Ab initio calculated magneto-optical Kerr effect of ferromagnetic metals: Fe and Ni

Magneto-optical properties of heavily Fe-doped GaAs: a density functional approach

The magneto-optical properties of heavily iron-doped GaAs are investigated. Complex permittivity, optical conductivity and absorption coefficients are mainly discussed using spin-polarized electronic band structures close to the Fermi energy level. Furthermore, prominent magneto-optical properties in visible light and ultraviolet regions, including magnetic circular dichroism as well as complex Kerr and Faraday rotation angles, are presented and discussed. A density functional approach corroborated by some experimental results indicates that GaAs with 25% Fe dopants either in As or Ga sites is a promising ferromagnetic material and a useful platform for optoelectronic and spintronic device applications.

Optically controlling the competition between spin flips and intersite spin transfer in a Heusler half-metal on sub-100-fs time scales

The direct manipulation of spins via light may provide a path toward ultrafast energy-efficient devices. However, distinguishing the microscopic processes that can occur during ultrafast laser excitation in magnetic alloys is challenging. Here, we study the Heusler compound Co2MnGa, a material that exhibits very strong light-induced spin transfers across the entire M-edge. By combining the element specificity of extreme ultraviolet high-harmonic probes with time-dependent density functional theory, we disentangle the competition between three ultrafast light-induced processes that occur in Co2MnGa: same-site Co-Co spin transfer, intersite Co-Mn spin transfer, and ultrafast spin flips mediated by spin-orbit coupling. By measuring the dynamic magnetic asymmetry across the entire M-edges of the two magnetic sublattices involved, we uncover the relative dominance of these processes at different probe energy regions and times during the laser pulse. Our combined approach enables a comprehensive microscopic interpretation of laser-induced magnetization dynamics on time scales shorter than 100 femtoseconds.

Spin-hedgehog-derived electromagnetic effects in itinerant magnets

In itinerant magnets, the indirect exchange coupling of Ruderman-Kittel-Kasuya-Yosida type is known to stabilize incommensurate spin spirals, whereas an account of higher order spin interactions favors the formation of a noncoplanar magnetic texture. This is manifested by the finite Berry phase the conduction electrons accumulate when their spins follow this texture, leading thus to the topological Hall effect. We herein utilize the effective spin model with bilinear-biquadratic exchange interactions for studying the formation of the magnetic hedgehog lattice, that represents a periodic array of magnetic anti- and monopoles and has been recently observed in the B20-type compounds, in a three-dimensional itinerant magnet. As opposed to widely used Monte Carlo simulations, we employ a neural-network-based approach for exploring the ground state spin configuration in a noncentrosymmetric crystal structure. Further, we address the topological Hall conductivity, associated with nonzero scalar spin chirality, in the itinerant magnet due to the coupling to the spin hedgehog lattice, and provide the evidence of a magneto-optic Kerr effect.

Band structure analysis of the magneto-optical effect in bcc Fe

Magneto-optical effects are among the basic tools for characterization of magnetic materials. Although these effects are routinely calculated by the ab initio codes, there is very little knowledge about their origin in the electronic structure. Here, we analyze the magneto-optical effect in bcc Fe and show that it originates in avoided band-crossings due to the spin-orbit interaction. Therefore, only limited number of bands and k-points in the Brillouin zone contribute to the effect. Furthermore, these contributions always come in pairs with opposite sign but they do not cancel out due to different band curvatures providing different number of contributing reciprocal points. The magneto-optical transitions are classified by the dimensionality of the manifold that is formed by the hybridization of the generating bands as one- or two-dimensional, and by the position relative to the magnetization direction as parallel and perpendicular. The strongest magneto-optical signal is provided by two-dimensional parallel transitions.

