films deposited on MgO(001) substrates and annealed from 300$^\circ$C to 500$^\circ$C. The amplitude of LinMOKE and QMOKE spectra scales linearly with $T_a$, and this effect is well pronounced at the resonant peaks below 2.0\,eV of the QMOKE spectra. Furthermore, the spectra of the MO parameters, which fully describe the MO response of Co$_2$MnSi up to the second order in $M$, are obtained dependend on $T_a$. Finally, the spectra are compared to ab-initio calculations of a purely L2$_1$ ordered Co$_2$MnSi Heusler compound., 4 pages, 3 figures, supplemental pdf, supplemental data files

Permalloy is a widespread material used in numerous fundamental experiments and novel spintronic, optoelectronic devices. In order to model their response or tailor the optimal experimental parameters it is necessary to know the optical and magneto-optical properties of this material over a wide spectral range. We report on the systematic study of optical and magneto-optical properties of 10 nm and 150 nm thick permalloy films by means of spectroscopic ellipsometry and magneto-optical spectroscopy. To study the influence of the surface oxidization, the samples were prepared with and without Au capping layer. Spectral dependence of the complete permittivity tensor was derived from experimental data in a broad spectral range covering IR, visible and UV regions. All samples exhibited metallic-like optical and magneto-optical properties with clear differences in 10 nm thick bare sample. These differences to overall optical and magneto-optical properties of nanometer-thick permalloy layers were ascribed to a strong influence of the surface oxide. Keywords: Permalloy, Thin films, Spectroscopic ellipsometry, Magnetooptical Kerr effect spectroscopy, Complex permittivity tensor, Oxidation

Unlike ferromagnetic materials, ferrimagnetic metals have recently received considerable attention due to their bulk perpendicular magnetic anisotropy, low net magnetization and tunable magnetic properties. This makes them perfect candidates for the research of recently discovered spin-torque related phenomena. Among other ferrimagnetic metals, GdFe has an advantage in relatively large magnetic moments in both sublattices and tunability of compensation point above the room temperature by small changes in its composition. We present a systematic study of optical and magneto-optical properties of amorphous GdxFe(100-x) thin films of various compositions (x = 18.3, 20.0, 24.7, 26.7) prepared by DC sputtering on thermally oxidized SiO2 substrates. A combination of spectroscopic ellipsometry and magneto-optical spectroscopy in the photon energy range from 1.5 to 5.5 eV with advanced theoretical models allowed us to deduce the spectral dependence of complete permittivity tensors across the compensation point. Such information is important for further optical detection of spin related phenomena driven by vicinity of compensation point in nanostructures containing GdFe.

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, two further complex spectra of the QMOKE parameters $G_s$ and $2G_{44}$ are yielded. The difference between those two parameters, known as $\Delta G$, denotes the strength of the QMOKE anisotropy. Those QMOKE parameters give rise to the QMOKE tensor $\bm{G}$, fully describing the perturbation of the permittivity tensor in the second order in $\bm{M}$ for cubic crystal structures. We further present experimental measurements of ellipsometry and linear MOKE spectra, wherefrom permittivity in the zeroth and the first order in $\bm{M}$ are obtained, respectively. Finally, all those spectra are described by ab-initio calculations., Comment: 15 pages + references, , 15 Figures

