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.

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 $200\mu \mathrm{A}$, 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.

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.

How does one determine the magnetization state and hysteresis loop corresponding to one of the ferromagnetic (FM) layers located at a given depth in a stack of FM/non-FM layers by means of the magneto-optical Kerr effect? For this purpose the representation of the Kerr effect in the complex rotation-ellipticity plane is introduced. A depth sensitivity function controlling the Kerr effect is defined and its dependence on the photon energy and angle of incidence is studied. A general way to determine the in-depth location of the FM layer, from which the Kerr signal originates, is proposed. In the case of a FM bilayer structure, previous proposed solutions are discussed within a unified formalism. For a system with three or more FM layers two approaches are proposed to extract selectively the magneto-optical signals originating at individual FM layers: the parallel Kerr vector and cascade numerical projection methods. These methods are successively checked experimentally on simple multilayer structures. Finally, on the basis of the developed approaches a readout solution for multivalued magneto-optical recording in a four-storage-layer structure is proposed.