Strong Interfacial Coupling of Tunable Ni-NiO Nanocomposite Thin Films Formed by Self-Decomposition

The next-generation spintronic devices including memristors, tunneling devices, or stochastic switching exert surging demands on magnetic nanostructures with novel coupling schemes. Taking advantage of a phase decomposition mechanism, a unique Ni-NiO nanocomposite has been demonstrated using a conventional pulsed laser deposition technique. Ni nanodomains are segregated from NiO and exhibit as faceted "emerald-cut" morphologies with tunable dimensions affected by the growth temperature. The sharp interfacial transition between ferromagnetic (002) Ni and antiferromagnetic (002) NiO, as characterized by high-resolution transmission electron microscopy, introduces a strong exchange bias effect and magneto-optical coupling at room temperature. In situ heating-cooling X-ray diffraction (XRD) study confirms an irreversible phase transformation between Ni and NiO under ambient atmosphere. Synthesizing highly functional two-phase nanocomposites with a simple bottom-up self-assembly via such a phase decomposition mechanism presents advantages in terms of epitaxial quality, surface coverage, interfacial coupling, and tunable nanomagnetism, which are valuable for new spintronic device implementation.

Frequency-Independent Terahertz Anomalous Hall Effect in DyCo5 , Co32 Fe68 , and Gd27 Fe73 Thin Films from DC to 40 THz

The anomalous Hall effect (AHE) is a fundamental spintronic charge-to-charge-current conversion phenomenon and closely related to spin-to-charge-current conversion by the spin Hall effect. Future high-speed spintronic devices will crucially rely on such conversion phenomena at terahertz (THz) frequencies. Here, it is revealed that the AHE remains operative from DC up to 40 THz with a flat frequency response in thin films of three technologically relevant magnetic materials: DyCo₅ , Co₃₂ Fe₆₈ , and Gd₂₇ Fe₇₃ . The frequency-dependent conductivity-tensor elements σ_xx and σ_yx  are measured, and good agreement with DC measurements is found. The experimental findings are fully consistent with ab initio calculations of σ_yx for CoFe and highlight the role of the large Drude scattering rate (≈100 THz) of metal thin films, which smears out any sharp spectral features of the THz AHE. Finally, it is found that the intrinsic contribution to the THz AHE dominates over the extrinsic mechanisms for the Co₃₂ Fe₆₈ sample. The results imply that the AHE and related effects such as the spin Hall effect are highly promising ingredients of future THz spintronic devices reliably operating from DC to 40 THz and beyond.

Element Specificity of Transient Extreme Ultraviolet Magnetic Dichroism

In this work we combine theory and experiment to study transient magnetic circular dichroism (TRMCD) in the extreme ultraviolet spectral range in bulk Co and CoPt. We use the ab initio method of real-time time-dependent density functional theory to simulate the magnetization dynamics in the presence of short laser pulses. From this we demonstrate how TRMCD may be calculated using an approximation to the excited-state linear response. We apply this approximation to Co and CoPt and show computationally that element-specific dynamics of the local spin moments can be extracted from the TRMCD in the extreme ultraviolet energy range, as is commonly assumed. We then compare our theoretical prediction for the TRMCD for CoPt with experimental measurement and find excellent agreement at many different frequencies including the M_{23} edge of Co and N_{67} and O_{23} edges of Pt.

Spectroscopic ellipsometry and magneto-optical Kerr effect spectroscopy study of thermally treated Co60Fe20B20 thin films

We report the optical and magneto-optical properties of amorphous and crystalline Co₆₀Fe₂₀B₂₀ films with thicknesses in the range of 10 nm to 20 nm characterized using spectroscopy ellipsometry (SE) and magneto-optical Kerr effect (MOKE) spectroscopy. We derived the spectral dependence of the dielectric tensor from experimental data for samples prior and after annealing in vacuum. The features of the dielectric function can be directly related to the transitions between electronic states and the observed changes upon annealing can be ascribed to an increase of the crystalline ordering of CoFeB.

Physical origin of giant excitonic and magneto-optical responses in two-dimensional ferromagnetic insulators

The recent discovery of magnetism in atomically thin layers of van der Waals crystals has created great opportunities for exploring light–matter interactions and magneto-optical phenomena in the two-dimensional limit. Optical and magneto-optical experiments have provided insights into these topics, revealing strong magnetic circular dichroism and giant Kerr signals in atomically thin ferromagnetic insulators. However, the nature of the giant magneto-optical responses and their microscopic mechanism remain unclear. Here, by performing first-principles GW and Bethe-Salpeter equation calculations, we show that excitonic effects dominate the optical and magneto-optical responses in the prototypical two-dimensional ferromagnetic insulator, CrI₃. We simulate the Kerr and Faraday effects in realistic experimental setups, and based on which we predict the sensitive frequency- and substrate-dependence of magneto-optical responses. These findings provide physical understanding of the phenomena as well as potential design principles for engineering magneto-optical and optoelectronic devices using two-dimensional magnets.

