Evolution of spin excitations from bulk to monolayer FeSe

Iron selenide (FeSe) is a minimal iron-based superconductor with a simple crystal structure and Tc ~ 8 K in bulk, undergoing a structural transition near 90 K. Its bulk Fermi surface comprises hole pockets at Γ and electron pockets at M, whereas in monolayer FeSe on SrTiO3 (FeSe/STO) only electron pockets at M remain, with Γ hole pockets pushed below EF due to ~0.1 e/Fe electron doping from STO. Bulk FeSe exhibits strong but competing Néel- and stripe-like spin fluctuations at q = (1,0) and (1,1) without long-range order, implying magnetic frustration. Probing spin excitations in monolayer FeSe is experimentally challenging: INS lacks sensitivity to single layers and optical probes mix substrate and interface responses. RIXS at the Fe L-edge overcomes these limitations via elemental selectivity and enhanced cross-section, enabling studies of ultrathin films. The purpose of this study is to determine how spin excitations evolve from bulk FeSe to monolayer FeSe/STO and to relate these changes to band structure and Fermi surface topology. Using high-resolution RIXS and DCA-QMC simulations of a bilayer Hubbard model, the authors find that bulk FeSe hosts dispersive, acoustic-like magnetic excitations, while FeSe/STO exhibits gapped, nearly dispersionless, and hardened spin excitations. Theoretical modeling links this reconfiguration to a Lifshitz transition that removes the Γ hole pocket, suppressing particle-hole scattering channels, flattening and gapping the dispersion, and increasing the excitation energy bandwidth.

The study builds on extensive work on spin dynamics in iron-based superconductors. Bulk FeSe shows simultaneous Néel- and stripe-like fluctuations without static order, consistent with magnetic frustration. Traditional probes such as INS are not feasible for monolayers, while Raman/optical spectroscopy suffer from substrate/interface contributions. Advances in Fe L-edge RIXS have enabled detection of spin excitations in Fe pnictides and chalcogenides, providing complementary information to INS (e.g., BaFe2As2, SmFeAsO, NaFeAs, EuFe2As2, β-FeSe). Prior doping studies in BaFe2As2 show modest evolution: hole doping softens excitations, electron doping leaves high-energy excitations largely unchanged, and isovalent P doping hardens excitations by ~40 meV—the largest reported before this work, yet still far smaller than the hardening observed in FeSe/STO. Theoretical frameworks such as Eliashberg/FLEX tie superconducting pairing to the spin susceptibility χ(q,ω), and prior models proposed spin-fluctuation-mediated pairing, including from incipient bands, relevant to FeSe monolayers and intercalates. The present work leverages these contexts to interpret how the Fermi surface Lifshitz transition in FeSe/STO restructures spin excitations.

Samples: Monolayer FeSe films were grown on Nb-doped (0.5 wt%) SrTiO3 (001). Substrates were chemically etched; growth occurred at ~500 °C by co-evaporation of Se and Fe with a 20:1 flux ratio, followed by annealing at 550 °C for 2 h. Films were capped with ~25 nm amorphous Se. ARPES characterization showed a superconducting gap ~13.4 meV (Tc ~60–65 K). Bulk FeSe single crystals were grown by flux under a temperature gradient (~400–330 °C) with Tc ~8 K. RIXS/XAS: High-resolution Fe L3-edge RIXS was performed at the I21 beamline (Diamond Light Source). Samples were aligned with (001) normal in the scattering plane; TEY was used for XAS. Incident polarization was employed; total energy resolution ~40 meV (FWHM) at ~710.5 eV. Scattering angle fixed at 154°, giving |Q|max ≈ 0.7 Å−1; in-plane momentum q was tuned by varying incidence angle. Reciprocal space used the 2-Fe unit cell (a = 3.76 Å, c = 5.4 Å), with Q in r.l.u. Spectra for bulk FeSe required ~30 min per q; FeSe/STO required ≥3 h per q. Measurements were at 20 K and ~5×10−10 mbar. Theory: A two-orbital (bilayer-equivalent) Hubbard model on a 2D square lattice was used, containing only local intra-orbital Hubbard repulsion U, identical to Ref. 19. Due to symmetry, the model maps to bonding (kz = 0) and antibonding (kz = π) bands; momentum transfers q = 0 (intraband) and q = π (interband). Energy units set by t = 1, with U = 8t; the nearest-neighbor interlayer hopping t1 and filling n were varied to tune from a two-band Fermi surface (hole and electron pockets) to an incipient-band case (only electron pocket, hole band below EF). Calculations employed the Dynamical Cluster Approximation (DCA) solved with continuous-time auxiliary field QMC (CTAUX). Real-frequency spectra (A(k,ω), χ''(q,ω)) were obtained via Maximum Entropy analytic continuation. Two parameter sets produced consistent two-band and incipient-band behaviors robust to parameter variations. Additional 1D Hubbard ladder exact-diagonalization RIXS calculations using the Kramers–Heisenberg formula were performed to establish correspondence between RIXS intensity and the dynamical spin structure factor and to demonstrate suppression of intraband susceptibility in the incipient-band regime. Conversion to physical units used t = 90 meV (bulk) and t = 160 meV (monolayer), implying U = 0.72 eV and 1.28 eV, respectively, consistent with downfolded effective interactions for Fe 3d-only models and prior FLEX studies.

