Prominent Role of Spin-Orbit Coupling in FeSe Revealed by Inelastic Neutron Scattering

In most existing theories for iron-based superconductors, spin-orbit coupling (SOC) has been assumed to be insignificant. Here, we use spin-polarized inelastic neutron scattering to show that collective low-energy spin excitations in the orthorhombic (or “nematic”) phase of FeSe possess nearly no in-plane component. Such spin-space anisotropy is present over an energy range greater than the superconducting gap $2{\mathrm{\Delta }}_{\mathrm{sc}}$ and gets fully inherited in the superconducting state, resulting in a $c$-axis polarized “spin resonance” without any noticeable isotropic spectral-weight rearrangement related to the superconductivity, which is distinct from observations in the superconducting iron pnictides. The contrast between the strong suppression of long-range magnetic order in FeSe and the persisting large spin-space anisotropy, which cannot be explained microscopically by introducing single-ion anisotropy into local-moment spin models, demonstrates the importance of SOC in an itinerant-electron description of the low-energy spin excitations. Our result helps to elucidate the nearby magnetic instabilities and the debated interplay between spin and orbital degrees of freedom in FeSe. The prominent role of SOC also implies a possible unusual nature of the superconducting state.

Popular Summary

Superconductors are a material that, once cooled below a certain temperature, can conduct electricity with zero resistance. This remarkable effect has led to the development of powerful electromagnets and offers the promise of a range of applications from high-performance power transmission to levitating trains. Research into iron-based superconductors, a relatively new type of compound that contains layers of iron, is largely focused on developing a theory that can explain ubiquitous electronic behavior at the microscopic level. This requires researchers to correctly identify, based on experimental facts, all indispensable ingredients for the proper theory, such as the relevant degrees of freedom and interactions. As a tempting shortcut, the electrons’ spin and orbital degrees of freedom have been assumed in most theories to be largely independent. Here, we report on experimental results that challenge this assumption.

We use a spin-polarized, inelastic neutron-scattering experiment to study low-energy magnetic excitations in a sample of FeSe, the structurally simplest iron-based superconductor. The excitations are nearly 100% polarized along the $c$ axis (the longest axis in a crystal) whether or not the sample is in a superconducting state. This polarization can occur only in the presence of strong spin-orbit coupling. Our data also suggest that the formation of Cooper pairs (loosely bound pairs of electrons thought to be responsible for superconductivity) is actively influenced by the spin-orbit interactions.

These results suggest that entanglement between spin and orbital degrees of freedom is an indispensable ingredient in any proper microscopic theory for iron-based superconductors.

Figure 1

Crystal structure, FS topology, and characterization of phase transition temperatures in FeSe single crystals. (a) Crystal structure and FS topology [20], with orbital characters color coded with the orbital shapes. Three Brillouin zone notations are shown for comparison: 1-Fe unit cell (black solid lines), 2-Fe unit cell (magenta solid lines), and 4-Fe unit cell (dashed lines, used throughout our presentation). (b) Photograph of our INS sample before the final assembly. (c) dc magnetic susceptibility $\chi$ shows a sharp superconducting transition at $T_c=8.3\mathrm{K}$ in zero-field-cooled measurement in a magnetic field of $\mathrm{H}=10\mathrm{Oe}$ applied parallel to the $ab$ plane. A consistent transition is observed for the entire INS sample using depolarization effect on the neutron beam. (d) Resistivity $\rho$ shows an abrupt change in slope versus $T$ at the nematic transition temperature $T_s=88\mathrm{K}$, below which an abrupt increase in the (2,2,0) Bragg scattering intensity is observed due to reduced extinction effects.

Figure 2

Spin-polarized INS selection rules and predominant $M_c$ contribution to the magnetic signal. (a) Distribution of low-energy magnetic signals in momentum space. (b) Total spin fluctuations ($M_{\text{total}}$) and its three components, two of which can be detected by INS at $\mathbf{Q}=(1,0,0)$ with selection rules described in the text. (c) Momentum scans at fixed energies ($E$) along a trajectory shown in (a). (d) Energy scans at fixed $\mathbf{Q}=(1,0,0)$. Panels (c) and (d) share the same legends that indicate the three spin-flip channels. The two sets of symbols in (d) represent data obtained with different sample-environment devices. The BG intensity is determined from the selection rule: $\mathrm{BG}={\mathrm{SF}}_b+{\mathrm{SF}}_c-{\mathrm{SF}}_{\mathbf{Q}}$, taking all available data points into account (see Supplemental Material [21]). Shaded area in (d) indicates statistical uncertainty of our BG determination.

Figure 3

Evolution of different spin-fluctuation components with temperature. (a)–(c) Net magnetic signal components at $\mathbf{Q}=(1,0,0)$ at three different temperatures, obtained by subtracting the globally determined BG intensity (see Fig. 2 and Supplemental Material [21]) from ${\mathrm{SF}}_{\mathbf{Q}}$, ${\mathrm{SF}}_b$, and ${\mathrm{SF}}_c$ data, respectively. (d) Intensity change across $T_c$ measured in different geometries. The non-spin-flip scattering geometry with incoming neutron spin polarization along $c$ (${\mathrm{NSF}}_c$) measures spin fluctuations along the $c$ direction and confirms the spin-flip (${\mathrm{SF}}_b$) result. Solid lines are guides to the eye. The two sets of symbols in (a)–(c) for 10 K represent data obtained with different sample-environment devices (see Supplemental Material [21]).