Researchers from PSI’s Quantum Materials Spectroscopy group and scientists from Beijing Normal University have solved a riddle at the forefront of iron-based superconductor research: the origin of FeSe’s electronic nematicity. Using resonant inelastic x-ray scattering (RIXS) at the Swiss Light Source (SLS), they surprisingly found that this electronic phenomenon is primarily spin-driven. Electronic nematicity is thought to be an important ingredient of high-temperature superconductivity, but whether it helps or hinders it is still unclear. Their findings are published in Natural Physics.
Near PSI, where the Swiss forest is ubiquitous in people’s lives, you often see piles of logs: incredibly neat piles of logs. Wedge-shaped logs for firewood are neatly stacked lengthwise, but without thinking about their rotation. When particles of a material spontaneously align themselves, like the logs in these piles of logs, so that they break rotational symmetry but preserve translational symmetry, a material is said to be in a nematic state. In a liquid crystal, this means that rod-shaped molecules can flow like a liquid in the direction of their alignment, but not in other directions. Electronic nematicity occurs when electron orbitals in a material align in this way. Typically, this electronic nematicity is manifested by anisotropic electronic properties: for example, resistivity or conductivity exhibiting very different amplitudes when measured along different axes.
Since their discovery in 2008, the last decade has seen enormous interest in the family of iron-based superconductors. Alongside the well-studied cuprate superconductors, these materials exhibit the mysterious phenomenon of high-temperature superconductivity. The electronic nematic state is a ubiquitous feature of iron-based superconductors. However, until now, the physical origin of this electronic nematicity is an enigma; in fact, arguably one of the most important puzzles in the study of iron-based superconductors.
But why is electronic nematicity so interesting? The answer lies in the ever-exciting puzzle: understanding how electrons pair up and achieve high-temperature superconductivity. The histories of electronic nematicity and superconductivity are inextricably linked – but how exactly, and even whether they compete or cooperate, is a hotly debated question.
The desire to understand electronic nematicity led researchers to focus their attention on a particular iron-based superconductor, iron selenide (FeSe). FeSe is something of an enigma, possessing both the simplest crystal structure of any iron-based superconductor and the most puzzling electronic properties.
FeSe enters its superconducting phase below a critical temperature (Tvs) of 9 K but tantalizingly has a tunable Tvs, which means that this temperature can be increased by pressure or doping of the material. The quasi-2D layered material has an extended electronic nematic phase, which appears below about 90 K. Curiously, this electronic nematicity appears without the long-range magnetic ordering it would typically go with, leading to lively debate about its origins. : namely, whether these are driven by orbital or spin degrees of freedom. The absence of long-range magnetic order in FeSe gives the opportunity to have a clearer view of electronic nematicity and its interaction with superconductivity. As a result, many researchers believe that FeSe may hold the key to understanding the puzzle of electronic nematicity in the family of iron-based superconductors.
Measuring spin excitation anisotropies with resonant inelastic X-ray scattering (RIXS)
To determine the origin of the electronic nematicity of FeSe, scientists from the Quantum Materials Spectroscopy group at PSI turned to the technique of resonant inelastic X-ray scattering (RIXS) on the ADRESS beamline of the Swiss light source (SLS). Combining the principles of X-ray absorption and emission spectroscopy, this technique is a very effective tool for exploring the magnetic or spin excitations of a material.
“At PSI, we have one of the most advanced facilities for RIXS in the world. Among the first to push this technique 15 years ago, we have now implemented a very well developed facility for this type of experiments” , says Thorsten Schmitt, who led the study with Xingye Lu of Beijing Normal University. “In particular, the synchrotron radiation characteristics due to the design of the SLS ring are ideal for the soft X-ray range in which these experiments were performed.”
To study the spin anisotropies of FeSe using RIXS, scientists first had to overcome a practical hurdle. In order to measure the anisotropic nematic behavior, the sample first had to be “untwinned”. Twinning occurs when crystals in stacked layers are aligned with equal probability in arbitrary directions, thereby obscuring any information about anisotropic behavior. Unpairing is a common crystallographic sample preparation technique, in which pressure is typically applied to the sample, which causes the crystals to align along structural directions.
For FeSe it doesn’t work. Apply that pressure to FeSe and the soft material simply deforms – or breaks. Therefore, the team used an indirect detwinning method, whereby FeSe is bonded to a material that can be unpacked: iron barium arsenide (BaFe2Like2). “When we apply uniaxial pressure to BaFe2Like2this generates a strain of about 0.36%, which is just enough to untangle FeSe at the same time,” says Xingye Lu, who had previously demonstrated its feasibility with Tong Chen and Pengcheng Dai of Rice University for studies of FeSe with inelastic neutrons. diffusion.
Inelastic neutron scattering experiments had revealed spin anisotropies in FeSe at low energy; but the measure of high– energetic spin excitations were essential to link these spin fluctuations to electronic nematicity. Measuring spin excitations at an energy scale of about 200 meV – well above the energy separation between orbital energy levels – would rule out orbital degrees of freedom as a source of electronic nematicity . With the successful unpairing, the researchers were able to probe the crucial high-energy spin excitations of FeSe, as well as BaFe2Like2using RIXS.
The researchers studied the spin anisotropy in the direction of the Fe-Fe bond. To judge spin anisotropy, the team measured spin excitations along two orthogonal directions and compared the responses. By carrying out measurements under increasing temperatures, the team was able to determine the critical temperature at which the nematic behavior disappeared and to compare the observations of spin anisotropies with the electronic anisotropies, observed by resistivity measurements.
The researchers first measured the demaculated BaFe2Like2, which has a well-characterized anisotropic spin structure and long-range magnetic order and used it as a reference. Measurements of the spin excitation response along the two orthogonal directions showed a clear asymmetry: the manifestation of nematicity.
The team then performed the same experiment in demaculated FeSe. Despite the absence of magnetic order, they observed a very strong spin anisotropy with respect to the two axes. “Extraordinarily, we were able to reveal a spin anisotropy comparable – if not superior – to that of the already highly anisotropic BaFe2Like2“, explains Xingye Lu. “This spin anisotropy decreases with increasing temperature and disappears around the nematic transition temperature – the temperature at which the material ceases to be in an electronic nematic state.”
The origin of electronic nematicity in FeSe: towards a better understanding of electronic behavior in iron-based superconductors
The energy scale of spin excitations of about 200 meV, which is much greater than the separation between orbital levels, demonstrates that electronic nematicity in FeSe is primarily spin-driven. “It was a big surprise,” says Thorsten Schmitt. “We could now relate electronic nematicity, manifesting as anisotropic resistivity, with the presence of nematicity in spin excitations.”
But what do these discoveries mean? The interaction between magnetism, electronic nematicity and superconductivity is a key problem in unconventional superconductors. It is believed that quantum fluctuations in electronic nematicity can promote high-temperature superconductivity in iron-based superconductors. These results provide long-sought insight into the mechanism of electronic nematicity in FeSe. But more broadly, they add an important piece to the puzzle of understanding electronic behavior in iron-based superconductors and ultimately how this relates to superconductivity. Next steps will be to determine whether spin-driven electronic nematic behavior persists in other members of the iron-based superconductor family, and further, whether suspicions that it may arise in directions other than the Fe-Fe bond axis are correct.
This work was a collaboration between the groups of Thorsten Schmitt at PSI and Xingye Lu at Peking Normal University, along with colleagues from Rice University, Zhejiang University and Renmin University of China. Thorsten Schmitt and Xingye Lu jointly designed this research project.