Antiferromagnetic spin excitations in single crystals of nonsuperconducting Li${}_{1-x}$FeAs

We use neutron scattering to determine spin excitations in single crystals of nonsuperconducting Li${}_{1-x}$FeAs throughout the Brillouin zone. Although angle resolved photoemission experiments and local density approximation calculations suggest poor Fermi surface nesting conditions for antiferromagnetic (AF) order, spin excitations in Li${}_{1-x}$FeAs occur at the AF wave vectors $Q=(1,0)$ at low energies, but move to wave vectors $Q=(\pm 0.5,\pm 0.5)$ near the zone boundary with a total magnetic bandwidth comparable to that of BaFe${}_2$As${}_2$. These results reveal that AF spin excitations still dominate the low-energy physics of these materials and suggest both itinerancy and strong electron-electron correlations are essential to understand the measured magnetic excitations.

Figure 1

(a) Fermi surfaces from the spin-restricted local density approximation calculation for LiFeAs.[18, 19] There are two hole-like Fermi surfaces near the $\Gamma (0,0)$ point with $d_{\mathit{yz}}$/$d_{\mathit{xz}}$ character and one electron-like Fermi surface near the $M(1,0)$ point. The nesting condition for the expected AF nesting wave vector $Q_{\mathrm{AFM}}=(1,0)$ is not favorable.[18] (b) Zero-field-cooled (ZFC) and field-cooled (FC) susceptibility measurements on Li${}_{0.94}$FeAs. No superconductivity was observed due to Li deficiency. (c,d) The dashed lines show spin wave dispersions along the $[H,0]$ and $[1,K]$ directions for BaFe${}_2$As${}_2$ at 5 K.[21] The filled circles show the measured spin excitation dispersions along the $[H,0]$ and $[1,K]$ directions for Li${}_{0.94}$FeAs. While spin waves in BaFe${}_2$As${}_2$ extend up to 200 meV along the $[1,K]$ direction, spin excitations in Li${}_{0.94}$FeAs reach the zone boundary near $Q=(1,0.5)$. (e) The energy dependence of the local susceptibility. The solid line is a guide to the eye.

Figure 2

Triple-axis measurements to search for static AF order and spin excitations in Li${}_{0.94}$FeAs. (a) Elastic scattering along the $[H,0,3]$ and (b) $[1,0,L]$ directions at 2 K show no evidence of AF order at the expected position $Q=(1,0,3)$. The arrows indicate Al sample holder scattering. (c) Constant-$Q$ scans at the wave vectors $Q=(1,0,3)$ (signal) and $Q=(0.4,0,3)$ (background) positions at 2 K. A clear spin gap is seen at $\Delta =13$meV. (d) Constant-energy scans at $E=9$, 16 meV along the $[H,0,3]$ direction. While the scan at $E=9$ meV is featureless, a clear peak is seen at $E=16$ meV confirming the spin gap. (e) Imaginary part of the dynamic susceptibility ${\chi }^{″}$ at 2 K and 190 K. The magnitude of the spin gap is unchanged between 2 and 190 K. (f) Temperature dependence of ${\chi }^{″}(Q)$ at $E=16$ meV for 2, 100, and 190 K. ${\chi }^{″}(Q)$ is almost temperature independent between 2 K and 190 K. Error bars where indicated represent one standard deviation.

Figure 3

Constant-energy images of the scattering in the $[H,K]$ zone as a function of increasing energy for Li${}_{0.94}$FeAs at energy transfers of (a) $E=25\pm 5$ meV; (b) $45\pm 5$ meV (with $E_i=80$ meV); (c) $70\pm 10$ meV; (d) $90\pm 10$ meV; (e) $110\pm 10$ meV; (f) $130\pm 10$ meV; (g) $150\pm 10$ meV; (h) $170\pm 10$ meV, all with $E_i=250$ meV. The scattering intensity is in absolute units. The box in (b) shows the Brillouin zone used to integrate the susceptibility.

Figure 4

Constant-energy cuts of the spin excitation dispersion as a function of increasing energy along the $[H,0]$ and $[1,K]$ directions for Li${}_{0.94}$FeAs. The dashed curves show identical cuts for spin waves of BaFe${}_2$As${}_2$ normalized per Fe.[21] Both are in absolute units. Constant-energy cuts along the $[H,0]$ direction at (a) $55\pm 5$, (b) $75\pm 5$, (c) $95\pm 10$, and (d) $135\pm 10$ meV. Similar cuts along the $[1,K,]$ direction are shown in (e)–(h). The dynamic spin correlation length is $\xi \approx 12\pm 3$ Å.