Three-dimensional spin susceptibility in Ba$_{0.75}$K$_{0.25}$Fe$_{2}$As$_{2}$: Out-of-plane modulation revealed by neutron spectroscopy and theoretical modeling

TL;DR

This study combines neutron spectroscopy and theoretical modeling to reveal the three-dimensional spin fluctuations and their energy-dependent crossover to two-dimensionality in Ba$_{0.75}$K$_{0.25}$Fe$_2$As$_2$, highlighting the importance of out-of-plane interactions.

Contribution

It provides a detailed 3D electronic and magnetic model that accurately reproduces experimental spin susceptibility features, emphasizing the role of states away from the Fermi level.

Findings

Out-of-plane spin modulation diminishes with increasing energy.

The DFT-based model reproduces the observed susceptibility peak at $f{q}_{ ext{AFM}}$.

Electronic states away from the Fermi level influence the out-of-plane AFM instability.

Abstract

We present a combined experimental and theoretical investigation of the spin dynamics in the iron-based superconductor Ba$_{0.75}$K$_{0.25}$Fe$_2$As$_2$. Time-of-flight inelastic neutron scattering measurements reveal the three-dimensional (3D) nature of the spin fluctuations, manifested as out-of-plane modulations of the low-energy magnetic intensity. As the energy increases, this 3D-like modulation gradually fades away, leading to a more two-dimensional (2D) profile -- a clear signature of a 3D-to-2D crossover in the spin dynamics. By incorporating a realistic 3D electronic band structure derived from density functional theory (DFT), we reproduce the experimentally observed features of the spin susceptibility, including the pronounced out-of-plane modulation at low energies and its gradual evolution into a more 2D character at higher energies. The calculated susceptibility exhibits a peak at the experimental ordering wavevector $\mathbf{q}_{\mathrm{AFM}} = (0.5, 0.5, 1)$, demonstrating that the DFT-derived 3D model accurately captures the tendency toward out-of-plane antiferromagnetic (AFM) order. Notably, electronic states away from the Fermi level play a crucial role in shaping the susceptibility peak at $\mathbf{q}_{\mathrm{AFM}}$, highlighting the limitations of the Fermi surface nesting picture in explaining the out-of-plane AFM instability. The demonstrated agreement between experiment and theory serves as a benchmark for validating the DFT-derived model as a realistic description of the material-specific electronic structure.