Disorder-induced damping of spin excitations in Cr-doped BaFe$_2$As$_2$

Abstract

In doped Hund's metals, such as the iron-based superconductors, effects like charge doping and chemical pressure are often considered the dominant factors. Partial chemical substitution, however, inevitably introduces disorder. Here, we investigate spin excitations in Ba(Fe$_{1-x}$Cr$_x$)$_2$As$_{2}$ (CrBFA) by high-resolution resonant inelastic x-ray scattering (RIXS) for samples with $x = 0, 0.035,$ and $ 0.085$. In CrBFA, Cr acts as a hole dopant, but also introduces localized spins that compete with Fe-derived magnetic excitations. We found that the Fe-derived magnetic excitations are softened and damped, becoming overdamped for $x = 0.085$. At this doping level, complementary angle-resolved photoemission spectroscopy measurements (ARPES) show increased electronic localization and a suppression of the nematic $d_{xz}/d_{yz}$ band splitting present in the parent compound. We thus propose a localized spin model that explicitly incorporates substitutional disorder and Cr local moments, successfully reproducing our key observations. Our findings reveal a case where disorder dominates over charge doping in the case of a Hund's metal.

Figures (16)

• Figure 1: Overview of RIXS results. (a) 2D magnetic lattice with the stripe order. The green and magenta dashed squares show the PM and the AFM phases' unit cells. (b) The respective reciprocal spaces for the 2D first Brillouin zones, the circle indicates the probed $\mathbf{q}$-range, with the dashed lines showing the high-symmetry directions for the RIXS experiments. The 1Fe BZ (black square) is used for the theory. (c)-(h) Momentum-dependent RIXS spectra for the samples with $x = 0, 0.035$ and $0.085$ (BFA, Cr$3.5\%$, and Cr$8.5\%$) and for different directions after background subtraction. The data are shifted for better comparison.
• Figure 2: (a) Polarization-dependent RIXS spectrum of the parent compound (BFA) measured at $|\mathbf{q}| = 0.56$ r.l.u.. (b,c) Representative fits of the quasi-elastic and magnon contributions at maximum momentum transfer for the BFA and Cr$3.5\%$ samples, respectively. (d) Peak energy of the magnetic excitation $\omega_\text{peak}$, (e) bare frequency $\omega_0$, and (f) damping coefficient $\gamma$ as functions of momentum, for different samples and high-symmetry directions. In panel (e), the solid line shows the linear spin wave dispersion at $L = 0$, using parameters from inelastic neutron scattering fits harriger_nematic_2011. The shaded area indicates the dispersion variation with $L$, considering the 3D Brillouin zone.
• Figure 3: ARPES band maps second derivatives at paramagnetic and ordered phases for (a) BFA and (b) Cr$8.5\%$ samples. The transition temperatures are $T=134$ and $T=79$ K, respectively. The minimum of the second derivatives denotes the Lorentzian-shaped bands' maximum position.
• Figure 4: (a,b) Calculated dynamical structure factor of the $J_1$–$J_2$ XXZ model for different doping levels ($x$). Insets show the RIXS probed region. The magenta dashed line marks the spin-wave dispersion for $x=0$. (c) Structure factor at $\mathbf{q}=\bar{Y}$ for different $x$. (d) Experimental magnon at $\mathbf{q}\approx (0.5,0)=\bar{X}/\bar{Y}$ for varying $x$ after elastic and phonon contributions subtraction. RIXS momentum maps for (e) BFA and (f) Cr$8.5\%$. Black dots are fitted $\omega_\text{peak}$, as in Fig. \ref{['fig:dispersion']}(d).
• Figure S1: MC samples $\textrm{C}_{S}(0)$ for two cases: (a) $x=5\%$ and (b) $x=15\%$. Circles around spins represent sites where Fe were substituted by Cr. The transverse components $S^{z}_{i}$ are omitted, these are always very small compared to the inplane components $S^{\space x,y}_{i}$ which define the vectors in the figure colored accordingly to the inset 4-color disk.