The X/Co 3 nm/Y (where X, Y = Au, Pt) trilayers with as deposited in-plane magnetization alignment were irradiated with 30 keV Ga+ ions in the wide range of ion fluence. The samples were investigated by means of complementary techniques: magneto-optical magnetometry and spectroscopy (in the photon energy range from 1.2 eV to 4.5 eV), magnetic force microscopy, positron annihilation spectroscopy, x-ray diffraction and reflectivity. Difference in miscibility of interface atoms is clearly manifested in various intermixing extent at Co/Pt and Co/Au interfaces and consequently in magnetic properties of the irradiated trilayers. Low irradiation fluence (∼1014 ions cm−2) leads to ∼1 nm interfaces broadening without visible surface etching for all samples, which is related with a distinct drop of magnetic anisotropy. However, the high irradiation fluence (∼5 × 1015 ions cm−2) results in enhanced interface broadening and significant surface etching (∼5 nm) partially removing also Co atoms. Tensile strains (up to 0.5%) were developed in the cover layers. The tensile strain, layers intermixing and the creation of Co–Pt(Au) alloys with different composition formed by irradiation are correlated with the increase of magnetic anisotropy. Moreover it was observed that substitution of Au instead of Pt (as a cap or buffer layer) results in substantial increase of perpendicular magnetic anisotropy. Maximal increase of magnetooptical parameters was observed for Pt/Co/Pt layer. Irradiation induced changes of concentration profiles are revealed using magnetooptical spectra, x-ray reflectivity spectra and simulations with use of binary collision approximation.

Lateral spin devices are an important concept in nowadays all-metallic spintronic devices. One of the key problems is to obtain large spin injection and detection efficiency. Several concepts has been envisaged, such as to use half-metallic ferromagnetic electrodes or spin-polarized interface barriers. Within this work, we address the optimization of spin devices (namely optimization of spin current density, spin current and spin accumulation) based on adjustment of the geometry (dimensions) of the lateral device, material selection of spin conductors, jointly with optimization of the interface resistance.

Tetragonal phase of CuMnAs progressively appears as one of the key materials for antiferromagnetic spintronics due to efficient current-induced spin-orbit torques whose existence can be directly inferred from crystal symmetry. Theoretical understanding of spintronic phenomena in this material, however, relies on the detailed knowledge of electronic structure (band structure and corresponding wave functions) which has so far been tested only to a limited extent. We show that AC permittivity (obtained from ellipsometry) and UV photoelectron spectra agree with density functional calculations. Together with the x-ray diffraction and precession electron diffraction tomography, our analysis confirms recent theoretical claim [Phys.Rev.B 96, 094406 (2017)] that copper atoms occupy lattice positions in the basal plane of the tetragonal unit cell., 5 pages, 5 figures + Supplementary Information

Nonlinear crystals are typically used when interaction of different frequencies of light is requested. In classical optics these nonlinear phenomena are used for second-harmonic generation, sum-frequency generation, optical parametric amplification and many other effects. In quantum optics, dealing with optical interaction on the level of individual photons, the most prominent process is spontaneous parametric down-conversion (SPDC),1 where the crystal is pumped by intensive laser light and the crystal can mediate the splitting of a pump photon to a photon pair. The two generated photons are typically called signal and idler. Influence of magnetic field on these nonlinear processes was not thoroughly tested yet. This topic deserves intensive study both from theoretical and experimental point of view, because the magnetic field can decrease the symmetry of the nonlinear crystal and so it may allow to use new types of phase-matching conditions. We started to test the SPDC process in BBO crystals. Nonlinear magneto-optic tensor of this material is not known and we can hardly predict it. According to our first theoretical derivations the efficiency of the nonlinear processes has to oscillate when rotating the magnetic-field orientation.

We present diagonal and off-diagonal elements of the permittivity and conductivity tensor up to the second order in magnetization for cubic crystals. We express all tensor elements as a function of a general sample orientation, for arbitrary magnetization direction and for (001), (011), and (111) surface orientations. Finally, we discuss, how to extract values of quadratic elements G of the second-order permittivity tensors for different sample surface orientations from both experiment and ab initio calculations.

We provide unified phenomenological description of magnetooptic effects being linear and quadratic in magnetization. The description is based on few principal spectra, describing elements of permittivity tensor up to the second order in magnetization. Each permittivity tensor element for any magnetization direction and any sample surface orientation is simply determined by weighted summation of the principal spectra, where weights are given by crystallographic and magnetization orientations. The number of principal spectra depends on the symmetry of the crystal. In cubic crystals owning point symmetry we need only four principal spectra. Here, the principal spectra are expressed by ab initio calculations for bcc Fe, fcc Co and fcc Ni in optical range as well as in hard and soft x-ray energy range, i.e. at the 2 p - and 3 p -edges. We also express principal spectra analytically using modified Kubo formula.

