Figure 1

(a) Projection of the real-space crystal structure onto the $\mathit{ab}$ plane, with As atoms omitted for clarity. The solid (black) square is the unit cell of the Fe sublattice, the dashed (blue) square is the orthorhombic unit cell (space group $\mathit{Fmmm}$), and the dotted (red) diamond is the tetragonal $I4/\mathit{mmm}$ unit cell. (b) Corresponding Brillouin zones. Referring to the Fe sublattice, the standard square-lattice symmetry points are $\Gamma =(0,0)$, $X=(0.5,0)$, and $M=(0.5,0.5)$, and $X$ is the AFM ordering wave vector. The arrows labeled $\alpha$ and $\beta$ indicate the direction of one-dimensional (1D) cuts and 2D slices shown in Figs. 2 and 3.Reuse & Permissions

Figure 2

Energy–wave-vector slices through the INS datasets at (a) $T=6$ K, (b) $T=212$ K, and (c) $T=300$ K. Panels (d) and (e) show simulations of the spectrum over the same $\mathbf{Q}$ and energy range using a local-moment spin-wave model with $J_{1a}\ne J_{1b}$, $J_{1b}<0$, and $J_{1a}=J_{1b}$, respectively. Panels (f) and (g) show the calculated $\chi {}^{″}(\mathbf{Q},E)$ for the AFM phase and the paramagnetic phase, respectively; both taken from Ref. 27, and convoluted with the instrumental resolution, with the energy rescaled by a factor 0.85. Data are from the run with $E_{\mathrm{i}}=450$ meV, and the intensity of both data and simulations have been multiplied by $E$ to improve clarity. The Fe form factor has been included in the simulations. Dashed lines in panels (d) and (e) indicate the simulated dispersion relations for the high-energy parameters (see caption to Fig. 3) and for $J_{1a}=J_{1b}$, respectively. Dashed lines in panels (f) and (g) are the loci of maximum intensity for the calculated $\chi {}^{″}(\mathbf{Q},E)$. (The calculated low-energy incommensurate behavior in (g) is discussed in Ref. 27 and likely arises from limitations of the model. See text for further discussion of this point.)Reuse & Permissions

Figure 3

Wave-vector cuts through the data taken at $T=6$ K with incident neutron energies (c) $E_{\mathrm{i}}=180$ meV; and (a), (b), and (d) $E_{\mathrm{i}}=450$ meV. Solid (red) and dashed (blue) lines are calculated from fits to the local-moment $J_{1a}-J_{1b}-J_2$ model with the low-energy and high-energy best-fit parameters, respectively. For lower energies best fits were obtained with $S_{\mathrm{eff}}=0.30\pm 0.01$, ${\mathit{SJ}}_{1a}=30.8\pm 1$ meV, ${\mathit{SJ}}_{1b}=-5\pm 5$ meV, ${\mathit{SJ}}_2=21.7\pm 0.4$ meV, and ${\mathit{SJ}}_c=2.3\pm 0.1$ meV. This is in contrast to higher energies, where we found $S_{\mathrm{eff}}=0.69\pm 0.02$, ${\mathit{SJ}}_{1a}=38.7\pm 2$ meV, ${\mathit{SJ}}_{1b}=-5\pm 5$ meV, and ${\mathit{SJ}}_2=27.3\pm 0.7$ meV. ${\mathit{SJ}}_c$ cannot be determined from cuts taken above the maximum of the dispersion along $(0,0,L)$ of $~$$53$ meV. Dotted (black) lines indicate the estimated nonmagnetic scattering at $\mathbf{Q}=(1,0)$.Reuse & Permissions

Figure 4

Energy cuts at constant in-plane $\mathbf{Q}$ through the data taken with $E_{\mathrm{i}}=450$ meV. The left-hand panels show data at $T=6$ K, with (a) $\mathbf{Q}=(0.5,0.15)$ and (d) $\mathbf{Q}=(0.5,0.5)$. The middle panels (b) and (e) show data at $T=212$ K at the same two wave vectors. The right-hand panels (c) and (f) show data at $T=300$ K, also at the same two wave vectors. Solid (red) and dashed (blue) lines are calculated from the low-energy and high-energy fit parameters, respectively. The dotted (black) lines indicate the background, which is zero here because the nonmagnetic background signal from $\mathbf{Q}=(1,0)$ has been subtracted from these data for clarity. The calculations for different temperatures differ only in the damping fitted—the exchange parameters are the same for all six cuts.Reuse & Permissions