Anisotropic Three-Dimensional Magnetism in ${\mathrm{CaFe}}_2{\mathrm{As}}_2$

Inelastic neutron scattering measurements of the magnetic excitations in ${\mathrm{CaFe}}_2{\mathrm{As}}_2$ indicate that the spin wave velocity in the Fe layers is exceptionally large and similar in magnitude to the cuprates. However, the spin wave velocity perpendicular to the layers is at least half as large that in the layer, so that the magnetism is more appropriately categorized as anisotropic three-dimensional, in contrast to the two-dimensional cuprates. Exchange constants derived from band structure calculations predict spin wave velocities that are consistent with the experimental data.

Figure 1

(a) The magnetic structure (showing Fe atoms only) and exchange interactions in ${\mathrm{CaFe}}_2{\mathrm{As}}_2$ [11]. (b) Schematic picture of an antiferromagnetic conical spin wave dispersion surface that is consistent with the data. The shaded plane indicates a constant-energy surface, and the shaded ellipses represent the orientation of the resolution ellipsoid for $H$ and $L$ scans. (c) Intensity as a function of neutron energy loss at $T=14\mathrm{K}$ at the magnetic zone center, ${\mathbf{Q}}_{\mathbf{A}\mathbf{F}\mathbf{M}}=(1,0,3)$. The solid black line shows fits to the data using the model dispersion [Eq. (1)] convoluted with the instrumental resolution function.

Figure 2

(a) Intensity along the $H$ direction near ${\mathbf{Q}}_{\mathbf{A}\mathbf{F}\mathbf{M}}=(1,0,3)$ at several different energies. Scans at different energies are vertically offset by 160 counts. (b) Constant-energy scans along $L$. In (a) and (b), the solid black lines are fits to the data using the model dispersion [Eq. (1)] convoluted with the instrumental resolution function. Dashed lines are estimates of the line shape at 25 meV that would result from an infinitely steep dispersion surface. (c) The plotted model dispersion along the ($H00$) direction (black line). (d) The model dispersion along the ($00L$) direction is plotted as a shaded region, indicating that the data only provide a lower bound on the spin wave velocity along $L$. In (c) and (d), fitted data points are indicated by black circles and lower bounds to the dispersion are indicated by vertical lines connected by a bar.