Similar zone-center gaps in the low-energy spin-wave spectra of Na${}_{1-\delta }$FeAs and BaFe${}_2$As${}_2$

We report results of inelastic-neutron-scattering measurements of low-energy spin-wave excitations in two structurally distinct families of iron-pnictide parent compounds: Na${}_{1-\delta }$FeAs and BaFe${}_2$As${}_2$. Despite their very different values of the ordered magnetic moment and Néel temperatures, $T_{\mathrm{N}}$, in the antiferromagnetic state both compounds exhibit similar spin gaps of the order of 10 meV at the magnetic Brillouin-zone center. The gap opens sharply below $T_{\mathrm{N}}$, with no signatures of a precursor gap at temperatures between the orthorhombic and magnetic phase transitions in Na${}_{1-\delta }$FeAs. We also find a relatively weak dispersion of the spin-wave gap in BaFe${}_2$As${}_2$ along the out-of-plane momentum component, $q_z$. At the magnetic zone boundary ($q_z=0$), spin excitations in the ordered state persist down to $\sim$20 meV, which implies a much smaller value of the effective out-of-plane exchange interaction, $J_{\mathrm{c}}$, as compared to previous estimates based on fitting the high-energy spin-wave dispersion to a Heisenberg-type model.

Figure 1

Determination of the structural and AFM transition temperatures in Na${}_{0.9}$FeAs from (a) magnetization measurements, (b) magnetic Bragg intensity, and (c) nuclear Bragg intensity. Magnetic susceptibility data in the inset of panel (a) show the SC transition.

Figure 2

Typical unprocessed constant-energy scans for Na${}_{0.9}$FeAs (left) and BaFe${}_2$As${}_2$ (right), measured above and below $T_{\mathrm{N}}$ along the $\left|\mathbf{Q}\right|=\text{const}$ trajectories in momentum space, centered at $\left(\frac{1}{0.8pt2}0L\right)$. The values of $L$ at the center of the scan and the energy transfer are indicated in every panel.

Figure 3

Temperature dependence of the background-subtracted low-energy INS signal in Na${}_{0.9}$FeAs (left) and BaFe${}_2$As${}_2$ (right), indicating the abrupt spin-gap opening below $T_{\mathrm{N}}$. Solid lines are guides to the eyes. Note the absence of any pronounced anomaly at the structural phase transition in Na${}_{0.9}$FeAs ($T_{\mathrm{s}}=57$ K).

Figure 4

Energy dependence of the background-subtracted magnetic INS intensity for Na${}_{0.9}$FeAs (left) and BaFe${}_2$As${}_2$ (right), measured above and below $T_{\mathrm{N}}$: (a), (b) at the ordering wave vector ($L=3/2$) and (c) at the magnetic zone boundary ($L=1,2$).