Au/Co(4–8 ML)/Au single magnetic layers and Au(8 ML)/Co(4 ML)/Au(8 ML)/Co(8 ML)/Au bilayer were sequentially grown by electrodeposition on an Au(1 1 1) buffer layer electrodeposited on Si(1 1 1). The technique used in this work provides full control on the structure and the chemical composition of the different layers (no alloying) as well as on the chemistry at interfaces. scanning tunneling microscopy (STM) and atomic force microscopy (AFM) imaging and X-ray diffraction measurements show that atomically flat continuous Co(0 0 0 1) layers (4–8 ML) can be grown in epitaxy with the Au(1 1 1) substrate and that the 2 nm-thick spacer is also a continuous Au(1 1 1) layer. The Co ultrathin layers (4 and 8 ML) exhibit perpendicular magnetic anisotropy. The lateral magnetic homogeneity and magnetization reversal process have been investigated by scanning magneto-optical Kerr effect (MOKE) magnetometry and global Kerr microscopy. The correlation between magnetization switching behaviour in each layer of the Co-bilayer stack has been evidenced from in-depth sensitive MOKE measurements and microscopy. The strong coupling observed between the two Co layers is attributed to magnetostatic interaction at domain wall boundaries.

To clarify the contributions of spin-polarized current and spin accumulation to the current-induced magnetization switching, the effects of the top electrode size of the magnetic nanopillar are investigated both theoretically and experimentally. Theoretical calculation demonstrates that the spin-polarized current and the spin accumulation can be adjusted in opposite directions by modifying the size of the top electrode. Increase in the size of the top electrode suppresses the spin accumulation but enhances the spin-polarized current inside the nanopillar. On the other hand, it is shown experimentally that the nanopillar with a wide top electrode exhibits small critical switching current compared to the nanopillar with a narrow top electrode. The results suggest that the spin-polarized current contributes to the current-induced magnetization switching dominantly over the spin accumulation.

X-ray magnetic linear dichroism spectra measured in reflection (XMLD-R) on crystalline bcc Fe thin films across the 3 p absorption edges are reported. A series of measurements with varying orientation of the electric field vector of the linear polarized synchrotron radiation with respect to the crystal axes reveals a strong magnetocrystalline anisotropy in the XMLD-R spectra. The spectra agree well with theoretical spectra calculated within the framework of the density-functional theory accounting for the spin-orbital and exchange splitting of the 3 p semicore states on an equal footing.

The paper deals with the electromagnetic theory of longitudinal and normal incidence polar magnetooptical Kerr effects (MOKE) in sandwich structures consisting of a magnetic film on a thick magnetic substrate separated by a nonmagnetic spacer. These structures are employed in fundamental studies of magnetic exchange coupling, tunnel magnetoresistance, spin polarized current,etc., as well as in the design of the magnetoelectronic devices,e.g., magnetic random access memories. The results are expressed in terms of the Jones reflection matrix. This makes the analysis of the observed MOKE in various experimental set-ups easier. To first order in off-diagonal elements of the permittivity tensor, the analytical expressions approximate the results obtained using rigorous matrix formalisms with a little loss in accuracy, provided the magnetooptical effects quadratic in the offdiagonal elements are negligible. The total MOKE is expressed as a a sum of components originating from magnetic film and magnetic substrate, respectively. The components enter the analytical expressions with different phases and may be identified separately by a proper control of the polarization state and photon energy of the incident radiation, angle of incidence, nonmagnetic spacer thickness, and radiation wavelength. The formulae are derived without any restriction on the magnetic film thickness. However, for a rapid evaluation of the trends the MOKE response is also treated under the assumption that the thickness of the magnetic film is much smaller than the radiation wavelength.

