Two-dimensional magnetic interactions in LaFeAsO

Inelastic neutron scattering measurements demonstrate that the magnetic interactions in antiferromagnetic LaFeAsO are two dimensional. Spin-wave velocities within the Fe layer and the magnitude of the spin gap are similar to the $A$Fe${}_2$As${}_2$ based materials. However, the ratio of interlayer and intralayer exchange is found to be less than $\sim {10}^{-4}$ in LaFeAsO, very similar to the cuprates, and $\sim$100 times smaller than that found in $A$Fe${}_2$As${}_2$ compounds. The results suggest that the effective dimensionality of the magnetic system is highly variable in the parent compounds of the iron arsenides and weak three-dimensional interactions may limit the maximum attainable superconducting $T_c$.

Figure 1

(a) Longitudinal and (b) transverse cuts through the inelastic neutron scattering spectrum of LaFeAsO at $T=5$ K as measured on the MERLIN spectrometer with $E_i=$150 meV after background subtraction (see text). (c) Data averaged over an energy transfer range from 35–75 meV showing anisotropic spin fluctuations in the $H-K$ plane centered at ${\mathbf{Q}}_{\text{AFM}}$. (d) Energy spectra at different average $K$ values along the transverse direction; 0, 0.1, and 0.15. Lines shown are fits described in the text. In these panels, the $L$ component of the wave vector varies with the in-plane wave vector and energy transfer because of the fixed crystal orientation with respect to the incident beam direction.

Figure 2

Measurements of the low-energy spin excitations in LaFeAsO at $T=5$ K as measured on HB3. Energy dependence of the magnetic scattering at (a) ${\mathbf{Q}}_{\text{AFM}}=$ (1,0,1/2) and (b) magnetic zone boundary position ${\mathbf{Q}}_{\text{ZB}}=(1,0,1)$. Constant energy scans depicting the $L$ dependence of the magnetic scattering along (1,0,$L$) (c) at gap onset at 5.5 meV, and (d) above the gap at 10 meV. Lines are fits to a damped spin-wave model as described in the text. Panels (c) and (d) and the two insets in panels (a) and (b) show the raw data (green squares) and background scans (crystal rotated from nominal $\mathbf{Q}$ by 20${}^{\circ }$, black diamonds) that were used to estimate the magnetic scattering (red symbols) in (a)–(d). The arrows in these panels are indicating the onset value of the energy gap.

Figure 3

Longitudinal cuts of the low-energy spin excitations in LaFeAsO at $T=$ 5 K as measured on HB3. Data are shown (a) at the onset of the gap at $E=$ 5.5 meV and ${\mathbf{Q}}_{\text{AFM}}=(1,0,1/2)$, (b) at 5.5 meV and ${\mathbf{Q}}_{\text{ZB}}=(1,0,1)$, (c) at 10 meV and ${\mathbf{Q}}_{\text{AFM}}$, and (d) at 10 meV and ${\mathbf{Q}}_{\text{ZB}}$. Lines show the fits to the damped spin-wave model, described in the text, with only a free amplitude and background. The rest of the parameters are fixed to the values given in Table . The quality of the agreement between data and the model is also a confirmation of the results.

Figure 4

Longitudinal (left) and transverse (right) constant energy cuts of the magnetic scattering in LaFeAsO up to 75 meV as measured on MERLIN. Global (blue line) and local (red line) fits to the damped spin-wave model described in the text are shown. The shoulders in the tails of transverse $E=$75 meV cut fit is due to the effect of the twinning of orthorhombic cyrstal, which is included in the model calculations. For these cuts, the $L$ component of the wave vector is a function of the in-plane momentum vectors and the energy transfer, as explained earlier.