Evolution of spin excitations from bulk to monolayer FeSe

Iron selenide (FeSe) stands out among iron-based superconductors due to its simple structure: a square Fe lattice with Se ions above and below. While exhibiting superconductivity at Tc ~ 8 K and a structural transition at ~90 K, its Fermi surface differs significantly between bulk and monolayer forms. Bulk FeSe possesses cylindrical hole pockets at the Γ point and elliptical electron pockets at the M point. However, in FeSe/STO monolayers, the hole pockets at Γ are pushed below the Fermi level, leaving only circular electron pockets at M, suggesting electron doping. Bulk FeSe shows Néel and stripe-like fluctuations despite lacking long-range antiferromagnetic order, indicating significant magnetic frustration. Studying spin excitations in FeSe/STO is challenging due to the limited volume contributing to magnetic scattering. Techniques like inelastic neutron scattering (INS) cannot probe single layers, and Raman/optical spectroscopy cannot separate signals from the substrate, FeSe, and the interface. Resonant Inelastic X-ray Scattering (RIXS), however, offers elemental selectivity and sensitivity to electronic excitations, making it ideal for studying ultrathin materials. This research combines high-energy-resolution RIXS and QMC calculations to explore spin dynamics in both bulk and monolayer FeSe/STO, aiming to understand the impact of the dimensional reduction on the magnetic excitations and their role in the enhanced superconductivity observed in FeSe/STO.

Previous research has extensively investigated spin excitations in Fe-based superconductors, employing techniques such as INS and RIXS. Studies on bulk FeSe have revealed the presence of significant magnetic fluctuations, consistent with the observed lack of long-range magnetic order. The impact of doping on the spin excitation spectrum has also been studied in detail in various Fe-based superconductors, revealing changes in spin excitation energy and dispersion depending on the doping type and level. However, the effect of dimensional reduction from bulk to monolayer FeSe on the spin excitation spectrum is less understood. The unique properties of FeSe/STO, notably its enhanced Tc, highlight the need for a detailed understanding of the spin excitations in this system. The present study builds upon this existing knowledge by using advanced RIXS techniques to probe the spin excitations in FeSe/STO monolayers and employing state-of-the-art theoretical calculations to interpret the experimental findings.

The study utilized high-energy-resolution RIXS measurements at the 121-RIXS beamline at Diamond Light Source. Bulk FeSe samples were cleaved in vacuum, and monolayer FeSe/STO samples were prepared by growing a single layer of FeSe on Nb-doped SrTiO3 substrate, followed by annealing and protection with a Se capping layer. Fe L-edge X-ray absorption spectroscopy (XAS) was performed to determine the optimal incident photon energy for RIXS measurements. High-resolution RIXS spectra were collected at various momentum points along high-symmetry directions, providing detailed information on the energy and dispersion of the spin excitations. The energy resolution achieved was ~40 meV. Quantum Monte Carlo (QMC) calculations within the dynamical cluster approximation (DCA) were performed using a two-orbital bilayer Hubbard model. This model, which incorporates intraorbital Hubbard repulsion, allows for tuning the electronic structure from a two-band system (similar to bulk FeSe) to an incipient band system (similar to FeSe/STO) by varying the interlayer hopping parameter. The QMC calculations yielded the single-particle spectral function and dynamical spin susceptibility, which were then compared to the experimental RIXS data. The model parameters, particularly the hopping parameter t, were adjusted to best match the experimental findings. Auxiliary calculations with a simplified 1D Hubbard ladder model helped to verify the sensitivity of the RIXS signal to the spin susceptibility and the suppression of intraband susceptibility in the incipient band model.

RIXS measurements revealed significant differences in spin excitations between bulk FeSe and FeSe/STO. Bulk FeSe exhibited dispersive spin excitations around 140 meV at q = (0.36, 0) r.l.u., decreasing in energy towards the zone center. In contrast, FeSe/STO showed a broad, gapped, and dispersionless peak centered at ~320 meV, extending up to 1 eV. This peak was identified as originating from the FeSe layer due to the resonant excitation. QMC calculations showed good agreement with experimental data: the two-band Hubbard model accurately reproduced the dispersive spin excitations in bulk FeSe, while the incipient band model accurately captured the gapped, dispersionless, and hardened excitations in FeSe/STO. The transition from a two-band to an incipient band system is the direct cause of these changes. The removal of the hole pocket at the Γ point in FeSe/STO strongly suppresses low-energy intraband scattering, resulting in the observed hardening and flattening of the spin excitations. The interband susceptibility has much larger intensity and dominates RIXS signal.

The dramatic evolution of spin excitations from bulk to monolayer FeSe highlights the significant impact of dimensionality and Fermiology on magnetic fluctuations. The observed hardening and flattening of the excitations in FeSe/STO provide crucial insights into the pairing mechanism responsible for the enhanced Tc. In Eliashberg and FLEX models, the spin susceptibility χ(q, ω) plays a key role in determining Tc, indicating that changes in χ(q, ω) from bulk to monolayer substantially affect the superconducting properties. The findings suggest a pivotal role for spin fluctuations in the unconventional superconductivity of FeSe/STO, while acknowledging the potential contribution of other interactions (like phonons or substrate doping) to Tc enhancement. Future studies should include the effects of orbital orientation and polarization in the theoretical model for more precise quantitative comparisons.

This study provides comprehensive experimental and theoretical evidence for a dramatic transformation in spin excitations from bulk to monolayer FeSe. The gapping, hardening, and suppression of dispersion in FeSe/STO monolayers are linked directly to the change in Fermiology, specifically the elimination of the hole pocket at the Γ point. This has major implications for understanding unconventional superconductivity in FeSe, particularly the mechanism of the remarkably increased Tc in FeSe/STO. Future work could focus on incorporating orbital and polarization effects into the theoretical model to achieve even more precise agreement with the RIXS data.

The theoretical model used in this study, a two-orbital bilayer Hubbard model, is a simplification of the complex electronic structure of FeSe. While it captures the essential features of the system, neglecting other details (like orbital-dependent interactions) might affect the quantitative accuracy of the results. Furthermore, RIXS matrix elements were not explicitly included in the theoretical calculations, limiting the quantitative comparison between theory and experiment. The analysis primarily focused on excitations along high-symmetry directions and did not cover the full Brillouin zone, potentially missing features in other regions. Although high quality FeSe/STO samples were used, slight variations in the monolayer quality and interface properties could influence the experimental results.