We investigate the dependance of the spin signal in a lateral spin-valve structure Ni–Fe/Cu ohmic junction on the probe configuration. The spin-valve signal is strongly affected by probe configuration because of the non-uniform spin-current distribution due to a wide non-magnetic probe.

Magnetic linear dichroism and birefringence in (Ga,Mn)As epitaxial layers is investigated by measuring the polarization plane rotation of reflected linearly polarized light when magnetization lies in the plane of the sample. We report on the spectral dependence of the rotation and ellipticity angles in a broad energy range of 0.12-2.7 eV for a series of optimized samples covering a wide range on Mn-dopings and Curie temperatures and find a clear blue shift of the dominant peak at energy exceeding the host material band gap. These results are discussed in the general context of the GaAs host band structure and also within the framework of the k.p and mean-field kinetic-exchange model of the (Ga,Mn)As band structure. We find a semi-quantitative agreement between experiment and theory and discuss the role of disorder-induced non-direct transitions on magneto-optical properties of (Ga,Mn)As., 18 pages

Half-metallic Co-based Heusler compounds are attracting attention due to their anticipated use as high-performance materials for spintronics applications, such as spin-source or spin-detector. In order to use these materials in applications, their structural and magnetic properties must be well understood. The important phenomena in those materials are, amongst others, exchange and spin–orbit coupling, the latter one giving rise to effect such as magnetic anisotropy and magneto-optical Kerr effect. In this chapter, we present our investigations of magnetic exchange stiffness, magnetic anisotropy, magnetization reversal, and magneto-optical Kerr effect in Co-based Heusler compound thin films. Furthermore, we have also investigated the modification of the compounds under He+ and Ga+ ion beam irradiation with the aim of improving and tailoring structural properties.

We propose a nonlocal spin-valve measurement combined with a local spin-valve structure to enlarge spin signal. The probe configuration consists of a lateral spin valve with three Ni–Fe wires bridged by a Cu wire. The advantage is that the spin polarization in the Cu wire induced by the spin injection can be enhanced compared to the conventional method.

We report the detection of clear spin-valve signal without any spurious magnetoresistive signal in a lateral spin-valve structure consisting of Cu∕Ni−Fe ohmic junction using local current injection. The obtained spin-valve signal is much larger than that of the nonlocal spin-valve configuration because of the efficient spin accumulation. The local current injection experiments with different probe configurations proved that the spin-valve signal is caused by the spin-dependent boundary resistance at the interface between the ferromagnetic voltage probe and the spin-polarized nonmagnetic wire.

The Heusler compound CoTiSb was synthesized and investigated theoretically and experimentally with respect to electronic structure and optical, mechanical, and vibrational properties. The optical properties were investigated in a wide spectral range from 10 meV to 6.5 eV and compared with ab initio calculations. The optical spectra confirm the semiconducting nature of CoTiSb, with a strong exciton absorption at 1.83 eV. The calculated phonon dispersion as well as elastic constants verify the mechanical stability of CoTiSb in the cubic $C{1}_{b}$ system. Furthermore, solid solution series of CoTi${}_{1\ensuremath{-}x}$${M}_{x}$Sb ($M=\text{Sc}$, V and $0\ensuremath{\leqslant}x\ensuremath{\leqslant}0.2$) were synthesized and investigated. The transport properties were calculated by all-electron ab initio methods and compared to the measurements. The thermoelectric properties were investigated by measuring the temperature dependence of electrical resistivity, Seebeck coefficient, and thermal conductivity. The thermal conductivity of the substituted compounds was significantly reduced. Sc substitution resulted in a $p$-type behavior with a high Seebeck coefficient of +177.8 $\ensuremath{\mu}$V/K (350 K) at 5$%$ Sc substitution. This value is in good agreement with the calculations. Fully relativistic Korringa--Kohn--Rostoker calculations in combination with the coherent potential approximation clarify the different contribution of states in the (001) plane of the Fermi surface for Sc- or V-substituted compounds CoTi${}_{0.95}$${M}_{x}$Sb ($M=\text{Sc}$, V).