• Bulk FeSe exhibits dispersive magnetic excitations detected by Fe L3-edge RIXS: a mode near ~140 meV at q = (0.36,0) r.l.u. disperses downward toward the zone center, merging into the elastic line, resembling acoustic-like spin excitations seen in antiferromagnets and prior pnictides (e.g., BaFe2As2).
• Monolayer FeSe/STO shows a strong elastic background but, after resonance enhancement, a broad inelastic peak is identified at ~320 meV at q = (0.36,0), with a pronounced asymmetric tail extending up to ~1 eV. This mode is gapped, nearly dispersionless across momentum, with energy ~320–400 meV along (H,0) and (H,H), and significantly broader than in bulk.
• The hardening and flattening of spin excitations from bulk to monolayer far exceed doping-induced changes reported in related iron pnictides; previous largest hardening (P-doped BaFe2As2) was ~40 meV, much smaller than observed here.
• DCA-QMC calculations of a bilayer Hubbard model capture these trends. In the two-band case (bulk-like), χ''(q,ω) is strongly dispersive: intraband (q = 0) shows a minimum at Γ and maxima near (0.5,0)/(0.5,0.5); interband (q = π) shows minima at (0.5,0)/(0.5,0.5) and a maximum at Γ. The interband spectral weight is ~4–5× larger than intraband.
• In the incipient-band case (monolayer-like), interband χ''(q,ω) becomes gapped and largely dispersionless across the Brillouin zone, matching RIXS peak energies (white diamonds in figures). Intraband low-energy scattering is strongly suppressed once the Γ hole pocket sinks below EF. Calculated spectral widths reproduce the experimental broadening in the incipient band case.
• Best agreement with experiment is obtained using t ≈ 90 meV (bulk) and 160 meV (monolayer), with U = 8t, consistent with reduced correlations in FeSe/STO relative to bulk (per DMFT+LDA) and effective 3d-only interaction strengths.
• Simplified ladder ED RIXS calculations confirm that RIXS intensity closely follows the spin dynamical structure factor and that transitioning to an incipient band suppresses intraband susceptibility, supporting the interpretation of the Fe L-edge RIXS features as spin excitations.
• Overall, the evolution of spin excitations is directly tied to the Fermi surface Lifshitz transition (loss of Γ hole pocket) in FeSe/STO, which quenches specific particle-hole channels, gaps and flattens the dispersion, and increases the energy scale of magnetic excitations.

The observed transformation of spin excitations from dispersive, lower-energy modes in bulk FeSe to gapped, nearly dispersionless, and higher-energy modes in monolayer FeSe/STO is directly linked to the Fermiology: removing the Γ hole pocket via electron doping/interface effects induces an incipient band structure. This Lifshitz transition closes key particle-hole scattering channels, suppressing low-energy intraband fluctuations and enhancing interband contributions at higher energies, as captured by DCA-QMC calculations. Since Eliashberg/FLEX-based pairing theories incorporate χ(q,ω) explicitly, the substantial reconfiguration and hardening of χ''(q,ω) in FeSe/STO implies a significant change in the spin-fluctuation pairing kernel and is consistent with spin fluctuations contributing to the elevated Tc in FeSe/STO. While the results strongly support a magnetic component to pairing, they do not exclude additional mechanisms, such as interfacial electron-phonon coupling or charge transfer from STO, which may act synergistically with spin fluctuations. The agreement between RIXS measurements and the model’s interband susceptibility in the incipient regime underscores the importance of interband spin fluctuations when the hole pocket is incipient, offering a coherent framework that connects Fermi surface topology, spin dynamics, and superconductivity in FeSe systems.

This work provides direct experimental evidence (Fe L-edge RIXS) and supporting DCA-QMC modeling that spin excitations in FeSe undergo a dramatic reconfiguration from bulk to monolayer FeSe/STO: bulk FeSe hosts dispersive, lower-energy magnetic modes, while FeSe/STO exhibits gapped, nearly dispersionless, and hardened excitations. Theoretical analysis attributes this to a Lifshitz transition that removes the Γ hole pocket, suppressing low-energy intraband scattering and enhancing interband processes at higher energies. These findings establish a strong link between Fermi surface topology and spin dynamics, with implications for spin-fluctuation-mediated pairing and the enhanced Tc in FeSe/STO. Future research directions include quantitative RIXS cross-section calculations incorporating multi-orbital matrix elements, orbital orientation and polarization effects; extended momentum and temperature-dependent RIXS studies across Tc; and integrated modeling that combines spin fluctuations with interfacial electron-phonon coupling to assess their combined impact on superconductivity.

• RIXS measurements on FeSe/STO exhibit a strong elastic background and broad inelastic features; finite energy resolution (~40 meV) and limited momentum reach (|Q|max ~0.7 Å−1) constrain detailed lineshape analysis.
• INS cannot probe single-unit-cell films, limiting cross-validation with neutron data; comparisons between INS and RIXS are nontrivial due to Brillouin zone conventions and absence of magnetic order in FeSe.
• Theoretical modeling employs a simplified bilayer (two-orbital) Hubbard model without full multi-orbital Hund’s coupling and without explicit Fe L-edge RIXS matrix elements; severe fermion sign problems prevent fully realistic multi-orbital QMC treatments.
• Conversion from model to physical energy scales relies on choosing t values (90 meV bulk, 160 meV monolayer) and U = 8t; while justified by correlation trends, these introduce uncertainties.
• Quantitative separation of intra- vs interband contributions in experimental RIXS spectra is limited; the comparison is primarily qualitative.
• Substrate, capping, and interface contributions may influence elastic scattering and potentially complicate weak inelastic features, though elemental selectivity mitigates this.