Landau level spectroscopy plays an important role in modern condensed-matter physics. In this technique, electrons in a solid are subjected to quantizing magnetic fields and probed experimentally, often through optical methods. Direct and detailed insights into the electronic properties of crystalline materials are obtained, particularly the properties related to their band structure. Landau level spectroscopy enables the precise extraction of key parameters such as effective mass, carrier density, mobility, and band gap, and serves as a powerful tool for studying interactions between electrons and other quasiparticles in solids. Over its more than seventy-year history, Landau level spectroscopy has been applied mainly to semiconductors and semimetals. Today, its scope also includes graphene-based systems, surface and bulk states in topological materials, and other emergent systems with a narrow or vanishing band gap. In this work, we review the fundamentals of Landau level spectroscopy and illustrate them with selected examples from the literature.

Ultrafast magnetism triggered by circularly polarized radiation underpins ultrafast spin control, relevant to future technologies, e.g., opto-spintronics and magnonics. The dynamics are often complicated and intertwined among correlated subsystems, such as electrons, spins, phonons, plasmons, topology, and lattice, due to many-body quantum coupling at ultrafast timescales. Here, we demonstrate light-induced effective magnetic fields generated by selective excitation between non-equidistant Landau quantized states in graphene, a prototypical Dirac material, using circularly polarized pulses. By magnetically tuning the Landau-level transition resonance away from other low-energy excitations, we obtain a clean electrostatically controllable platform and identify the microscopic origin of the light-induced magnetic signals, independent of sublattice coupling. Because different Landau levels carry distinct optical Hall conductivities, direct modification of their occupancies via optical excitations creates transient Faraday rotation signals with dispersive magnetic-field dependence, mirroring the static magneto-optical lineshape. The induced effective magnetic field normalized by the pump electric field exceeds typical reported values for the inverse Faraday effect of electronic origin. Our results establish a clear microscopic picture of the inverse Faraday effect of electronic origin, which can trigger hierarchical dynamics among correlated sublattices once Landau-level transitions are magnetically tuned to coincide with other low-energy excitations in Dirac systems and related materials.

We investigate the near-infrared optical response of the semiconducting van der Waals antiferromagnet CrPS4 and identify previously unreported spin-entangled optical resonances. The strong and anisotropic magnetic-field dependence of these resonances reflects the underlying magnetic order and confirms the biaxial antiferromagnetic nature of CrPS4. From the magnetic field evolution of the optical transition, we extract key magnetic parameters, including the spin-flop (≈0.9 T) and spin-saturation (≈8 T) fields. These results demonstrate a potential pathway for all-optical probing of spin states in van der Waals antiferromagnets, with relevance for spin-sensitive optoelectronic and magneto-optical devices.

When the energy gap, Δ, between the lowest-lying spin manifolds within a spin-exchange coupled molecule approaches Δ/kB ≈ 300 K, the traditional temperature-dependence (T < 400 K) of the molar magnetic susceptibility is not always a reliable way to obtain a good estimate of intramolecular exchange couplings. We develop a spectroscopic approach capable of accurately parametrizing complex magnetic Hamiltonians by exploiting the separation of the anisotropy and exchange energy scales in strongly coupled magnetic molecules. Specifically, we combine inelastic neutron scattering, high-frequency electron paramagnetic resonance, far-infrared magneto-spectroscopy and magnetometry, and obtain detailed information about the magnetic properties of a series of diiron complexes derived from [[Fe(cth)]2(dxbq)]3+ (H2dxbq: 2,5-dihydroxy-1,4-benzoquinone (x = h) or 3,6-dichloro-2,5-dihydroxy-1,4-benzoquinone (x = c), cth: 5,5,7,12,12,14-hexamethyl-1,4,8,11-tetraazacyclotetradecane). Well-isolated S = 9/2 ground states emerge due to strong direct antiferromagnetic exchange between the Fe3+ centers (S = 5/2) and the radical bridging benzoquinone ligand (S = 1/2). The specific sensitivities and transition selection rules of the applied methods allow us to determine the parameters of the microscopic Hamiltonian including exchange coupling, fourth-order Stevens operators and g-factors. Our methodology is directly portable to other strongly coupled molecular compounds.

