Dilute magnetic semiconductors (DMS) exhibit unique optical properties due to the incorporation of transition metal or rare-earth ions into a semiconductor host lattice. These materials combine semiconducting behavior with magnetic ordering, leading to phenomena such as giant Zeeman splitting, magneto-optical effects, and spin-dependent optical transitions. Key optical characteristics include the magneto-optical Kerr effect (MOKE), magnetic circular dichroism (MCD), and interactions between excitons and magnetic ions. Spectroscopic techniques are essential for probing these properties, revealing insights into spin-polarized band structures and exchange interactions.

The magneto-optical Kerr effect (MOKE) is a prominent tool for studying DMS materials. It involves the rotation of the polarization plane of reflected light when the material is subjected to an external magnetic field. This rotation arises from the spin-split electronic bands induced by the exchange interaction between charge carriers and localized magnetic moments. In DMS such as GaMnAs or ZnMnSe, MOKE measurements provide direct evidence of ferromagnetic ordering and the strength of the exchange coupling. The Kerr rotation angle is proportional to the magnetization, allowing for the determination of Curie temperatures and magnetic anisotropy. Spectrally resolved MOKE can further reveal the energy-dependent nature of spin polarization in the valence and conduction bands.

Magnetic circular dichroism (MCD) is another critical technique for investigating DMS. MCD measures the differential absorption of left- and right-circularly polarized light in the presence of a magnetic field. This effect originates from the Zeeman splitting of electronic states and the selection rules for optical transitions between spin-polarized bands. In materials like CdMnTe or InMnAs, MCD spectra exhibit pronounced features near the bandgap energy, reflecting the exchange interaction between sp-band electrons and localized d-electrons of magnetic ions. The magnitude and sign of the MCD signal depend on the spin polarization of the involved states, providing a fingerprint of the magnetic ion’s influence on the host semiconductor. Temperature- and field-dependent MCD studies help quantify the exchange constants and the nature of magnetic interactions.

Exciton-magnetic ion interactions play a central role in the optical response of DMS. Excitons, or bound electron-hole pairs, couple strongly with the spins of magnetic ions, leading to giant Zeeman splitting. This splitting can exceed typical values in non-magnetic semiconductors by orders of magnitude due to the strong sp-d exchange interaction. In materials like ZnCoO or GaFeN, the excitonic transitions split into spin-polarized components under an external magnetic field, observable in photoluminescence (PL) and absorption spectra. The energy separation between these components scales with the magnetization of the system, offering a means to probe the magnetic properties optically. Time-resolved PL spectroscopy further reveals the spin dynamics of excitons, including their relaxation and recombination processes in the presence of magnetic ions.

Spectroscopic techniques such as photoluminescence excitation (PLE) and resonant Raman scattering are also employed to study DMS. PLE spectroscopy maps the absorption profile by monitoring the PL intensity as a function of excitation energy, revealing the density of states modified by magnetic impurities. Resonant Raman scattering, on the other hand, provides information about spin-flip processes and magnon-phonon interactions. In Mn-doped GaAs or ZnO, Raman spectra show additional peaks corresponding to spin-dependent excitations, which are absent in the non-magnetic host. These features are sensitive to the magnetic phase transitions and the local environment of the dopant ions.

Faraday rotation is another magneto-optical phenomenon widely used in DMS research. Unlike MOKE, which measures reflection, Faraday rotation occurs in transmission and involves the rotation of the polarization plane of light passing through the material. The rotation angle is proportional to the Verdet constant, which depends on the material’s magnetization and the wavelength of light. In DMS like HgCrSe or PbSnMnTe, Faraday rotation measurements are used to determine the carrier spin polarization and the effective g-factor of the bands. The spectral dependence of Faraday rotation also offers insights into the interplay between band structure and magnetic ordering.

The optical properties of DMS are highly tunable through doping concentration, temperature, and external fields. For instance, increasing the Mn concentration in GaMnAs enhances the exchange interaction, leading to larger Zeeman splittings and more pronounced magneto-optical effects. Similarly, applying hydrostatic pressure can modify the band alignment and the strength of sp-d coupling, as observed in CdMnSe under high-pressure conditions. Temperature-dependent studies reveal the interplay between thermal fluctuations and magnetic ordering, with distinct signatures in the optical spectra across the Curie or Néel temperature.

In summary, the optical properties of dilute magnetic semiconductors are governed by the interplay between semiconducting and magnetic order. Magneto-optical effects such as MOKE and MCD provide direct probes of spin polarization and exchange interactions, while exciton-magnetic ion coupling leads to giant Zeeman splitting and spin-dependent recombination. Advanced spectroscopic techniques enable detailed characterization of these phenomena, offering a pathway to engineer DMS for spintronic and optoelectronic applications. The ability to control these properties through doping, fields, and external stimuli makes DMS a versatile platform for exploring spin-photon interactions in solid-state systems.