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arXiv:2512.16014

Magneto-optical Kerr effect in pump-probe setups

Amir Eskandari-asl, Adolfo Avella

cond-mat.mtrl-sciphysics.opticsquant-phSubmitted Dec 17, 2025• Announced Dec 19, 2025
arXivHTMLPDF

Abstract

We develop a general theoretical framework for computing the time-resolved magneto-optical Kerr effect in ultrafast pump-probe setups, formulated within the Dynamical Projective Operatorial Approach (DPOA) and its application to the generalized linear-response theory for pumped systems. Furthermore, we exploit this formalism to express the post-pump optical conductivity and consequently the Kerr rotation in terms of the time-evolved single-particle density matrix (SPDM), providing a transparent and computationally efficient description of photo-excited multi-band systems. This extension, in addition to its lower computational cost, has the advantage of allowing the inclusion of phenomenological damping. We illustrate the formalism using both (i) a two-band tight-binding model, which captures the essential physics of ultrafast spin-charge dynamics and the Kerr rotation, and (ii) weakly spin-polarized germanium, as a realistic playground with a complex band structure. The results demonstrate that, by exploiting DPOA and/or its SPDM extension, one can reliably reproduce both the short-time features under the pump-pulse envelope and the long-time dynamics after excitation, offering a versatile framework for analyzing time-resolved magneto-optical Kerr effect experiments in complex materials. Moreover, this analysis clearly shows that the Kerr rotation can be used to deduce experimentally the relevant n-photon resonances for a given specific material.

Journal reference
Phys. Rev. A 113, 013738 (2026)
DOI
10.1103/wfcr-75gl
Comments
14 pages, 5 figures, 18 panels

