Competition between stripe and checkerboard magnetic instabilities in Mn-doped BaFe${}_2$As${}_2$

Inelastic neutron scattering measurements on $\mathrm{Ba}{\left({\mathrm{Fe}}_{0.925}{\mathrm{Mn}}_{0.075}\right)}_2{\mathrm{As}}_2$ manifest spin fluctuations at two different wave vectors, ${\mathbf{Q}}_{\mathrm{stripe}}=(\frac{1}{2},\frac{1}{2},1)$ and ${\mathbf{Q}}_{\text{Néel}}=(1,0,1)$, corresponding to the expected stripe spin-density wave order and checkerboard antiferromagnetic order in the tetragonal $I4/mmm$ cell, respectively. Below $T_N=80$ K, long-range stripe magnetic ordering occurs and sharp spin wave excitations appear at ${\mathbf{Q}}_{\mathrm{stripe}}$ while broad and diffusive spin fluctuations remain at ${\mathbf{Q}}_{\text{Néel}}$ at all temperatures. Low concentrations of Mn dopants nucleate local moment spin fluctuations at ${\mathbf{Q}}_{\text{Néel}}$ that compete with itinerant spin fluctuations at ${\mathbf{Q}}_{\mathrm{stripe}}$ and may disrupt the development of superconductivity.

Figure 1

(a) Spin excitations in $\mathrm{Ba}{\left({\mathrm{Fe}}_{0.925}{\mathrm{Mn}}_{0.075}\right)}_2{\mathrm{As}}_2$ as measured on SEQUOIA with incident energy $E_{\mathrm{i}}=74.8$ meV and the crystallographic $\mathit{c}$ axis parallel to the incident beam. Data are displayed in the $(H+K,H-K)$ plane and averaged over an energy transfer of $E=$ 5–15 meV. Because of the fixed crystal orientation with incident beam, the $L$ component of the wave vector varies slightly with the in-plane wave vector and energy transfer. The indicated vectors are ${\mathbf{Q}}_{\mathrm{stripe}}=(\frac{1}{2},\frac{1}{2},L\approx 1)$ [$H=\frac{1}{2}$,$K=0$], ${\mathbf{Q}}_{\text{Néel}}=(1,0,L\approx 1)$ [$H=\frac{1}{2}$,$K=\frac{1}{2}$] in the coordinate system of the $I4/mmm$ tetragonal lattice. (b) A cut of the Mn-doped data (black symbols) and estimated phonon background (shaded symbols) along the $[K,-K]$-direction, as indicated by the dashed line in panel (a). (c) Spin excitations in $\mathrm{Ba}{\left({\mathrm{Fe}}_{0.926}{\mathrm{Co}}_{0.074}\right)}_2{\mathrm{As}}_2$ averaged over an energy transfer range of 5–15 meV as measured on the ARCS spectrometer with $E_{\mathrm{i}}=49.8$ meV and the $c$ axis parallel to the incident beam. (d) A cut of the Co-doped data (black symbols) and background (shaded symbols) along the $[K,-K]$-direction. In panels (a) and (c), an estimate of the instrumental background has been subtracted.

Figure 2

(a) Spin excitations in $\mathrm{Ba}{\left({\mathrm{Fe}}_{0.925}{\mathrm{Mn}}_{0.075}\right)}_2{\mathrm{As}}_2$ measured along $[1,0,L]$ at $T=10$ K on HB1A with $E=3$ meV, $E_{\mathrm{i}}=14.7$ meV, ${48}^{\prime }$-${40}^{\prime }$-${80}^{\prime }$-${136}^{\prime }$ horizontal collimation, and the sample mounted in the $\left[100\right]$-$\left[001\right]$ scattering plane. (b) Spectrum of spin excitations emanating from ${\mathbf{Q}}_{\text{Néel}}$ and ${\mathbf{Q}}_{\mathrm{stripe}}$ as measured on SEQUOIA after averaging over the range $H=0.50\pm 0.05$. (c) Energy spectrum at ${\mathbf{Q}}_{\text{Néel}}$ from SEQUOIA data after averaging over the Q region $K=-0.50\pm 0.05$, $H=0.50\pm 0.05$. The lines in panels (a) and (c) are a fit to a model of paramagnetic spin fluctuations as described in the text.

Figure 3

Spin excitations in $\mathrm{Ba}{\left({\mathrm{Fe}}_{0.925}{\mathrm{Mn}}_{0.075}\right)}_2{\mathrm{As}}_2$ measured on SEQUOIA at (a) 250 K, (b) 125 K, (c) 85 K, and (d) 6 K in a section of the $(H+K,H-K)$ plane after averaging over an energy transfer range of $10\pm 5$ meV, and (e) measured on HB3 along the $[K,-K]$ direction at several different temperatures (offset) and an energy transfer $E=7.5$ meV with $E_{\mathrm{f}}=30.5$ meV, collimation ${48}^{\prime }$-${60}^{\prime }$-${80}^{\prime }$-${120}^{\prime }$, and the sample mounted in the [112]-[1$\overline{1}$0] scattering plane. Lines in panel (e) are fits to a model of paramagnetic spin fluctuations as described in the text.

Figure 4

(a) ${\chi }^{\prime \prime }({\mathbf{Q}}_{\text{Néel}},E)$ measured at $E=3$ meV on HB1A (open symbols) and 7.5 meV on HB3 (closed symbols) as a function of temperature. (b) Temperature dependence of ${\chi }^{\prime \prime }({\mathbf{Q}}_{\mathrm{stripe}},E=7.5$ meV) (black circle symbols) as measured on HB3. The intensity of the magnetic Bragg peak at ${\mathbf{Q}}_{\mathrm{stripe}}=(\frac{1}{2},\frac{1}{2},1)$ (blue square symbols) indicates the development of stripe magnetic order below $T_{\text{N}}$. The dashed lines in panels (a) and (b) are guides to the eye.

Figure 5

Temperature dependence of the model parameters (a) ${\xi }_{\mathrm{N}}\left(T\right)$, (b) ${\xi }_{\mathrm{S}}\left(T\right)$, (c) ${\Gamma }_i\left(T\right)$, and (d) $\eta$ obtained by fitting the inelastic neutron scattering data. Blue square symbols correspond to parameters for ${\chi }_{\mathrm{N}}^{\prime \prime }$ and red diamond symbols for ${\chi }_{\mathrm{S}}^{\prime \prime }$. Closed symbols were determined from SEQUOIA data and open symbols from HB3 data. Lines in panels (a) and (b) correspond to fits to Eqs. (6) and (5), respectively. The lines in panel (c) correspond to those obtained after applying the scaling relation Eq. (4).