Figure 1: Fe L X-ray absorption spectrum (XAS) and RIXS spectra of BFA.

(a) Schematics of RIXS 130° back-scattering geometry with an included angle of 50° between the incoming and outgoing light vectors, k_i and k_f, respectively. The sample a-b plane lies perpendicular to the scattering plane. q_// is the projection of the momentum transfer q along the a-b plane. The incoming light is polarized either parallel (π) or perpendicular (σ) to the scattering plane with a grazing incident angle (θ). (b) Schematic view of the reciprocal space which can be covered by Fe L₃ RIXS shaded by a yellow circle. Γ,B and C in Fig. 1d are the reciprocal space positions at which RIXS spectra were collected. Black (blue) squares represent the tetragonal (orthorhombic) Brillouin zone (BZ). All RIXS spectra use the orthorhombic BZ convention for defining relative momentum transfer values. Γ point is the structural zone center, while ΓΜ is the AF ordering wave vector. (c) A representative Fe L XAS of BFA collected with π polarized incoming light at 15 K. The arrow denotes the fixed incident energy of the Fe L₃ resonance for all RIXS spectra. (d) Three typical RIXS spectra of BFA collected at 15 K with π polarized incoming light, at (q_x, q_y)=(0, 0) (Γ), (0.5, 0) (B) and (0.35, 0.35) (C) using relative lattice units. The relation (H, K)=(q_xa/2π, q_yb/2π) is adopted where a=5.62 Å and b=5.57 Å are the orthorhombic unit cell lattice parameters in the spin-density wave phase. (e) Zoom into the low-energy region of Fig. 1d.