The magneto-optical (MO) effects probe the electronic and magnetic properties of a material, particularly useful for 2D magnets. Here, the authors show that the large optical and MO responses in ferromagnetic monolayer CrI₃ arise from strongly bound excitons, extending over several atoms.

Magneto-optical properties of Au upon the injection of hot spin-polarized electrons across Fe/Au(0 0 1) interfaces

We demonstrate a novel method for the excitation of sizable magneto-optical effects in Au by means of the laser-induced injection of hot spin-polarized electrons in Au/Fe/MgO(0 0 1) heterostructures. It is based on the energy- and spin-dependent electron transmittance of Fe/Au interface which acts as a spin filter for non-thermalized electrons optically excited in Fe. We show that after crossing the interface, majority electrons propagate through the Au layer with the velocity on the order of 1 nm fs^-1 (close to the Fermi velocity) and the decay length on the order of 100 nm. Featuring ultrafast functionality and requiring no strong external magnetic fields, spin injection results in a distinct magneto-optical response of Au. We develop a formalism based on the phase of the transient complex MOKE response and demonstrate its robustness in a plethora of experimental and theoretical MOKE studies on Au, including our ab initio calculations. Our work introduces a flexible tool to manipulate magneto-optical properties of metals on the femtosecond timescale that holds high potential for active magneto-photonics, plasmonics, and spintronics.

Magneto-Optical Detection of the Spin Hall Effect in Pt and W Thin Films

The conversion of charge currents into spin currents in nonmagnetic conductors is a hallmark manifestation of spin-orbit coupling that has important implications for spintronic devices. Here we report the measurement of the interfacial spin accumulation induced by the spin Hall effect in Pt and W thin films using magneto-optical Kerr microscopy. We show that the Kerr rotation has opposite sign in Pt and W and scales linearly with current density. By comparing the experimental results with ab initio calculations of the spin Hall and magneto-optical Kerr effects, we quantitatively determine the current-induced spin accumulation at the Pt interface as 5×10^{-12}  μ_{B} A^{-1} cm^{2} per atom. From thickness-dependent measurements, we determine the spin diffusion length in a single Pt film to be 11±3  nm, which is significantly larger compared to that of Pt adjacent to a magnetic layer.

Bulk Rashba Semiconductors and Related Quantum Phenomena

Bithmuth tellurohalides BiTeX (X = Cl, Br and I) are model examples of bulk Rashba semiconductors, exhibiting a giant Rashba-type spin splitting among their both valence and conduction bands. Extensive spectroscopic and transport experiments combined with the state-of-the-art first-principles calculations have revealed many unique quantum phenomena emerging from the bulk Rashba effect in these systems. The novel features such as the exotic inter- and intra-band optical transitions, enhanced magneto-optical response, divergent orbital dia-/para-magnetic susceptibility and helical spin textures with a nontrivial Berry's phase in the momentum space are among the salient discoveries, all arising from this effect. Also, it is theoretically proposed and indications have been experimentally reported that bulk Rashba semiconductors such as BiTeI have the capability of becoming a topological insulator under the application of a hydrostatic pressure. Here, we overview these studies and show that BiTeX are an ideal platform to explore the next aspects of quantum matter, which could ultimately be utilized to create spintronic devices with novel functionalities.

Signatures of relativistic spin-light coupling in magneto-optical pump-probe experiments

Femtosecond magneto-optical pump-probe measurements of ultrafast demagnetization show an intriguing difference in the first 100 fs of the magneto-optical Kerr response depending on whether the polarization of the pump and probe beams are in parallel or perpendicular configuration (Bigot et al 2009 Nat. Phys. 5 515). Starting from a most general relativistic Hamiltonian we focus on the ultra-relativistic light-spin interaction and show that this coupling term leads to different light-induced opto-magnetic fields when pump and probe polarization are parallel and perpendicular to each other, providing thus an explanation for the measurements. We also analyze other pump-probe configurations where the pump laser is circularly polarized and the employed probe contains only linearly polarized light and show that similar opto-magnetic effects can be anticipated.