A series of Al and MgO-capped Co${}_{2}$FeAl${}_{0.5}$Si${}_{0.5}$ epitaxial thin films grown on MgO with various levels of L2${}_{1}$ ordering was obtained by in situ annealing. The films were studied by means of x-ray absorption spectroscopy, x-ray magnetic circular dichroism (XMCD), magneto-optical Kerr effect magnetometry, and Brillouin light scattering. We find the anisotropy constants decrease, while the spin wave stiffness increases as the samples are annealed to higher temperatures. The magnetization as determined by Brillouin light scattering reveals a maximum value at intermediate annealing temperatures. Surprisingly, the orbital-to-spin-moment ratio (as seen from XMCD) is essentially stable through the sample series and does not change upon annealing, despite the observed changes in anisotropy and exchange.

We determine the dynamic magnetization induced in non-magnetic metal wedges composed of silver, copper and platinum by means of Brillouin light scattering (BLS) microscopy. The magnetization is transferred from a ferromagnetic Ni80Fe20 layer to the metal wedge via the spin pumping effect. The spin pumping efficiency can be controlled by adding an insulating but transparent interlayer between the magnetic and non-magnetic layer. By comparing the experimental results to a dynamical macroscopic spin-transport model we determine the transverse relaxation time of the pumped spin current which is much smaller than the longitudinal relaxation time.

The spin-wave relaxation mechanisms after intense laser excitation in ferromagnetic nickel films are investigated with all-optical pump-probe experiments. Uniform precession (Kittel mode), Damon-Eshbach surface modes and perpendicular standing spin waves can be identified by their dispersion f(H). However, different to other ferromagnets f(H) deviates from the expected behavior. Namely, a mode discontinuity is observed, that can be attributed to a non-linear process. Above a critical field the power spectrum reveals a redistribution of the energy within the spin-wave spectrum populated.

International audience; Cobalt-based full-Heusler compounds with composition Co2M ′ Z (where M ′ is a transition metal and Z is a main group element) are attracting attention due to their predicted half-metallic behaviour , a considerably desired property for spin-dependent electron transport devices. Knowledge of the basic magnetic properties of these materials, in particular in the form of thin films, is required both to fully exploit these promising materials, and to understand their underlying electronic structure and establish structure-property relationships. In this Topical Review, we present a survey of the magnetic anisotropy, exchange, and damping of Co2M ′ Z compounds. These properties are directly related to spin-spin and spin-orbit interactions.

A recently reported phase sensitive Brillouin light scattering technique is improved by use of a magnetic modulator. This modulator is based on Brillouin light scattering in a thin ferrite film. Using this magnetic modulator in time and space Brillouin light scattering measurements, we have increased phase contrast and excluded influence of optical inhomogeneities in the sample. We also demonstrate that the quality of the resulting interference patterns can be improved by data postprocessing using the simultaneously recorded information about the reference light.

The thermal magnonic spectra of Co$_{2}$Cr$_{0.6}$Fe$_{0.4}$Al (CCFA) and Co$_2$FeAl were investigated using Brillouin light scattering spectroscopy (BLS). For CCFA, the exchange constant A (exchange stiffness D) is found to be 0.48 $\mu$erg/cm (203 meV A$^2$), while for Co$_2$FeAl the corresponding values of 1.55 $\mu$erg/cm (370 meV A$^2$) were found. The observed asymmetry in the BLS spectra between the Stokes and anti-Stokes frequencies was assigned to an interplay between the asymmetrical profiles of hybridized Damon-Esbach and perpendicular standing spin-wave modes, combined with the optical sensitivity of the BLS signal to the upper side of the CCFA or Co$_2$FeAl film.

