Kimel, Alexey, Zvezdin, Anatoly, Sharma, Sangeeta, Shallcross, Samuel, de Sousa, Nuno, Garcia-Martin, Antonio, Salvan, Georgeta, Hamrle, Jaroslav, Stejskal, Ondrej, McCord, Jeffrey, Tacchi, Silvia, Carlotti, Giovanni, Gambardella, Pietro, Salis, Gian, Muenzenberg, Markus, Schultze, Martin, Temnov, Vasily, Bychkov, Igor V, Kotov, Leonid N., Maccaferri, Nicolo, Ignatyeva, Daria, Belotelov, Vladimir, Donnelly, Claire, Rodriguez, Aurelio Hierro, Matsuda, Iwao, Ruchon, Thierry, Fanciulli, Mauro, Sacchi, Maurizio, Du, Chunhui Rita, Wang, Hailong, Armitage, N. Peter, Schubert, Mathias, Darakchieva, Vanya, Liu, Bilu, Huang, Ziyang, Ding, Baofu, Berger, Andreas, Vavassori, Paolo, Kimel, Alexey, Zvezdin, Anatoly, Sharma, Sangeeta, Shallcross, Samuel, de Sousa, Nuno, Garcia-Martin, Antonio, Salvan, Georgeta, Hamrle, Jaroslav, Stejskal, Ondrej, McCord, Jeffrey, Tacchi, Silvia, Carlotti, Giovanni, Gambardella, Pietro, Salis, Gian, Muenzenberg, Markus, Schultze, Martin, Temnov, Vasily, Bychkov, Igor V, Kotov, Leonid N., Maccaferri, Nicolo, Ignatyeva, Daria, Belotelov, Vladimir, Donnelly, Claire, Rodriguez, Aurelio Hierro, Matsuda, Iwao, Ruchon, Thierry, Fanciulli, Mauro, Sacchi, Maurizio, Du, Chunhui Rita, Wang, Hailong, Armitage, N. Peter, Schubert, Mathias, Darakchieva, Vanya, Liu, Bilu, Huang, Ziyang, Ding, Baofu, Berger, Andreas, and Vavassori, Paolo
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 todays 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, Funding Agencies|DFG [TRR227, SH498/4-1]; Ministerio de Ciencia e Innovacion [PID2019-109905GA-C22]; Deutsche Forschungsgemeinschaft (DFG) [282193534]; Czech Science Foundation [1913310S]; OP VVV project MATFUN [CZ.02.1.01/0.0/0.0/15_003/0000487]; German Science Foundation [DFG MC9/9]; Collaborative Research Centre [SFB 1261]; italian Ministery of University and Research through the PRIN-2020 project entitled `The Italian factory of micromagnetic modeling and spintronics [2020LWPKH7]; NCCR QSIT; Swiss National Science Foundation [200020_200465]; Spanish Ministry of Science and Innovation under the Maria de Maeztu Units of Excellence Programme [CEX2020-001038-M]; MICINN/FEDER [RTI2018-094881-B-100]; Agence Nationale de la Recherche [ANR-15-CE24-0032-PPMI-NANO]; Russian Science Foundation [21-72-20048]; Russian Foundation of Basic Research [RFBR 20-07-00466]; Luxembourg National Research Fund [C19/MS/13624497]; European Union [FETOPEN-01-2018-20192020, 964363]; Swedish Research Council [2021-05784]; Russian Ministry of Science and Higher Education of the Russian Federation, Megagrant Project [075-15-2022-1108]; Max Planck Society Lise Meitner Excellence Program; Spanish AEI [PID2019-220 104604RB/AEI/10.13039/501100011033]; French ANR [ANR-10-LABX-0039 -PALM, ANR-11EQPX0005 -ATTOLAB, ANR-21-CE30-0037 HELIMAG]; Scientific Cooperation Foundation of ParisSaclay University through the funding of the OPT2X research project (Lidex 2014); Ile-de-France region through the Pulse-X project; European Unions Horizon 2020 Research and Innovation Programme [EU-H2020LASERLAB-EUROPE-654148]; Swiss SNSF [P2ELP2_181877]; Air Force Office of Scientific Research [FA9550-21-1-0125]; ARO MURI [W911NF2020166]; NSF [DMR-1905519]; Institute for Quantum Matter, an EFRC - DOE BES [DE-SC0019331]; National Science Foundation [DMR 1808715, OIA-2044049]; Air Force Office of Scientific Research Awards [FA9550-18-1-0360, FA9550-19S-0003, FA9550-21-1-0259]; Knut and Alice Wallenbergs Foundation; Uni