Ab Initio Theory of Coherent Laser-Induced Magnetization in Metals

We present the first materials specific ab initio theory of the magnetization induced by circularly polarized laser light in metals. Our calculations are based on nonlinear density matrix theory and include the effect of absorption. We show that the induced magnetization, commonly referred to as inverse Faraday effect, is strongly materials and frequency dependent, and demonstrate the existence of both spin and orbital induced magnetizations which exhibit a surprisingly different behavior. We show that for nonmagnetic metals (such as Cu, Au, Pd, Pt) and antiferromagnetic metals the induced magnetization is antisymmetric in the light's helicity, whereas for ferromagnetic metals (Fe, Co, Ni, FePt) the imparted magnetization is only asymmetric in the helicity. We compute effective optomagnetic fields that correspond to the induced magnetizations and provide guidelines for achieving all-optical helicity-dependent switching.

Exciting: a full-potential all-electron package implementing density-functional theory and many-body perturbation theory

Linearized augmented planewave methods are known as the most precise numerical schemes for solving the Kohn-Sham equations of density-functional theory (DFT). In this review, we describe how this method is realized in the all-electron full-potential computer package, exciting. We emphasize the variety of different related basis sets, subsumed as (linearized) augmented planewave plus local orbital methods, discussing their pros and cons and we show that extremely high accuracy (microhartrees) can be achieved if the basis is chosen carefully. As the name of the code suggests, exciting is not restricted to ground-state calculations, but has a major focus on excited-state properties. It includes time-dependent DFT in the linear-response regime with various static and dynamical exchange-correlation kernels. These are preferably used to compute optical and electron-loss spectra for metals, molecules and semiconductors with weak electron-hole interactions. exciting makes use of many-body perturbation theory for charged and neutral excitations. To obtain the quasi-particle band structure, the GW approach is implemented in the single-shot approximation, known as G(0)W(0). Optical absorption spectra for valence and core excitations are handled by the solution of the Bethe-Salpeter equation, which allows for the description of strongly bound excitons. Besides these aspects concerning methodology, we demonstrate the broad range of possible applications by prototypical examples, comprising elastic properties, phonons, thermal-expansion coefficients, dielectric tensors and loss functions, magneto-optical Kerr effect, core-level spectra and more.

Enhanced infrared magneto-optical response of the nonmagnetic semiconductor BiTeI driven by bulk Rashba splitting

We study the magneto-optical (MO) response of the polar semiconductor BiTeI with giant bulk Rashba spin splitting at various carrier densities. Despite being nonmagnetic, the material is found to yield a huge MO activity in the infrared region under moderate magnetic fields (up to 3 T). Our first-principles calculations show that the enhanced MO response of BiTeI comes mainly from the intraband transitions between the Rashba-split bulk conduction bands. These transitions connecting electronic states with opposite spin directions become active due to the presence of strong spin-orbit interaction and give rise to distinct features in the MO spectra with a systematic doping dependence. We predict an even more pronounced enhancement in the low-energy MO response and dc Hall effect near the crossing (Dirac) point of the conduction bands.

Magneto-Optical Spectra of Copt3: Experiments and First Principles Calculations

The Magneto-optical Kerr effect of CoPt3 ordered compounds and alloys is investigated experimentally and analyzed theoretically using first principles band structure calculations.

The calculations confirm the experimental results and allow for the first time a detailed, bandstructure based interpretation of the electronic transitions leading to the well known strong uv peak at around 4eV. This feature can be unambiguously attributed to Magneto-optical transitions within the Pt p and d bands.

