Magnetic excitons of EuS revealed by resonant inelastic X-ray scattering

Europium monochalcogenides (EuX, X = O, S, Se, Te) are rare examples of intrinsic magnetic semiconductors. These compounds crystallize in the rock salt structure, with the Eu²⁺ ions exhibiting a half-filled 4f shell (4f⁷ configuration) and carrying a purely spin magnetic moment, making them prototypical Heisenberg magnets. The semiconducting gap lies between the occupied 4f states and the empty conduction band of predominantly Eu 5d character, while the S 3p states form an occupied valence band located below the 4f states.

Discovered in 1960s, Eu monochalcogenides initially drew significant scientific interest due to the coexistence of magnetic and semiconducting properties, promising traits for spintronics and magneto-optical applications [1]. However, once it became clear that doping could not raise the Curie temperature to room temperature, interest diminished. Over the past two decades, attention has revived following discoveries such as strain-induced enhancement of Curie temperature in multilayers [2] and ultrafast optical control of magnetization [3].

These developments have prompted renewed investigations into the electronic structure across the ferromagnetic transition and the mechanisms underlying ferromagnetic ordering. Less attention has been paid to an unsettled debate regarding the interpretation of optical absorption spectrum. EuX compounds exhibit two prominent absorption peaks: one near the onset and another along the rising edge. These are generally attributed to transitions in which a 4f electron is excited to crystal-field-split 5d sub-bands (5d(t₂g) and 5d(e_g)). However, the spatial character of the excited states remains controversial.

One interpretation, proposed by Wachter and collaborators, suggests that the excited electron resides in a delocalized Bloch state within the narrow 5d band, whose limited bandwidth (smaller than the crystal-field splitting) explains the absorption profile [4]. Kasuya and collaborators, however, argued that the Coulomb attraction of the localized 4f hole inhibits delocalization of the excited electron. Instead, they proposed the formation of localized many-body states 4f⁶5d¹(t_2g) and 4f⁶5d¹(e_g), known as magnetic excitons [5]. These excitons would give rise to the sharp features without invoking a narrow 5d band. In the absence of direct experimental evidence, this debate remained unresolved.

This study provides the first direct experimental confirmation of the excitonic interpretation for the absorption onset in EuS. Using valence-to-core RIXS at the Eu L edge, measured at beamline ID26 and supported by density functional theory-based calculations, the data reveal distinct excitonic signatures.

In the RIXS process (Figure 1), absorption of an X-ray photon (ω₁) excites an Eu 2p_3/2 core electron to the conduction band, resulting in an intermediate state with a core hole that perturbs the valence electronic structure. An electron from an occupied valence-band level then fills the 2p_3/2 core hole, with the energy difference emitted as a second X-ray photon (ω₂), detected by a spectrometer. The final state corresponds to an electron transferred from the valence to the conduction band, analogous (but not identical) to that produced in optical spectroscopy through absorption of a single photon in the UV–visible range.

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Fig. 1: Schematic of the RIXS process. An incoming photon (𝜔₁) excites a core electron into an unoccupied state. A valence electron subsequently fills the core hole, and the excess energy is released through the emission of a photon 𝜔₂. The final state corresponds to a valence electron promoted to the conduction band.

The measured RIXS spectra show two distinct sets of excitations (Figure 2). Comparison with electronic-structure calculations reveals that one set originates from transitions involving a hole in the S 3p valence band and an electron in the delocalized Eu 5d band. The other set corresponds to a hole in the Eu 4f states and an electron bound in a localized Eu 5d orbital, forming a magnetic exciton stabilized by the Coulomb interaction.

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Fig. 2: Assignment of features in the RIXS spectra. a) Experimental RIXS spectrum. b) Comparison between the optical absorption spectrum and the RIXS integrated along the incident-energy axis. c) Theoretical RIXS spectrum, decomposed into contributions from dipole (Eu 5d → Eu 2p) and quadrupole (Eu 4f → Eu 2p) transitions. Features labelled A and B correspond to localized magnetic excitons, while feature C is attributed to delocalized transitions involving the Eu 5d conduction band.

The delocalized excitations arise from dipole-allowed 5d→2p emissions, while the localized excitations result from dipole-forbidden (quadrupole-allowed) 4f→2p emissions. Despite being dipole-forbidden, the 4f → 2p channel shows comparable intensity, due to the large number of occupied 4f states (seven) compared to the small number of occupied 5d states (~0.6), resulting in an intensity enhancement by a factor of ~12. 

These results conclusively validate the excitonic model proposed by Kasuya and collaborators [5], offering definitive experimental support for the interpretation of sharp features in the optical absorption spectra of europium monochalcogenides. They further highlight the complex interplay between electronic structure and magnetism in intrinsic magnetic semiconductors.

Principal publication and authors
Magnetic Exciton of EuS Revealed by Resonant Inelastic X-Ray Scattering, L. Amidani (a,b), J. J. Joos (c,d), P. Glatzel (a), J. Kolorenč (e), Phys. Rev. Lett. 134, 046401 (2025); https://doi.org/10.1103/PhysRevLett.134.046401
(a) ESRF
(b) Institute of Resource Ecology, Helmholtz-Zentrum Dresden-Rossendorf (HZDR), Dresden (Germany)
(c) LumiLab, Department of Solid State Sciences, Ghent University, Gent (Belgium)
(d) Antwerp Maritime Academy, Antwerp (Belgium)
(e) Institute of Physics (FZU), Czech Academy of Sciences, Prague (Czech Republic)

References
[1] B.T. Matthias et al., Phys. Rev. Lett. 7, 160 (1961). 
[2] R.T. Lechner et al., Phys. Rev. Lett. 94, 157201 (2005). 
[3] M. Matsubara et al., Nat. Commun. 6, 6724 (2015). 
[4] P. Wachter, Crit. Rev. Solid State Sci. 3, 189 (1972). 
[5] T. Kasuya, Crit. Rev. Solid State Sci. 3, 131 (1972).