The recent discovery of excitons coupled to the magnetic order, and the consequent strong magneto-optic responses, in some van der Waals magnetic semiconductors has triggered intense activity at the interface of magnetism and semiconductor optics. Here, we present an analytically tractable minimal model that describes magnetic order, electrons, holes, and excitons within a unified framework, thereby capturing a wide range of phenomena. It treats the magnetic order and itinerant carriers to be comprised by distinct electronic orbitals that are mutually coupled via orbital-dependent onsite exchange, similar to the treatment of metallic magnets using an s-d model. Investigating CrSBr bilayer as a case study, we benchmark our model and its predictions against recent experimental and ab-initio results finding good agreement as well as new insights enabled by the model's simplicity. Examining the optical selection rules, we find the conservation of a quantum number formed from a combination of spin and layer pseudospin to be a useful guiding principle, even in noncollinear magnetic configurations. Our analysis finds a series of bright and dark excitonic states in such layered A-type antiferromagnets. The presented framework should be valuable in achieving intuitive understanding of recently discovered excitonic phenomena and guiding the discovery of other excitonic states in layered magnetic semiconductors.
The recent discovery of excitons coupled to the magnetic order, and the consequent strong magneto-optic responses, in some van der Waals magnetic semiconductors has triggered intense activity at the interface of magnetism and semiconductor optics. Here, we present an analytically tractable minimal model that describes magnetic order, electrons, holes, and excitons within a unified framework, thereby capturing a wide range of phenomena. It treats the magnetic order and itinerant carriers to be comprised by distinct electronic orbitals that are mutually coupled via orbital-dependent onsite exchange, similar to the treatment of metallic magnets using an s-d model. Investigating CrSBr bilayer as a case study, we benchmark our model and its predictions against recent experimental and ab-initio results finding good agreement as well as new insights enabled by the model's simplicity. Examining the optical selection rules, we find the conservation of a quantum number formed from a combination of spin and layer pseudospin to be a useful guiding principle, even in noncollinear magnetic configurations. Our analysis finds a series of bright and dark excitonic states in such layered A-type antiferromagnets. The presented framework should be valuable in achieving intuitive understanding of recently discovered excitonic phenomena and guiding the discovery of other excitonic states in layered magnetic semiconductors.
We develop a microscopic theory of magnon-exciton drag effect in a bilayer van der Waals antiferromagnetic semiconductor CrSBr. Effective exciton-magnon coupling arises from an orbital mechanism: Magnons tilt the layer magnetizations, enabling charge carrier tunneling that mixes intra- and interlayer excitons and thereby modulate the exciton energy. We derive the effective Hamiltonian of exciton-magnon coupling, based on our calculation of the magnon spectrum taking into account short-range exchange interaction between Cr-ion spins, single-ion anisotropy, and long-range dipole-dipole interactions. The latter produces a negative group velocity of magnons at small wavevectors. We show that despite rather small renormalization of exciton's energy and effective mass by the exciton-magnon interaction, the three key two-magnon processes: exciton-magnon scattering, two-magnon absorption by exciton, and two-magnon emission are highly efficient. By solving the Boltzmann kinetic equation, we evaluate short exciton-magnon scattering time which is in the sub-ps range and strongly decreases with the increase of magnon population. Hence, exciton-magnon scattering is likely to be dominant over other scattering processes related to the exciton-phonon and exciton-disorder interactions. We demonstrate that magnons can efficiently drag excitons, resulting in a large and nearly isotropic exciton propagation that can significantly exceed the intrinsic anisotropic diffusion. Our results provide a theoretical basis for recent observations of anomalous exciton transport in CrSBr [F. Dirnberger, et al., Nat. Nano. (2025)] and establish magnon-exciton drag as a powerful mechanism for controlling exciton propagation in magnetic systems.
Excitons in anisotropic two-dimensional (2D) materials, defined by direction-dependent effective masses, are of pronounced interest for their roles in excitonic and magneto-optical phenomena. A perpendicular magnetic field complicates the separation of center-of-mass (c.m.) and relative motions, especially when electron and hole masses are comparable. Conventional theories often employ an approximate c.m. separation using factorized wave functions, modifying magnetic Hamiltonian terms and possibly introducing inaccuracies in magnetoexciton energy predictions. This work develops an exact analytical framework for c.m. and relative motion separation in anisotropic 2D magnetoexcitons, without resorting to the stationary-c.m. approximation. Starting from the full electron-hole Hamiltonian in a homogeneous magnetic field, the formalism uses the conserved pseudomomentum to derive a relative-motion Hamiltonian, revealing new anisotropy-dependent couplings and magnetic coefficients absent in approximate models. The resulting Schrödinger equation is treated via the Feranchuk-Komarov operator method and Levi-Civita transformation, allowing non-perturbative, systematically convergent solutions. Application to monolayer black phosphorus and titanium trisulfide, both freestanding and encapsulated in hexagonal boron nitride, yields magnetoexciton energies, diamagnetic coefficients, and probability densities for the ten lowest states across considerable magnetic-field ranges. The results demonstrate the significant influence of anisotropy-dependent coupling on magnetic response in systems with strong mass anisotropy. This formalism is generalizable to other anisotropic 2D semiconductors, establishing a foundation for advanced magneto-optical studies.