This review describes the current state of the art of optical techniques used to study the magnetization dynamics in ferromagnetic materials. Most optical techniques provide a spatial resolution defined by the wavelength limit of the used light. The techniques can be roughly divided into the two classes (a) frequency-scale techniques such as Brillouin light scattering and Kerr effect ferromagnetic resonance and (b) timescale techniques such as time-resolved, stroboscopic Kerr effect magnetometry. These techniques are presented and illustrated with selected experiments. Keywords: Kerr effect; spin waves; dynamic modes; confined modes; magnetic anisotropy; exchange constant; spin-wave propagation; spin-wave tunneling; optical ferromagnetic resonance

We report on the development of an analytical theory and a method of experimental observation of dynamic properties of magnetic vortices excited in cylindrical ferromagnetic discs magnetostatically coupled into arrays. The theory, based on Thiele's equation of motion and the approximative rigid-vortex model, enables us to determine the eigenfrequencies of the vortices' harmonic oscillation within pairs [J. Shibata et al., Phys. Rev. B 67, 224404 (2003)] and large arrays [J. Shibata and Y. Otani, Phys. Rev. B 70, 012404 (2004)] of the discs, the latter being a proposal to design a new type of artificial crystals with magnonic band structures. Then we briefly describe the basic principles of our time-resolved Kerr microscope and show the capabilities of our method to detect all the features studied theoretically. Finally we present an experimental example of observation of the dynamic evolution of short-pulse magnetic field excitation of a vortex weakly coupled within an array of cylindrical Permalloy discs.

Magnetic anisotropies and magnetization reversal properties of the epitaxial Heusler compound Co$_2$Cr$_{0.6}$Fe$_{0.4}$Al (CCFA) deposited on Fe and Cr buffer layers are studied. Both samples exhibit a growth-induced fourfold anisotropy, and magnetization reversal occurs through the formation of stripy domains or 90 degree domains. During rotational magnetometric scans the sample deposited on Cr exhibits about 2 degree sharp peaks in the angular dependence of the coercive field, which are oriented along the hard axis directions. These peaks are a consequence of the specific domain structure appearing in this particular measurement geometry. A corresponding feature in the sample deposited on Fe is not observed., 11 pages, 7 figures

The junction size dependence of the spin accumulation in a nonmagnet is studied by using lateral spin valves geometry consisting of the Py/Cu ohmic junctions. We experimentally demonstrate that reducing the size of the junction drastically improves the efficiency of the spin injection into the Cu wire because of the enhancement of the spin resistance for the Py wire. The spin polarization in the Cu wire increases exponentially with reducing the junction area irrespective of the same spacing between the injector and the detector. The junction size dependence of the spin signal yields the spin diffusion lengths and the spin polarization which are reasonable values compared with previous experiments.

Co$_2$FeSi(100) films with L2$_1$ structure deposited onto MgO(100) were studied exploiting both longitudinal (LMOKE) and quadratic (QMOKE) magneto-optical Kerr effect. The films exhibit a huge QMOKE signal with a maximum contribution of up to 30 mdeg, which is the largest QMOKE signal in reflection that has been measured thus far. This large value is a fingerprint of an exceptionally large spin-orbit coupling of second or higher order. The Co$_2$FeSi(100) films exhibit a rather large coercivity of 350 and 70 Oe for film thicknesses of 22 and 98 nm, respectively. Despite the fact that the films are epitaxial, they do not provide an angular dependence of the anisotropy and the remanence in excess of 1% and 2%, respectively.

We have performed nonlocal spin injection into a nanoscale ferromagnetic particle configured in a lateral spin-valve structure to switch its magnetization only by spin current. The nonlocal spin injection aligns the magnetization of the particle parallel to the magnetization of the spin injector. The spin current responsible for switching is estimated from the experiment to be about $200\text{ }\text{ }\ensuremath{\mu}\mathrm{A}$, which is reasonable compared with the values obtained for conventional pillar structures. Interestingly, the switching always occurs from antiparallel to parallel in the particle-injector magnetic configurations, where no opposite switching is observed. Possible reasons for this discrepancy are discussed.

