Neutron scattering studies of spin excitations in superconducting Rb${}_{0.82}$Fe${}_{1.68}$Se${}_2$

We use inelastic neutron scattering to show that superconducting (SC) rubidium iron selenide Rb${}_{0.82}$Fe${}_{1.68}$Se${}_2$ exhibits antiferromagnetic (AF) spin excitations near the in-plane wave vector $Q=(\pi ,0)$ identical to that for iron arsenide superconductors. Moreover, we find that these excitations change from incommensurate to commensurate with increasing energy and occur at the expense of spin waves associated with the coexisting $\sqrt{5}\times \sqrt{5}$ block AF phase. Since these spin excitations cannot come from Fermi surface nesting based on angle resolved photoemission experiments, our results indicate the presence of local moments in SC Rb${}_{0.82}$Fe${}_{1.68}$Se${}_2$ that may have a similar origin as the hourglass-like spin excitations in copper oxide superconductors.

Figure 1

(a) The block AF order of the insulating $A_y$Fe${}_{1.6+x}$Se${}_2$, where the $\sqrt{5}\times \sqrt{5}$ superlattice structure is marked as gray with lattice parameter $a_s=8.663$ Å and the orthorhombic lattice cell is shaded green.[29] (b) The reciprocal space in the $[H_o,K_o]$ plane, where the red circles indicate the AF Bragg peak positions. (c) Schematics of the Fermi surfaces of the SC $A_y$Fe${}_{1.6+x}$Se${}_2$. There are four large electron pockets at $Q=(\pm 1,0)/(0,\pm 1)$ and a small electron pocket at $\Gamma (0,0)$.[22, 23, 24] The neutron spin resonance should originate from the electron-electron pocket excitations.[27, 28] The green arrow indicates the $\Gamma \leftrightarrow M$ transition. (d) Positions of observed spin excitations in the SC Rb${}_{0.82}$Fe${}_{1.68}$Se${}_2$, where spin waves from the block AF phase, neutron spin resonance, and $(\pi ,0)$ excitations are marked as red solid circles, purple ellipses, and light-blue cross shapes, respectively. (e) Integrated intensity comparison of several samples at $E=14\pm 2$ meV. Olive green: spin waves in the insulating Rb${}_{0.89}$Fe${}_{1.58}$Se${}_2$; Dark red, light blue, and light violet are spin waves, $(\pi ,0)$ excitations, and resonance in SC Rb${}_{0.82}$Fe${}_{1.68}$Se${}_2$; Orange: spin wave in BaFe${}_2$As${}_2$. (f) Susceptibility measurement indicates $T_c=32$ K.

Figure 2

(a,c,e,g) Wave-vector dependence of spin-wave excitations at different energies for the NSC Rb${}_{0.89}$Fe${}_{1.58}$Se${}_2$ at 10 K obtained with incident neutron energy of $E_i=80$ meV.[29] (b,d,f,h) Identical images for the SC Rb${}_{0.82}$Fe${}_{1.68}$Se${}_2$ at 6 K. The red squares are the Brillouin zone for iron pnictides.[35] The vertical color bars indicate intensity scale in mbarns/sr/meV/f.u.

Figure 3

(a–d) Expanded view of the excitations near $Q=(1,0)$. The data in (b,c) are collected with $E_i=35$ meV, while (a,d) are taken with $E_i=80$ meV. The dashed ellipses in (b) mark positions of the resonance.

Figure 4

Constant energy cuts of data described in the legend of Fig. 2 converted into units of magnetic response ${\chi }^{\prime \prime }(Q,\omega )$ (after subtracting constant backgrounds and correcting for the Bose factor.) for the SC Rb${}_{0.82}$Fe${}_{1.68}$Se${}_2$ and insulating Rb${}_{0.89}$Fe${}_{1.58}$Se${}_2$. (a) Along the incommensurate positions at $E=8\pm 2$ meV, (c) along the commensurate positions at $E=14\pm 2$ meV, and (e) along the commensurate positions at $E=30\pm 2$ meV. Temperature dependence of ${\chi }^{\prime \prime }(Q,\omega )$ for spin waves from the $\sqrt{5}\times \sqrt{5}$ AF block phase at 6, 35, and 250 K with spin-wave energies of (b) $E=12\pm 2$, (d) $20\pm 2$, and (f) $34\pm 2$ meV.

Figure 5

Cuts of ${\chi }^{\prime \prime }(Q,\omega )$ along (a) the $[-0.8\pm 0.1,K]$, (c,e) $[-1\pm 0.1,K]$ directions for the $Q=(-1,0)$ excitations at different temperatures. (b,d,f) Comparison of the low-temperature spin wave intensities for SC and insulating samples using the same cuts along the $[-0.6\pm 0.1,K]$ direction. The spin wave intensity of the SC sample are lower at (b) $E=12\pm 2$ and (d) $20\pm 2$ meV but become similar as that of the insulating sample at (f) $E=34\pm 2$ meV. (g) The black squares are the ratio of spin-wave intensity in the yellow area for SC and insulating samples. The orange circles are the ratio of excitations in (h) yellow area + green area for SC and insulating samples.

Figure 6

(a) Energy cut at the resonance position by integrating $Q=(-0.5\pm 0.1,1\pm 0.1)$. (b) 6 K–35 K data shows a resonance at $E=14$ meV with solid curve guides to the eye. The horizontal bar is the instrumental energy resolution. (c,e) Constant-energy cuts along the $[H,1\pm 0.1]$ and $[0.5\pm 0.1,K]$ directions, respectively. (d,f) 6–35 K data confirm the resonance peak at $(1,-0.5)$ with a width $FWHM=0.13\pm 0.04$ along the $H$ direction and $FWHM=0.20\pm 0.05$ along the $K$ direction. The black curves are Gaussian fits to the peaks in (d,f).