Chapter 3 Magneto-optical kerr spectra

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.

Orbitally dominated Rashba-Edelstein effect in noncentrosymmetric antiferromagnets

Efficient manipulation of magnetic order with electric current pulses is desirable for achieving fast spintronic devices. The Rashba-Edelstein effect, wherein spin polarization is electrically induced in noncentrosymmetric systems, provides a mean to achieve staggered spin-orbit torques. Initially predicted for spin, its orbital counterpart has been disregarded up to now. Here we report a generalized Rashba-Edelstein effect, which generates not only spin polarization but also orbital polarization, which we find to be far from being negligible. We show that the orbital Rashba-Edelstein effect does not require spin-orbit coupling to exist. We present first-principles calculations of the frequency-dependent spin and orbital Rashba-Edelstein tensors for the noncentrosymmetric antiferromagnets CuMnAs and Mn[Formula: see text]Au. We show that the electrically induced local magnetization can exhibit Rashba-like or Dresselhaus-like symmetries, depending on the magnetic configuration. We compute sizable induced magnetizations at optical frequencies, which suggest that electric-field driven switching could be achieved at much higher frequencies.

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.

Polarization Analysis in Mössbauer Reflectometry with Synchrotron Mössbauer Source

Polarization selection of the reflected radiation has been employed in Mössbauer reflectivity measurements with a synchrotron Mössbauer source (SMS). The polarization of resonantly scattered radiation differs from the polarization of an incident wave so the Mössbauer reflectivity contains a scattering component with 90° rotated polarization relative to the π-polarization of the SMS for some hyperfine transitions. We have shown that the selection of this rotated π→σ component from total reflectivity gives an unusual angular dependence of reflectivity characterized by a peak near the critical angle of the total external reflection. In the case of collinear antiferromagnetic interlayer ordering, the “magnetic” maxima on the reflectivity angular curve are formed practically only by radiation with this rotated polarization. The first experiment on Mössbauer reflectivity with a selection of the rotated polarization discovers the predicted peak near the critical angle. The measurement of the rotated π→σ polarization component in Mössbauer reflectivity spectra excludes the interference with non-resonant electronic scattering and simplifies the spectrum shape near the critical angle allowing for an improved data interpretation in the case of poorly resolved spectra. It is shown that the selected component of Mössbauer reflectivity with rotated polarization is characterized by enhanced surface sensitivity, determined by the “squared standing waves” depth dependence. Therefore, the new approach has interesting perspectives for investigations of surfaces, ultrathin layers and multilayers having complicated magnetic structures.

Large magneto-optical Kerr effect and imaging of magnetic octupole domains in an antiferromagnetic metal

When a polarized light beam is incident upon the surface of a magnetic material, the reflected light undergoes a polarization rotation1. This magneto-optical Kerr effect (MOKE) has been intensively studied in a variety of ferro- and ferrimagnetic materials because it provides a powerful probe for electronic and magnetic properties2, 3 as well as for various applications including magneto-optical recording4. Recently, there has been a surge of interest in antiferromagnets (AFMs) as prospective spintronic materials for high-density and ultrafast memory devices, owing to their vanishingly small stray field and orders of magnitude faster spin dynamics compared to their ferromagnetic counterparts5-9. In fact, the MOKE has proven useful for the study and application of the antiferromagnetic (AF) state. Although limited to insulators, certain types of AFMs are known to exhibit a large MOKE, as they are weak ferromagnets due to canting of the otherwise collinear spin structure10-14. Here we report the first observation of a large MOKE signal in an AF metal at room temperature. In particular, we find that despite a vanishingly small magnetization of M ~0.002 µB/Mn, the non-collinear AF metal Mn3Sn15 exhibits a large zero-field MOKE with a polar Kerr rotation angle of 20 milli-degrees, comparable to ferromagnetic metals. Our first-principles calculations have clarified that ferroic ordering of magnetic octupoles in the non-collinear Néel state16 may cause a large MOKE even in its fully compensated AF state without spin magnetization. This large MOKE further allows imaging of the magnetic octupole domains and their reversal induced by magnetic field. The observation of a large MOKE in an AF metal should open new avenues for the study of domain dynamics as well as spintronics using AFMs.

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.

Bright circularly polarized soft X-ray high harmonics for X-ray magnetic circular dichroism

We demonstrate, to our knowledge, the first bright circularly polarized high-harmonic beams in the soft X-ray region of the electromagnetic spectrum, and use them to implement X-ray magnetic circular dichroism measurements in a tabletop-scale setup. Using counterrotating circularly polarized laser fields at 1.3 and 0.79 µm, we generate circularly polarized harmonics with photon energies exceeding 160 eV. The harmonic spectra emerge as a sequence of closely spaced pairs of left and right circularly polarized peaks, with energies determined by conservation of energy and spin angular momentum. We explain the single-atom and macroscopic physics by identifying the dominant electron quantum trajectories and optimal phase-matching conditions. The first advanced phase-matched propagation simulations for circularly polarized harmonics reveal the influence of the finite phase-matching temporal window on the spectrum, as well as the unique polarization-shaped attosecond pulse train. Finally, we use, to our knowledge, the first tabletop X-ray magnetic circular dichroism measurements at the N4,5 absorption edges of Gd to validate the high degree of circularity, brightness, and stability of this light source. These results demonstrate the feasibility of manipulating the polarization, spectrum, and temporal shape of high harmonics in the soft X-ray region by manipulating the driving laser waveform.

Ultrafast spin-switching of a ferrimagnetic alloy at room temperature traced by resonant magneto-optical Kerr effect using a seeded free electron laser

Ultrafast magnetization reversal of a ferrimagnetic metallic alloy GdFeCo was investigated by time-resolved resonant magneto-optical Kerr effect measurements using a seeded free electron laser. The GdFeCo alloy was pumped by a linearly polarized optical laser pulse, and the following temporal evolution of the magnetization of Fe in GdFeCo was element-selectively traced by a probe free electron laser pulse with a photon energy tuned to the Fe M-edge. The results have been measured using rotating analyzer ellipsometry method and confirmed magnetization switching caused by ultrafast heating.

Magneto-optical Kramers-Kronig analysis

We describe a simple magneto-optical experiment and introduce a magneto-optical Kramers-Kronig analysis (MOKKA) that together allow extracting the complex dielectric function for left- and right-handed circular polarizations in a broad range of frequencies without actually generating circularly polarized light. The experiment consists of measuring reflectivity and Kerr rotation, or alternatively transmission and Faraday rotation, at normal incidence using only standard broadband polarizers without retarders or quarter-wave plates. In a common case, where the magneto-optical rotation is small (below ∼0.2 rad), a fast measurement protocol can be realized, where the polarizers are fixed at 45(∘) with respect to each other. Apart from the time-effectiveness, the advantage of this protocol is that it can be implemented at ultra-high magnetic fields and in other situations, where an in-situ polarizer rotation is difficult. Overall, the proposed technique can be regarded as a magneto-optical generalization of the conventional Kramers-Kronig analysis of reflectivity on bulk samples and the Kramers-Kronig constrained variational analysis of more complex types of spectral data. We demonstrate the application of this method to the textbook semimetals bismuth and graphite and also use it to obtain handedness-resolved magneto-absorption spectra of graphene on SiC.