Low Energy Spin Waves and Magnetic Interactions in ${\mathrm{SrFe}}_2{\mathrm{As}}_2$

We report inelastic neutron scattering studies of magnetic excitations in antiferromagnetically ordered ${\mathrm{SrFe}}_2{\mathrm{As}}_2$ ($T_N=200–220\mathrm{K}$), the parent compound of the FeAs-based superconductors. At low temperatures ($T=7\mathrm{K}$), the magnetic spectrum $S(Q,\hslash \omega )$ consists of a Bragg peak at the elastic position ($\hslash \omega =0\mathrm{meV}$), a spin gap ($\Delta \le 6.5\mathrm{meV}$), and sharp spin-wave excitations at higher energies. Based on the observed dispersion relation, we estimate the effective magnetic exchange coupling using a Heisenberg model. On warming across $T_N$, the low-temperature spin gap rapidly closes, with weak critical scattering and spin-spin correlations in the paramagnetic state. The antiferromagnetic order in ${\mathrm{SrFe}}_2{\mathrm{As}}_2$ is therefore consistent with a first order phase transition, similar to the structural lattice distortion.

Figure 1

(a) The Fe spin ordering in the ${\mathrm{SrFe}}_2{\mathrm{As}}_2$ chemical unit cell and magnetic exchange couplings along different high-symmetry directions. (b) The AF Néel temperature and the temperature dependence of the structural (2, 2, 0) Bragg peak for one of the ${\mathrm{SrFe}}_2{\mathrm{Sr}}_2$ crystals used in the experiment 15. The inset shows positions in reciprocal space probed in the experiment. (c) Observed spin-wave dispersion along the [$H$, 0, 0] direction at 160 K. (d) Similar dispersion along the [0, 0, $L$] direction. (e) Calculated three-dimensional spin-wave dispersions using $J_{1a}=20$, $J_{1b}=10$, $J_2=40$, $J_z=5$, and $J_s=0.015\mathrm{meV}$. (f) Temperature dependence of the anisotropy spin gap $\Delta (T)$.

Figure 2

Wave vector dependence of the spin-wave excitations at 160 K obtained on cold [(a) and (e)] and thermal [(b)–(d) and (f)–(h)] triple-axis spectrometers at different energies. (a) $Q$ scan along the [$H$, 0, 1] direction at $\hslash \omega =1\mathrm{meV}$ using SPINS. The spectrum is featureless indicating the presence of a spin gap exceeding 1 meV. Identical scan at $\hslash \omega =5\mathrm{meV}$ in (e) shows clear evidence of spin-wave excitations centered at (1, 0, 1). (b–d) $Q$ scans along the [$H$, 0, 1] or [$H$, 0, 3] directions at different energies. The spectra clearly broaden with increasing energy. (f–h) Similar scans along the [1, 0, $L$] direction, which probe the exchange coupling $J_z$.

Figure 3

Temperature dependence of the spin gap obtained from energy scans around the (1,0,1) and (1,0,3) Bragg peaks. (a) Low-temperature ($T=7\mathrm{K}$) constant-$Q$ scans at the signal [$Q=(1,0,1)$] and background [$Q=(1.2,0,1)$] positions show a clear spingap of $\Delta =6.5\mathrm{meV}$. (b) Similar scans at $Q=(1,0,3)$ and $Q=(0.8,0,3)$ which again show $\Delta =6.5\mathrm{meV}$. (c), (d) Temperature dependence of the spin gap, where $\Delta =4.5\mathrm{meV}$ at 80 K and $\Delta =3.5\mathrm{meV}$ at 160 K.

Figure 4

Temperature dependence of the quasielastic magnetic scattering and spin-wave excitations below and above $T_N$. Data in (a)–(c) are obtained on SPINS. (a) Constant-$Q$ scans at the $Q=(1,0,1)$ Bragg peak position at different temperatures. Except for the dramatic increase in the elastic component below $T_N$, the quasielastic scattering above $\hslash \omega =0.5\mathrm{meV}$ is essentially temperature independent, revealing no evidence for the Lorentzian-like paramagnetic scattering above $T_N$ observed in Cr [20]. (b) Temperature difference spectra using $T=280\mathrm{K}$ scattering as background. The data again show little evidence of critical scattering at $\hslash \omega =1\mathrm{meV}$. (c) $Q$ scans at $\hslash \omega =1\mathrm{meV}$ at different temperatures. We speculate that the slight increase in overall scattering at 240 K from 280 K shown in (e) is due to weakly correlated paramagnetic spins. (d) $\hslash \omega =10\mathrm{meV}$ spin-wave excitations at 160 and 200 K obtained on BT-7. (f) $\hslash \omega =16\mathrm{meV}$ spin-wave excitations at 7 and 160 K obtained on HB-1. The intensity increase is due to the Bose population factor.