Quantum well States in Fe (100) Ultrathin Films Observed by Magneto-Optical Effect

We report on the Magneto-optical Kerr rotation (<φ>K) spectra of ultrathin Fe films on Au or Ag (100) substrates and the φK oscillation due to interlayer thickness in Fe/Au/Fe sandwich films. In 3.5–4.5 eV, a new φK peak appears in the bcc-Fe (100) ultrathin films on the fcc-Au (100) surface and it shifts towards the higher energy side with increasing Fe layer thickness. The absolute value of eXy for 3Å (2ML) thick Fe layers is twice as large as that of bulk Fe at 3.7 eV. The thickness dependence of the transition energy of this new peak in the spectra is well explained by the concept of quantum well states in the Fe ultrathin layers, attributing the new transition to a transition from the majority spin Δ5 band ({px±i py), {dxz±i dyZ}; M=±l) to the Δ1 quantum well states (s, pz, dz2; M=0). The new peak is also observed in the Fe/Au (100) artificial superlattices. Using the εxy obtained experimentally for the Fe ultrathin films and the εxy of literature, we can reproduce the experimental φK spectra of the artificial superlattices by optical calculation. On the other hand, we cannot observe the same behavior for the ultrathin Fe films grown on a fcc-Ag (100) surface and covered by a Au (100) ultrathin film, although the εXy of Fe is different from that of the bulk and shows some structures in 2–3 eV. These structures around 2.5 eV are thought to be due to polarized Au atoms adjacent to an Fe layer.

An oscillation of φK as a function of interlayer thickness, d, was observed in photon energy region between about 2.5 and 3.8 eV for the Fe (6Å) /Au (dÅ) /Fe (6A) sandwiched film. The oscillation period was about 10Å (5ML) of Au. The oscillation is thought to be closely related with a formation of spin polarized quantum well states of Δ1 band in Au layers sandwiched by magnetic layers.

Surface plasmons and magneto-optic activity in hexagonal Ni anti-dot arrays

The influence of surface plasmons on the magneto-optic activity in a two-dimensional hexagonal array is addressed. The experiments were performed using hexagonal array of circular holes in a ferromagnetic Ni film. Well pronounced troughs are observed in the optical reflectivity, resulting from the presence of surface plasmons. The surface plasmons are found to strongly enhance the magneto-optic response (Kerr rotation), as compared to a continuous film of the same composition. The influence of the hexagonal symmetry of the pattern on the coupling between the plasmonic excitations is demonstrated, using optical diffraction measurements and theoretical calculations of the magneto-optic and of the angular dependence of the optical activity.

Coupling between magnetic and optical properties of stable Au-Fe solid solution nanoparticles

Au-Fe nanoparticles constitute one of the simplest prototypes of a multifunctional nanomaterial that can exhibit both magnetic and optical (plasmonic) properties. This solid solution, not feasible in the bulk phase diagram in thermal equilibrium, can be formed as a nanostructure by out-of-equilibrium processes. Here, the novel magnetic, optical and magneto-optical properties of ion-implanted Au-Fe solid solution nanoparticles dispersed in a SiO(2) matrix are investigated and correlated. The surface plasmon resonance of the Au-Fe nanoparticles with almost equicomposition is strongly damped when compared to pure Au and to Au-rich Au-Fe nanoparticles. In all cases, the Au atoms are magnetically polarized, as measured by x-ray magnetic circular dichroism, and ferromagnetically coupled with Fe atoms. Although the chemical stability of Au-Fe nanoparticles is larger than that of Fe nanoparticles, both the magnetic moment per Fe atom and the order temperature are smaller. These results suggest that electronic and magnetic properties are more influenced by the hybridization of the electronic bands in the Au-Fe solid solution than by size effects. On the other hand, the magneto-optical transitions allowed in the vis-nIR spectral regions are very similar. In addition, we also observe, after studying the properties of thermally treated samples, that the Au-Fe alloy is stabilized, not by surface effects, but by the combination of the out-of-equilibrium nature of the ion implantation technique and by changes in the properties due to size effects.

Full potential results on the magneto-optical properties of the Heusler compounds Co(2)FeX (X = Al, Ga, Si and Ge)

We have calculated the magneto-optical (MO) properties of Co(2)FeX (X =  Al, Ga, Si and Ge) Heusler compounds using the full potential linearized augmented plane wave (FPLAPW) method as implemented in the WIEN2K code using the local spin density approximation (LSDA) and also by using the generalized gradient approximation (GGA) for the electronic exchange and correlation. In all the compounds, Kerr rotation θ(K) has a strong minimum near 2 eV, the value of |θ(K)| corresponding to this minimum being almost as large as in pure Co-Fe compounds. The calculated MO spectra help to identify the features of the experimental spectra. A comparison of the results shows that the Kerr spectrum is quite similar from both LSDA and GGA but the latter gives better agreement with experiment. Moreover, we find that inclusion of correlation effects using GGA+U removes the discrepancy in magnetic moment of Co(2)FeX (X =  Si, Ge) though it has an insignificant effect on the Kerr spectra.

