Effects of charge doping and constrained magnetization on the electronic structure of an FeSe monolayer

The electronic structural properties in the presence of constrained magnetization and a charged background are studied for a monolayer of FeSe in non-magnetic, checkerboard-, and striped-antiferromagnetic (AFM) spin configurations. First principles techniques based on the pseudopotential density functional approach and the local spin density approximation are utilized. Our findings show that the experimentally observed shape of the Fermi surface is best described by the checkerboard AFM spin pattern. To explore the underlying pairing mechanism, we study the evolution of the non-magnetic to the AFM-ordered structures under constrained magnetization. We estimate the strength of electronic coupling to magnetic excitations involving an increase in local moment and, separately, a partial moment transfer from one Fe atom to another. We also show that the charge doping in the FeSe can lead to an increase in the density of states at the Fermi level and possibly produce higher superconducting transition temperatures.

💡 Research Summary

This paper investigates how charge doping and constrained magnetization affect the electronic structure of a single‑layer FeSe film. Using first‑principles density‑functional theory (DFT) within the local spin‑density approximation (LSDA) and generalized gradient approximation (GGA), the authors model three magnetic configurations: non‑magnetic (NM), checkerboard antiferromagnetic (CH), and striped antiferromagnetic (STR). Structural relaxations are performed with a plane‑wave cutoff of 40 Ry and a charge‑density cutoff of 600 Ry; forces are converged below 0.5 mRy/Å. The NM unit cell contains four atoms, the CH cell also contains four atoms, while the STR cell contains eight atoms to accommodate the lattice distortion induced by the stripe order. Equilibrium lattice constants are 6.97 a.u. (NM), 7.10 a.u. (CH), and 7.11 a.u. (STR); Se‑Fe heights are 2.57, 2.70, and 2.72 a.u., respectively. Magnetic moments are 0 µB (NM), 2.28 µB (CH) and 2.62 µB (STR). The CH and STR phases are 13 mRy and 20 mRy lower in total energy than NM, indicating that antiferromagnetic ordering is energetically favored for an isolated monolayer.

The calculated Fermi surfaces reveal distinct differences among the three phases. The NM surface resembles bulk FeSe, with three hole pockets at Γ and two electron pockets at the Brillouin‑zone corners (M). The STR surface also shows a hole pocket at Γ and electron‑like features displaced toward the Y direction, again similar to bulk. In contrast, the CH surface displays a single electron pocket at M and only small hole‑like features near Γ directed toward X. This topology matches angle‑resolved photoemission spectroscopy (ARPES) observations on FeSe monolayers, which report only an M‑centered electron pocket. The authors attribute this agreement to a “flat band” that lies just below the Fermi level (EF) in the CH configuration, producing a sharp peak in the density of states (DOS).

To explore the evolution from NM to AFM order, the authors impose constrained magnetic moments on the Fe atoms. As the imposed moment increases from 0 to 2.28 µB, the band structure undergoes a pronounced reconstruction: bands near Γ and M split, a flat band forms, and the DOS at EF rises sharply. Two types of magnetic perturbations are compared: (i) a uniform increase of the local moment on each Fe atom, and (ii) a transfer of magnetic moment from one Fe atom to its neighbor (moment redistribution). The latter produces band shifts up to an order of magnitude larger than the former, indicating that magnetic‑moment transfer couples more strongly to the electronic states than a simple uniform spin polarization. This suggests that magnetic fluctuations could provide a coupling strength far exceeding that of conventional phonons.

Charge doping is modeled by adding a uniform jellium background ranging from –0.5 e to +0.5 e per unit cell. In the CH phase, positive doping pushes EF into the flat‑band peak, dramatically increasing DOS, while negative doping creates a new electron pocket at Γ. The NM and STR phases respond mainly with a rigid shift of the entire band structure, but the CH phase shows a highly non‑rigid response, with the flat band’s width and position being especially sensitive to carrier concentration. In all cases, both electron and hole doping raise the DOS at EF, which the authors argue could enhance the superconducting transition temperature (Tc) by providing more electronic states for pairing.

The paper also discusses the possible role of the substrate. Prior experimental work has shown that SrTiO₃ can induce antiferromagnetic order at the FeSe interface. Since the CH antiferromagnetic pattern best reproduces the experimental Fermi surface, the authors suggest that substrate‑induced magnetic ordering may be a key factor in the high‑Tc behavior of FeSe monolayers. They further note that the presence of only an M‑centered electron pocket challenges the conventional s± pairing model, which relies on both electron and hole pockets, and may require revision to accommodate the observed electronic structure.

In summary, the study provides three major insights: (1) the checkerboard AFM spin configuration accurately captures the experimentally observed Fermi surface of FeSe monolayers; (2) constrained magnetization reveals that magnetic‑moment redistribution can induce large electronic‑structure shifts, implying strong electron‑magnetic‑fluctuation coupling; and (3) charge doping, both electron and hole, enhances the DOS at the Fermi level, offering a plausible route to higher Tc. These findings advance the understanding of the interplay between spin order, carrier concentration, and superconductivity in FeSe monolayers and suggest practical pathways—such as substrate engineering and controlled doping—to optimize their superconducting properties.