Magnetic excitations in quantum materials can acquire chirality when time-reversal or spatial-inversion symmetries are broken, giving rise to nonreciprocal spin dynamics and circular dichroism. Such chiral magnons play a central role in contemporary condensed-matter physics, exist in magnetic, topological, and multiferroic materials, and thereby promote chiral spintronics. The underlying phenomena range from nonreciprocal magnon transport and optical activity to chiral spin textures such as skyrmions. They also include recently identified unconventional magnetic states, such as $g$-wave altermagnets and odd-parity $p$-wave magnets. In this context, bond-dependent magnetic interactions, such as those in Kitaev materials, provide a natural microscopic mechanism that can generate unconventional magnetic textures and anisotropic spin dynamics. While signatures of Kitaev physics have been widely sought in honeycomb magnets, direct experimental evidence for chiral magnons arising from Kitaev exchange remains scarce. Here we show, both experimentally and theoretically, that the zero-field splitting and field-dependent optical handedness of the chiral electromagnons in the helical magnetic order of NiI$_2$, arise from the interplay of Kitaev-type exchange and single-ion anisotropy.

We report on antiferromagnetic resonance experiments in bulk tetragonal NaMnAs – a room-temperature antiferromagnetic semiconductor. Our results corroborate previous ab initio studies, which propose that NaMnAs is an easy-axis antiferromagnet with the Néel vector oriented along the tetragonal axis. At B = 0, we find a single antiferromagnetic resonance line at 7 meV and associate it with a doubly degenerate (k = 0) magnon mode. Its energy softens considerably with increasing T, but remains clearly visible in the data up to room temperature. From the experimental data, we estimate the single-ion anisotropy of the Mn ions in NaMnAs to be D ≈ 0.2 meV, a value that is relatively large compared to other manganese-based antiferromagnets.

Bond-dependent magnetic interactions, particularly those described by the Kitaev model, have emerged as a key pathway toward realizing unconventional magnetic states such as quantum spin liquids and topologically nontrivial excitations, including skyrmions. These interactions frustrate conventional magnetic order and give rise to rich collective behavior that continues to challenge both theory and experiment. While Kitaev physics has been extensively explored in the context of honeycomb magnets, direct evidence for its role in real materials remains scarce. Magnetic van der Waals (vdW) materials have emerged as a versatile platform for exploring low-dimensional electrical, magnetic, and correlated electronic phenomena, and provide a fertile ground for potential applications ranging from spintronics to multiferroic devices and quantum information technologies. Here, we demonstrate, through magneto-transmission, Faraday angle rotation, and magnetic circular dichroism measurements, that the magnetic excitation spectrum of NiI_2, a van der Waals multiferroic material, is more accurately captured by a Kitaev-based spin model than by the previously invoked helical spin framework.

The structural, magneto-optical, and magnetotransport properties as well as the electronic band structure of the bulk crystalline topological insulator (TI) Sb2Te2Se, grown by the vertical Bridgman technique, were studied. The high structural quality of the grown crystals was established by x-ray diffraction and Raman spectroscopy. Angular resolved photoelectron spectroscopy revealed a single Dirac cone with the Dirac point, away from the valence as well as conduction bands, 0.22 eV above the Fermi level. The magnetotransport data exhibited a distinct single-frequency Shubnikov-de Haas oscillation in the magnetic fields above B = 10 T. The Lifshitz-Kosevich analysis of the data suggests that this oscillation originates from the Dirac-type states. A sharp fundamental absorption edge in the mid-infrared transmission spectra measured at 4.2 K demonstrated a direct band gap of 0.377 eV located at a momentum of 0.1 & Aring;-1 along the P- K directions of the Brillouin zone. A two-band model developed for massive Dirac electrons in the bulk of topological insulators with the direct band gap at a non-& Gcy; point suggests hyperbolic dispersion relations for the conduction and valence bands displaying the full electron-hole symmetry. Equal magnitude of the electron and hole effective masses me mh 0.21m0 and g factors ge gh 10 were estimated.

2D magnetic materials have attracted extensive research interest due to their potential application in nanospintronics, optospintronics, and magnonics. Ferromagnetic- and antiferromagnetic-layered materials have been demonstrated and successfully inserted into van der Waals heterostructures. However, the effects of magnetic frustration in van der Waals materials and the possibilities offered by spin configurations characterized by nonlinear spin arrangements have not been fully considered yet. Herein, we establish the magnetic phase diagram of bulk CrOCl, a frustrated van der Waals magnet, using magnetization and magneto-optical spectroscopy techniques. In particular, we use the magnetic superstructures relative to the crystallographic unit cell and the associated rich zone-folded phonon series to describe the magnetic-field-induced phases. Theoretical calculations taking into account the competing nearest neighbors' magnetic exchange interactions provide insight into the lattice vibrations of this class of magnetic system. This study expands the scope of 2D magnetic materials and provides a methodology to characterize frustrated van der Waals magnets.