Magnetic circular dichroism in two-photon photoemission

We report the observation of magnetic circular dichroism (MCD) in two-photon photoemission (2PPE). The Heusler alloys Ni2MnGa and Co2FeSi were investigated by excitation with femtosecond laser light, showing MCD asymmetries of A=(3.5+/-0.5)x10;{-3} for Ni2MnGa and of A=(2.1+/-1.0)x10;{-3} for Co2FeSi, respectively. A theoretical explanation is provided based on local spin-density calculations for the magnetic dichroic response; the computed 2PPE MCD agrees well with the experiment. The observed 2PPE magnetic contrast represents an interesting alternative for future time-resolved photoemission studies on surface magnetism practicable in the laboratory.

Calculated magneto-optical Kerr spectra of the half-Heusler compounds AuMnX (X = In, Sn, Sb)

The ferromagnetic ground states of the half-Heusler compounds AuMnX (X = In, Sn, Sb) have been calculated in the framework of the local spin-density approximation (LSDA) to density functional theory (DFT). AuMnSn is computed to be a half-metallic ferromagnet, whereas AuMnIn and AuMnSb are not half-metallic, due to their different band filling. The computed relativistic electronic structures served as inputs to calculate the magneto-optical Kerr rotations and ellipticities for all three materials. In the case of AuMnSn the largest, zero-temperature, polar Kerr rotation has been found to be -0.45° at about 1 eV photon energy. The computed MOKE spectra of AuMnSn are in qualitative agreement with recent experiments. The largest Kerr rotations of AuMnIn and AuMnSb have been calculated to be +0.64° at 4.3 eV and -0.85° at 0.9 eV, respectively.

Magnetic circular dichroism near the Fermi level

We report the observation of enhanced magnetic circular dichroism (MCD) near the Fermi level using visible and ultraviolet lasers. More than 10% MCD asymmetry is achieved for a perpendicularly magnetized 12 ML (monolayer) Ni film on Cu(001). By changing the work function with the aid of cesium adsorption, the MCD asymmetry of is found to be enhanced only near the photoemission threshold and to drop down to 0.1% at the photon energy larger than the work function by 0.6 eV. A theoretical calculation also shows enhanced MCD near the photoemission threshold, qualitatively in agreement with the experimental results. Other ultrathin films of 6 ML Ni, 15 ML Co, and 3 and 15 ML Fe on Cu(001) are also investigated. It is found that the perpendicularly magnetized films show much larger MCD asymmetries than the in-plane magnetized films as in the Kerr effect.

Observation of the x-ray magneto-optical Voigt effect

The existence of the x-ray magneto-optical Voigt effect is demonstrated. By means of polarization analysis the Voigt rotation and ellipticity of linearly polarized synchrotron radiation are measured at the Co L3 edge upon transmission through an amorphous Co film. The observed x-ray Voigt rotation is about 7.5 degrees /microm. On the basis of ab initio calculations it is shown that the x-ray Voigt effect follows sensitively the amount of spin polarization of the 2p core states. Therefore it provides a unique measure of the spin splitting of the core states.

Magneto-optical linear dichroism in threshold photoemission electron microscopy of polycrystalline Fe films

Magnetic linear dichroism in threshold photoemission has been exploited to obtain magnetic contrast in a photoemission electron microscope using a mercury arc lamp. The dichroism at threshold can be described similar to the magneto-optical Kerr effect in the region of visible light. The asymmetry of electron intensity observed for a 100 nm polycrystalline Fe film on silicon is A=(0.37+/-0.05)%. The asymmetry occurs for the geometry of the transverse Kerr effect. For unpolarized light the asymmetry was about half the value observed for linearly polarized light. Threshold photoemission microscopy has a large potential for high resolution magnetic domain imaging with fast data acquisition.