We demonstrate the method to calculate the spatial distributions of the spin current and accumulation in the multiterminal ferromagnetic/nonmagnetic hybrid structure using an approximate electrotransmission line. The analyses based on the obtained equation yield the results, in good agreement with the experimental ones. This implies that the method allows us to determine the spin diffusion length of an additionally connected electrically floating wire from the reduction of the spin signal.

Spectroscopic ellipsometry (SE) and magneto-optical (MO) spectroscopy are applied to analyze three sets of shallow magnetic gratings. The experimental data of SE are used to extract geometrical parameters of several samples. A half-micrometer thick transparent interlayer present between the periodic magnetic wires and the substrate in one of the sets of the samples is used to increase the sensitivity of SE and MO measurements. Thanks to this sensitivity the geometrical parameters can be extracted together with the material composition of the magnetic film. In order to interpret the magneto-optical Kerr effect (MOKE) measurement, three theoretical approaches are used in the simulations, the rigorous coupled-wave method (CWM), the local mode method (LMM), and a new approach based on comparing CWM with LMM with defining a 'quality factor' of the grating with respect to the wire edges. Using the MOKE spectra in the 0th and -1st diffraction orders, one set of the samples made with a protection capping is analyzed with respect to the native-oxidation process. The quality factor of these samples is extracted from MOKE in the -1st diffraction order for p-polarized incidence. The monitoring system based on both SE and MOKE is rated as highly sensitive and precise, and with accurate determination of the optical and magneto-optical constants it could by applied in multi-parameter fitting.

Within diffusive transport, we calculate three-dimensional current distribution inside a $(\mathrm{Cu}∕\mathrm{Co})$ pillar structure, where the pillar is terminated either by an infinitely large $\mathrm{Cu}$ layer, or by a $\mathrm{Cu}$ wire with a cross-sectional area identical to that of the pillar. We study how pillar terminations (infinitely large or finite) influence the magnitudes and inhomogeneities of the spin-polarized current and electrochemical potential. We found that infinitely large $\mathrm{Cu}$ layers work as strong spin scatterers, increasing the magnitude of spin-polarized current inside the pillar twice and reducing spin accumulation to nearly zero. The inhomogeneities of the electrochemical potential are found to be much smaller than those of the spin-polarized current.

We have investigated experimentally the non-local voltage signal (NLVS) in the lateral permalloy (Py)/Cu/Py spin valve devices with different width of Cu stripes. We found that NLVS strongly depends on the distribution of the spin-polarized current inside Cu strip in the vicinity of the Py-detector. To explain these data we have developed a diffusion model describing spatial (3D) distribution of the spin-polarized current in the device. The results of our calculations show that NLVS is decreased by factor of 10 due to spin flip-scattering occurring at Py/Cu interface. The interface resistivity on Py/Cu interface is also present, but its contribution to reduction of NLVS is minor. We also found that most of the spin-polarized current is injected within the region 30 nm from Py-injector/Cu interface. In the area at Py-detector/Cu interface, the spin-polarized current is found to flow mainly close on the injector side, with 1/e exponential decay in the magnitude within the distance 80 nm.

A longitudinal magneto-optical Kerr effect and magnetization-induced second-harmonic generation (MSHG) of light (at 2omega) have been measured in a SiO2/Fe96Si4/Dy30Fe58Co12/glass exchange-coupled magnetic bilayer system with competitive anisotropies. Theoretical MSHG predictions in this structure that give rise to an effect proportional to magnetization components and that are allowed by an electric dipole mechanism are reported and discussed. The magnitude of the MSHG effect depends on the electric field of the incoming radiation at each interface and on the corresponding incoming (at omega) and outgoing (at 2omega) Fresnel coefficients. It is demonstrated that transverse pp MSHG selectively probes the magnetization of the first SiO2/Fe96Si4 interface, while transverse sp and longitudinal ps MSHG is sensitive, but less selectively, to the Fe96Si4/Dy30Fe58Co12 interface that supports a planar magnetic domain wall. (p and s are the usual parallel and perpendicular polarizations to the plane of incidence.) The contribution to MSHG by gradient magnetization terms is negligible.