Probing the quantum geometry and topology in condensed matter systems has relied heavily on static electronic transport experiments in magnetic fields. Yet, contact-free optical measurements have rarely been explored. Here, we report the observation of resonant magnetic circular dichroism (MCD) in the infrared range in thin film MnBi_{2}Te_{4} exhibiting a spectral intensity that correlates with the anomalous Hall effect. Both phenomena emerge with a field-driven phase transition from an antiferromagnet to a canted ferromagnet. By theoretically relating the MCD to the anomalous Hall effect via Berry curvature for a metallic state, we show that this transition accompanies an abrupt onset of Berry curvature, signaling a topological phase transition from a topological insulator to a doped Chern insulator. Our density functional theory calculation suggests the MCD signal mainly originates from an optical transition at the Brillouin zone edge, hinting at a potential new source of Berry curvature away from the commonly considered Γ point. Our findings demonstrate a novel experimental approach for detecting Berry curvature through spectroscopy of the interband MCD, generally applicable to magnetic materials.

The electronic properties of thin single crystals of the topological insulator Bi1.1Sb0.9Te2S were studied by magneto-optical spectroscopy. A sharp edge of the absorption band and Fabry-Perot oscillations in the transmission spectra measured at a temperature of 4.2 K made it possible to estimate the band gap as 0.31 eV and the refractive index 6. The application of magnetic fields up to 11 T induced a decrease in the amplitude of the oscillations attributed to the Faraday effect with an average (over the spectral range from 0.05 to 0.31 eV) Verdet constant of 2.5 & sdot;103 degrees/cm/T.

Magneto-optical excitations in antiferromagnetic d systems can originate from a multiplicity of light-spin and spin-spin interactions, as the light and spin degrees of freedom can be entangled. This is exemplified in van der Waals systems with attendant strong anisotropy between in-plane and out-of-plane directions, such as MnPS 3 ${\rm MnPS}_3$ and NiPS 3 ${\rm NiPS}_3$ films studied here. The rich interplay between the magnetic ordering and sub-bandgap optical transitions poses a challenge to resolve the mechanisms driving spin-entangled optical transitions, as well as the single-particle bandgap itself. Here, a high-fidelity ab initio theory is applied to find a realistic estimation of the bandgap by elucidating the atom- and orbital-resolved contributions to the fundamental sub-bands. It is further demonstrated that the spin-entangled excitations, observable as photoluminescence and absorption resonances, originate from an on-site spin-flip transition confined to a magnetic atom (Mn or Ni). The evolution of the spin-flip transition in a magnetic field is used to deduce the effective exchange coupling and anisotropy constants.

The Raman scattering response of the biaxial antiferromagnet CoPS3 has been investigated as a function of both magnetic field and temperature. The peaks observed in the low-frequency spectral range (90-200 cm-1) have been identified as hybrid magnon-phonon excitations. The energies of the bare magnon and phonon modes and the effective coupling strengths between different excitation pairs have been determined. The strong and selective magnon-phonon interaction largely accounts for the pronounced splitting of two phononlike modes observed at 152 and 158 cm-1 in the antiferromagnetic phase of CoPS3. Based on the identification of bare magnon excitations and their magnetic-field dependence, we propose an updated set of parameters for the effective exchange (Jeff = 9.9 meV) and biaxial magnetic anisotropy (D = 4.3 meV and E = -0.7 meV) and advocate for an apparent anisotropic g factor (gx = gy = 2, gz = 4) in the CoPS3 antiferromagnet.

