Role of photonic interference in exciton-mediated magneto-optic responses

Abstract

Coupled optical and magnetic excitations can give rise to remarkably strong magneto-optic responses. This is particularly evident in van der Waals magnets, such as the antiferromagnet CrSBr, where excitons and magnons emerge from the same electronic orbitals. While previous work has primarily focused on uncovering the magneto-electric origin of the resulting exciton-magnon interactions, the influence of photonic effects has received comparatively little attention. Here, we use numerical simulations to disentangle exciton-magnon coupling from the exciton-mediated magnon-photon interactions observed in optical experiments. Our simulations show the strong dependence of these interactions on photonic interference and dispersion effects near excitonic resonances. Such effects shape the optical response to coherent magnons and make it intrinsically non-linear in the magnon-induced exciton energy shift. Thermal magnons, which have a particularly pronounced impact on excitons, are found to even produce qualitatively different trends in optical signatures. Depending on weak or strong coupling of excitons and photons, the same exciton-magnon interaction can lead to a red-shift of optical modes, a nearly vanishing response, or their blue-shift. Finally, we demonstrate first steps towards optimizing the multi-parameter problem of efficient magnon-photon transduction using a machine-learning approach.

Figures (5)

• Figure 1: Role of magnons in the exciton-dominated range of the dielectric function. a) Sketch of a thin CrSBr crystal on top of a silicon substrate covered by an oxide layer. b) Magnons couple to photons by changing the exciton resonance. c) Exciton-magnon interactions can shift, quench, or broaden the exciton resonance. d) Dielectric function of CrSBr in the near infrared region modeled using parameters from Ref. shao2025magnetically.
• Figure 2: Coherent magnon-induced reflectance modulation mediated by excitons. a) Schematic pump-probe measurement of a 5 nm-thin CrSBr crystal on top of a Silicon substrate covered by an oxide of thickness $d$. b) Calculated reflectance spectra with ($R_M$) and without ($R$) a shift of the exciton energy induced by magnons. Left and right panels compare spectra obtained at oxide thickness $d_1 = 140$ nm and $d_2=240$ nm. The electric field distribution calculated at $E = E_X$ respectively exhibits a maximum or minimum at the position of the CrSBr crystal for these thicknesses, as indicated in the inset. c) Magnon-induced reflectance contrast, $\Delta R_M = R_M - R$, and amplitude $|\Delta R_{M,max} - \Delta R_{M,min}|$. d) $\Delta R_M$ as a function of energy and SiO2 thickness. e) Maximum amplitude of $\Delta R_M$ as a function of the magnon-induced exciton energy shift $\Delta E_X$ for $d=d_1$ and $d=d_2$. Dashed line indicates the exciton energy shift used in our simulations. f) Energy and time-dependence of $\Delta R_M$. g) Line cuts from f) taken at the maximum amplitude of $\Delta R_M$ for $\Delta t = 0$.
• Figure 3: Temperature dependence of the optical response. a-c) Temperature dependence of excitonic parameters determined by the experiments in Ref. shao2025magnetically (red dots) approximated by polynomial functions (blue lines) used for calculations. Reflectance of a 5 nm-thin CrSBr crystal placed on a substrate with d) $d_1 = 140$ nm and e) $d_2 = 240$ nm oxide thickness. Black dashed lines show $E_X(T)$
• Figure 4: Magneto-optic responses of a CrSBr microcavity. a) Microcavity structure. b) Reflectance calculated for spacer thickness $d =$ 117 nm at different angle of incidence, $\theta$. Fits of upper ($E_{UP}$) and lower ($E_{LP}$) polariton energies derived from a Hopfield model deng2010exciton are plotted as red dashed curves. Energy of bare exciton ($E_X$) and cavity mode ($E_{cav}$) are indicated by white dashed lines. c) Transient reflectance induced by coherent magnons for $|X(0)|^2=0.8$. d) Amplitude of $\Delta R_M$ as a function of exciton fraction. Inset: Dependence of $|X|^2$ on spacer layer thickness for $\theta = 0^\text{o}$. e) Temperature dependence of lower polariton energies for different exciton fractions $|X(0)|^2$.
• Figure 5: Optimization of multilayer stacks. a) Schematic of different sample configurations with layer thicknesses optimized by BOSS. b) Optimized $\Delta R_M$ spectra for scenarios (1) to (3). Vertical arrows indicate the amplitude of each $\Delta R_M$ curve.