Magnetic Resonant Mode in the Low-Energy Spin-Excitation Spectrum of Superconducting ${\mathrm{Rb}}_2{\mathrm{Fe}}_4{\mathrm{Se}}_5$ Single Crystals

We have studied the low-energy spin-excitation spectrum of the single-crystalline ${\mathrm{Rb}}_2{\mathrm{Fe}}_4{\mathrm{Se}}_5$ superconductor ($T_c=32\mathrm{K}$) by means of inelastic neutron scattering. In the superconducting state, we observe a magnetic resonant mode centered at an energy of $\hslash {\omega }_{\mathrm{res}}=14\mathrm{meV}$ and at the (0.5 0.25 0.5) wave vector (unfolded Fe-sublattice notation), which differs from the ones characterizing magnetic resonant modes in other iron-based superconductors. Our finding suggests that the 245-iron selenides are unconventional superconductors with a sign-changing order parameter, in which bulk superconductivity coexists with the $\sqrt{5}\times \sqrt{5}$ magnetic superstructure. The estimated ratios of $\hslash {\omega }_{\mathrm{res}}/k_B{T}_c\approx 5.1\pm 0.4$ and $\hslash {\omega }_{\mathrm{res}}/2\Delta \approx 0.7\pm 0.1$, where $\Delta$ is the superconducting gap, indicate moderate pairing strength in this compound, similar to that in optimally doped 1111 and 122 pnictides.

Figure 1

The dc magnetic susceptibility measurements on three representative single-crystalline ${\mathrm{Rb}}_2{\mathrm{Fe}}_4{\mathrm{Se}}_5$ samples from the same batch. A sharp diamagnetic response is observed in the ZFC measurement right below 32 K, indicating $\sim 100\%$ exclusion of the external magnetic field.

Figure 2

(a) The in-plane projection of twinned magnetic and nuclear Bragg peak positions arising from the $\sqrt{5}\times \sqrt{5}$ Fe-vacancy superstructure. The two sets of dots and the corresponding dashed lines denote magnetic superstructure Bragg reflections and the magnetic BZ boundaries for the right and left twin domains, respectively. Black dotted lines represent the ${\mathrm{Fe}}_1$ unfolded BZ boundary. The arrow shows the trajectory of elastic momentum scans. (b) Elastic scans along the $K$ direction [arrow in (a) and equivalent scans] measured at 1.5 K. The almost identical neutron intensities of two symmetric magnetic Bragg peaks indicate the nearly equal population of the two twin domains in the sample. (c) INS intensity at 11.5 meV in the vicinity of the magnetic ordering wave vector $(1.30.10.5{)}_{{\mathrm{Fe}}_1}$. The intense spin-wave excitation peak is consistent with recent time-of-flight INS measurements on an insulating ${\mathrm{Rb}}_{2+\delta }{\mathrm{Fe}}_4{\mathrm{Se}}_5$ compound [26].

Figure 3

(a),(b) Raw energy scans measured in the SC (1.5 K) and normal (35 K) states at $\mathbf{Q}=(0.50.31250.5{)}_{{\mathrm{Fe}}_1}$ and $(0.500.5{)}_{{\mathrm{Fe}}_1}$, respectively. The inset in (a) shows the zoomed-in part of the resonant peak in the raw data. (c) Intensity difference between the SC state and the normal state at three $\mathbf{Q}$ vectors: $(0.50.250.5{)}_{{\mathrm{Fe}}_1}$, $(0.50.31250.5{)}_{{\mathrm{Fe}}_1}$, and $(0.50.50.5{)}_{{\mathrm{Fe}}_1}$. While there is no positive intensity at (0.5 0.5 0.5), a clear resonance peak (shaded region) is observed around 14 meV both at $(0.50.250.5{)}_{{\mathrm{Fe}}_1}$ and $(0.50.31250.5{)}_{{\mathrm{Fe}}_1}$. (d) The same plot as in (c) but for $\mathbf{Q}=(0.500.5{)}_{{\mathrm{Fe}}_1}$ and $(0.500{)}_{{\mathrm{Fe}}_1}$, where the magnetic resonant mode has been found in other Fe-based superconductors but is absent here. The base line in (c),(d) is the difference of the Bose factors. (e) Temperature dependence of the raw INS intensity at 14 meV and $\mathbf{Q}=(0.50.31250.5{)}_{{\mathrm{Fe}}_1}$ that demonstrates an order-parameter-like behavior with an onset at $T_c$. (f) Intensity difference of momentum scans along the BZ boundary, measured below and above $T_c$, with a maximum at the commensurate wave vector ${\mathbf{Q}}_{\mathrm{res}}=(0.50.250.5{)}_{{\mathrm{Fe}}_1}$. The solid line is a Gaussian fit with a linear background. Different symbols represent identical momentum scans measured in different experiments, rescaled to the (002) nuclear Bragg peak intensity. The position of the resonant mode predicted by Maier et al. [12] is shown by the arrow.

Figure 4

Normalized resonance energy, $\hslash {\omega }_{\mathrm{res}}/k_B{T}_c$, in Fe-based superconductors for $q_z=0$ and $q_z=\pi$ [29]. This ratio for RFS is slightly higher than for 122 compounds but comparable to 11-, 111-, and 1111-type superconductors.