The diamond-like allotrope of Sn (alpha-Sn) is tantalizing, being an elemental semimetal that hosts a range of topological properties. Despite the intriguing potential of this quantum material, a detailed understanding of its nontrivial electronic structure remains relatively poor. Here, we prepared alpha-Sn in a well-defined quantum phase (i.e., topological Dirac semimetal) by applying a compressive strain via epitaxial growth on the (111) surface of an InSb substrate. We varied the thickness of the alpha-Sn epilayer to single out the emergence of quantum confinement effects. Our electrical investigation suggests a thickness-dependent modification of transport mechanisms. These results are complemented by the measurement of the cyclotron resonance, which manifests the role of quantum confinement in defining the effective mass of topological Dirac fermions as bulk carriers. Our results contribute to deepening the knowledge of the alpha-Sn electronic properties. This is pivotal to increase the future applicability of Sn-based architectures into beyond-stateof-the-art devices.

The Mott-Ioffe-Regel limit sets the lower bound of the carrier mean free path for coherent quasiparticle transport. Metallicity beyond this limit is of great interest because it is often closely related to quantum criticality and unconventional superconductivity. Progress along this direction mainly focuses on the strange-metal behaviors originating from the evolution of the quasiparticle scattering rate, such as linear-in-temperature resistivity, while the quasiparticle coherence phenomena in this regime are much less explored due to the short mean free path at the diffusive bound. Here we report the observation of quantum oscillations from Landau quantization near the Mott-Ioffe-Regel limit in CaAs3. Despite the insulator-like temperature dependence of resistivity, CaAs3 presents giant magnetoresistance and prominent Shubnikov-de Haas oscillations from Fermi surfaces, indicating highly coherent band transport. In contrast, quantum oscillation is absent in the magnetic torque. The quasiparticle effective mass increases systematically with magnetic fields, manifesting a much larger value than what is expected based on magneto-infrared spectroscopy. This suggests a strong many-body renormalization effect near the Fermi surface. We find that these unconventional behaviors may be explained by the interplay between the mobility edge and the van Hove singularity, which results in the formation of coherent cyclotron orbits emerging at the diffusive bound. Our results call for further study on the electron correlation effect of the van Hove singularity.

Electric fields represent an ideal means for controlling spins at the nanoscale and, more specifically, for manipulating protected degrees of freedom in multispin systems. Here we perform low-temperature magnetic far-IR spectroscopy on a molecular spin triangle (Fe3) and provide the first experimental evidence of spin-electric transitions in polynuclear complexes. The co-presence of electric- and magnetic-dipole transitions, allows us to estimate the spin-electric coupling. Based on spin Hamiltonian simulations of the spectra, we identify the observed transitions and introduce the concept of a generalized exchange qubit. This applies to a wide class of molecular spin triangles, and includes the scalar chirality and the partial spin sum qubits as special cases.

Two hexacoordinated Co( ii ) complexes were prepared, characterised, and deposited on silicon surface in the logical structures. The magnetic anisotropy and slow relaxation of magnetisation was studied by experimental and theoretical approaches.

Modulation-doped CdTe quantum wells (QWs) with Cd0.7Mg0.3Te barriers were studied by photoluminescence (PL) and far-infrared Fourier spectroscopy under a magnetic field at 4.2 K and by Raman spectroscopy at room temperature. Two samples were tested: a sample which contained ten QWs (MQW) and a sample with one QW (SQW). The width of each QW was equal to 20 nm, and each of them was modulation-doped with iodine donors introduced in a 4 nm thick layer. The concentration of donors in each doped layer was nominally identical, but the thickness of the spacer in SQW and MQW samples was 20 and 10 nm, respectively. This resulted in a two times higher electron concentration per well in the MQW sample than in the SQW sample. We observed differences in PL from the two samples: the energy range of PL was different, and one observed phonon replicas in MQW which were absent in the SQW sample. An analysis of oscillations of the PL intensity as a function of magnetic field indicated that PL resulted from the recombination of free electrons in the conduction band with free or localized holes in the case of SQW and MQW samples, respectively.

Competition between exchange interactions and magnetocrystalline anisotropy may bring new magnetic states that are of great current interest. An applied hydrostatic pressure can further be used to tune their balance. In this work, we investigate the magnetization process of a biaxial antiferromagnet in an external magnetic field applied along the easy axis. We find that the single metamagnetic transition of the Ising type observed in this material under ambient pressure transforms under hydrostatic pressure into two transitions, a first-order spin-flop transition followed by a second-order transition toward a polarized ferromagnetic state near saturation. This reversible tuning into a new magnetic phase is obtained in layered bulk CrSBr at low temperature by varying the interlayer distance using high hydrostatic pressure, which efficiently acts on the interlayer magnetic exchange and is probed by magneto-optical spectroscopy.