The recently discovered magnetic exciton in the van der Waals (vdW) antiferromagnet NiPS3 exemplifies these phenomena, exhibiting several distinctive characteristics. Despite extensive investigation, much of its physics remains unresolved, with key questions about why the NiPS3 magnetic exciton is so sharp and optically bright despite the nominally spin-forbidden transition, posing significant challenges to a proper understanding and practical manipulation of the exciton. An urgent question is to what extent it is due to chemical disorder, magnetic weakening, lattice modification, or intrinsic instability of the bright exciton itself: answers to which will put stringent constraints on possible theoretical models. Here we address these questions using hydrostatic pressure as a clean, continuous, reversible, and in-situ tuning parameter. We find that the sharp photoluminescence peak is drastically suppressed by as little as 0.4 GPa and completely quenched by 1.5 GPa, with demonstrating its reversibility. Crucially, this bright-to-dark conversion occurs without magnetic, crystallographic, or electronic reconstruction despite an increase in the Neel temperature, as established by Raman, X-ray absorption, nuclear magnetic resonance spectroscopy, and first-principles many-body calculations. Our results demonstrate that the optical brightness of the magnetic exciton is independent of chemical disorder, lattice expansion, and weakening of magnetic order, indicating that a higher-order correlated mechanism governs the bright exciton. We further propose experimentally constrained microscopic scenarios involving exciton pairing, crystal-field-controlled spin-orbit mixing, and symmetry breaking, providing a framework for future tests of entangled magnetic exciton in correlated quantum magnets.
It has been demonstrated that small plaquettes of quantum dot spin qubits are capable of simulating condensed matter phenomena that arise from the Hubbard model, such as the collective Coulomb blockade and Nagaoka ferromagnetism. Motivated by recent materials developments, we investigate a bilayer arrangement of quantum dots with four dots in each layer which exhibits a complex ground state behavior. We find using a generalized Hubbard model with long-range Coulomb interactions, several distinct magnetic configurations occur as the Coulomb interaction strength is varied, with possible ground states that are ferromagnetic, antiferromagnetic, or having both one antiferromagnetic and one ferromagnetic layer. We map out the full phase diagram of the system as it depends on the inter- and intralayer Coulomb interaction strengths, and find that for a single layer, a similar but simpler effect occurs. We also predict interesting contrasts among electron, hole, and electron-hole bilayer systems arising from complex correlation physics. Observing the predicted magnetic configuration in already-existing few-dot semiconductor bilayer structures could prove to be an important assessment of current experimental quantum dot devices, particularly in the context of spin-qubit-based analog quantum simulations.
A phase diagram of two Mott-Hubbard planes interacting with a short-range Coulomb repulsion is presented. Considering the case of equal amount of doping by holes in one layer as electrons in the other, a holon-doublon inter-layer exciton formation is shown to be a natural consequence of Coulomb attraction. Quasiparticle spectrum is gapped and incoherent below a critical doping δc due to the formation of excitons. A spin liquid insulator (SLI) phase is thus realized without the lattice frustration. The critical value δc sensitively depends on the inter-layer interaction strength. In the tJ model description of each layer with the d-wave pairing, δc marks the crossover between SLI and d-wave superconductor. The SLI phase, despite being non-superconducting and charge-gapped, still shows electromagnetic response similar to that of a superfluid due to the exciton transport. Including antiferromagnetic order in the tJ model introduces magnetically ordered phases at low doping and pushes the spin liquid phase to a larger inter-layer interaction strength and higher doping concentrations.
A phase diagram of two Mott-Hubbard planes interacting with a short-range Coulomb repulsion is presented. Considering the case of equal amount of doping by holes in one layer as electrons in the other, a holon-doublon interlayer exciton formation is shown to be a natural consequence of Coulomb attraction. Quasiparticle spectrum is gapped and incoherent below a critical doping ${\ensuremath{\delta}}_{c}$ due to the formation of excitons. A spin-liquid-insulator (SLI) phase is thus realized without the lattice frustration. The critical value ${\ensuremath{\delta}}_{c}$ sensitively depends on the interlayer interaction strength. In the $t\text{\ensuremath{-}}J$ model description of each layer with the d-wave pairing, ${\ensuremath{\delta}}_{c}$ marks the crossover between SLI and d-wave superconductor. The SLI phase, despite being nonsuperconducting and charge gapped, still shows an electromagnetic response similar to that of a superfluid due to the exciton transport. Including antiferromagnetic order in the $t\text{\ensuremath{-}}J$ model introduces magnetically ordered phases at low doping and pushes the spin-liquid phase to a larger interlayer interaction strength and higher doping concentrations.