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We develop a general theoretical framework for computing the time-resolved magneto-optical Kerr effect in ultrafast pump-probe setups, formulated within the Dynamical Projective Operatorial Approach (DPOA) and its application to the generalized linear-response theory for pumped systems. Furthermore, we exploit this formalism to express the post-pump optical conductivity and consequently the Kerr rotation in terms of the time-evolved single-particle density matrix (SPDM), providing a transparent and computationally efficient description of photo-excited multi-band systems. This extension, in addition to its lower computational cost, has the advantage of allowing the inclusion of phenomenological damping. We illustrate the formalism using both (i) a two-band tight-binding model, which captures the essential physics of ultrafast spin-charge dynamics and the Kerr rotation, and (ii) weakly spin-polarized germanium, as a realistic playground with a complex band structure. The results demonstrate that, by exploiting DPOA and/or its SPDM extension, one can reliably reproduce both the short-time features under the pump-pulse envelope and the long-time dynamics after excitation, offering a versatile framework for analyzing time-resolved magneto-optical Kerr effect experiments in complex materials. Moreover, this analysis clearly shows that the Kerr rotation can be used to deduce experimentally the relevant n-photon resonances for a given specific material.
Recent experimental advancements in ultrafast pump-probe setups drive a growing need for efficient and insightful theoretical methods. This study will delve into the intricacies of our newly developed approach, the Dynamical Projective Operatorial Approach (DPOA). DPOA stands out as a highly efficient model-Hamiltonian method capable of calculating a wide range of single/multi-time single/multi-particle properties, such as excitation populations, out-of-equilibrium Green's functions, TR-ARPES signals, and various response functions. When dealing with transient optical properties, utilizing the DPOA formulation and capitalizing on the weak intensity of the probe pulse, we efficiently compute the linear response of the pumped system to a generic probe pulse, significantly accelerating calculations. Alongside the theoretical framework, we present noteworthy results that experimentalists can utilize to establish connections between observed effects and their underlying physical phenomena.
We derive the two-time linear response theory for out-of-equilibrium pumped systems, generic pump-probe delays, and probe frequencies. Such a theory enormously simplifies the numerical calculations, for instance, of the optical conductivity with respect to the actual procedure, which requires computing the effect of the probe pulse for each time delay with respect to the pump pulse. The theory is given for a generic observable and pumped Hamiltonian and then specialized for a system with a quadratic Hamiltonian and its transient optical properties, exploiting the dynamical projective operatorial approach (DPOA). The theory is complemented by a set of crucial numerical guidelines that help perform actual calculations in a computationally affordable way. The optical response (differential transient reflectivity and absorption) of a prototypical three-band (core, valence, and conduction) model in the extreme ultraviolet regime is analyzed in detail to illustrate the theory and its application. Using some generalizations of the density of states, we provide a systematic approach to exploring the optical properties in terms of the system band-structure features and the pump parameters. Such an analysis can be extremely helpful in understanding the actual results of experimental optical measurements. Moreover, we study the effects of interband and intraband transitions, the local dipole coupling, and single and multiphoton processes. The latter is further investigated by varying the central frequency of the pump pulse to have different regions of the first Brillouin zone in resonance with it. We also study the effect of varying the pump pulse intensity. Finally, we study and analyze the transient optical properties in the probe pulse regime of the infrared and visible.
We employ the Dynamical Projective Operatorial Approach (DPOA) to investigate the ultrafast optical excitations of germanium under intense, ultrashort pump pulses. The method has very low resource demand relative to many other available approaches and enables detailed calculation of the residual electron and hole populations induced by the pump pulse. It provides direct access to the energy distribution of excited carriers and to the total energy transferred to the system. By decomposing the response into contributions from different multi-photon resonant processes, we systematically study the dependence of excited-carrier density and absorbed energy on key pump-pulse parameters: duration, amplitude, and photon energy. Our results reveal a complex interplay between these parameters, governed by resonant Rabi-like dynamics and competition between different multi-photon absorption channels. For the studied germanium setup, we find that two-photon processes are generally dominant, while one- and three-photon channels become significant under specific conditions of pump-pulse frequency, duration, and intensity. This comprehensive analysis offers practical insights for optimizing ultrafast optical control in semiconductors by targeting specific multi-photon pathways.
Optical control of the spin coherence of quantum well electrons by short laser pulses with circular or linear polarization is studied experimentally and theoretically. For that purpose the coherent electron spin dynamics in a nnn-doped CdTe/(Cd,Mg)Te quantum well structure was measured by time-resolved pump-probe Kerr rotation, using resonant excitation of the negatively charged exciton (trion) state. The amplitude and phase shifts of the electron spin beat signal in an external magnetic field, that are induced by laser control pulses, depend on the pump-control delay and polarization of the control relative to the pump pulse. Additive and nonadditive contributions to pump-induced signal due to the control are isolated experimentally. These contributions can be well described in the framework of a two-level model for the optical excitation of the resident electron to the trion.
Ultrafast characterization and control of many-body interactions and elementary excitations are critical to understanding and manipulating emergent phenomena in strongly correlated systems. In particular, spin interaction plays an important role in unconventional superconductivity, but efficient tools for probing spin dynamics, especially out of equilibrium, are still lacking. To address this question, we develop a theory for nonresonant time-resolved Raman scattering, which can be a generic and powerful tool for nonequilibrium studies. We also use exact diagonalization to simulate the pump-probe dynamics of correlated electrons in the square-lattice single-band Hubbard model. Different ultrafast processes are shown to exist in the time-resolved Raman spectra and dominate under different pump conditions. For high-frequency and off-resonance pumps, we show that the Floquet theory works well in capturing the softening of bimagnon excitation. By comparing the Stokes and anti-Stokes spectra, we also show that effective heating dominates at small pump fluences, while a coherent many-body effect starts to take over at larger pump amplitudes and frequencies on resonance to the Mott gap. Time-resolved Raman scattering thereby provides the platform to explore different ultrafast processes and design material properties out of equilibrium.
Ultrafast magneto-optical (MO) experiments constitute a powerful tool to explore the magnetization dynamics of diverse materials. Over the last decade, there have been many theoretical and experimental developments on this subject. However, the relation between the magnetization dynamics and the transient MO response still remains unclear. In this work, we calculate the magnetization of a material, as well as the magneto-optical rotation and ellipticity angles measured in a single-beam experiment. Then, we compare the magnetization to the MO response. The magnetic material is modeled by a three-level Λ-type system, which represents a simple model to describe MO effects induced by an ultrafast laser pulse. Our calculations use the density matrix formalism, while the dynamics of the system is obtained by solving the Lindblad equation taking into account population relaxation and dephasing processes. Furthermore, we consider the Faraday rotation of the optical waves that simultaneously causes spin-flip. We show that the Faraday angles remain proportional to the magnetization only if the system has reached the equilibrium-state, and that this proportionality is directly related to the population and coherence decay rates. For the non-equilibrium situation, the previous proportionality relation is no longer valid. We show that our model is able to interpret some recent experimental results obtained in a single-pulse experiment. We further show that, after a critical pulse duration, the decrease of the ellipticity as a function of the absorbed energy is a characteristic of the system.