Single-domain stripe order in a high-temperature superconductor

Understanding the microscopic coupling of spin, charge, and lattice degrees of freedom is crucial for comprehending novel quantum states in strongly correlated electron materials. Unconventional superconductivity in cuprates, for instance, is believed to arise from intertwined charge density wave (CDW) and spin density wave (SDW) fluctuations. While experimental and theoretical evidence suggests near-degeneracy of ground state energies for static CDW, SDW orders, and unconventional superconductivity, the precise nature of the charge-spin coupling remains elusive. This study focuses on La_1.88Sr_0.12CuO₄ (LSCO), a prototypical high-temperature superconductor, to investigate this coupling. Previous research has shown that density-wave orders are most stable around a hole concentration of p ≈ 1/8, coinciding with superconductivity suppression. However, the relationship between CDW and SDW orders, and their temperature and doping dependencies, varies across different cuprate families. In LSCO, both orders coexist within a specific doping range (~0.1 < x < ~0.135), raising the question of their microscopic coupling and its role in unconventional superconductivity. This work employs uniaxial pressure as a tuning parameter to probe this relationship in LSCO.

Extensive research has explored the interplay of charge and spin density waves with superconductivity in cuprates. Studies using various techniques, including neutron scattering and resonant x-ray scattering, have revealed the presence of static and fluctuating CDW and SDW orders in various cuprate materials. Theoretical models based on the Hubbard model have shown the near degeneracy of different ordered states, highlighting the complexity of the underlying physics. However, the direct coupling between CDW and SDW orders and their connection to superconductivity remain open questions. Existing literature shows different behaviors in different cuprate families. For example, static CDW and SDW orders do not seem to coexist in YBa₂Cu₃O_7−y, contrasting with La-based cuprates exhibiting coexistence and signatures of coupling. The different temperature and doping dependencies of CDW and SDW orders further complicate the picture. This study builds upon recent x-ray experiments that demonstrated the tunability of CDW domains via uniaxial strain, providing a pathway to investigate the related behavior of SDW orders.

This study overcomes the experimental challenges of probing weak SDW order in small single crystals under high strain by combining three technical advancements. First, it utilizes advanced neutron-ray-tracing simulations (McStas) to optimize the signal-to-background ratio. These simulations account for background scattering from cryostats and pressure cells, revealing that longer wavelengths are advantageous. Second, it leverages the focusing capabilities of the ThALES cold neutron triple-axis spectrometer at the Institut Laue-Langevin, using a double focusing Si(111) monochromator to maximize the neutron flux on a small (55 mg) LSCO single crystal. This is a substantial reduction from previous experiments (1.06g) allowing for more effective application of pressure. Finally, a scaled-up version of a uniaxial pressure cell, previously developed for x-ray studies, is employed without compromising pressure application. The experiment involved applying compressive strain (ε ≈ 0.02%) along the Cu-O bond direction (a-axis). Elastic neutron scattering measurements were performed at T = 2 K and 40 K (above the SDW onset temperature) to identify SDW order peaks at specific wavevectors. Data analysis involved fitting Gaussian line shapes to the peaks to extract parameters like incommensurability (δ_spw) and in-plane correlation length (ξ_||). Ambient pressure measurements on a larger (1.06 g) sample were used for comparison. Background subtraction was performed to facilitate a quantitative comparison between strained and unstrained conditions.

The neutron scattering measurements at ambient pressure reveal magnetic intensity at two wavevectors, Q_SDW = (0.5 ± δ_spw, 0.5, 0) and Q_SDW = (0.5, 0.5 ± δ_spw, 0), consistent with the presence of two orthogonal magnetic domains or a single-domain multi-Q magnetic order. Under uniaxial pressure, a significant redistribution of magnetic peak intensity is observed. The peak associated with one wavevector (Q_SDW) becomes significantly stronger, while the other (Q_SDW) disappears. This indicates that uniaxial pressure leads to a single-domain state, where the magnetic domains are aligned along a single direction. There is no change in the SDW ordering vector, correlation length, or onset temperature (T_N), suggesting the pressure merely repopulates the domains without altering the underlying order. The observed response of the SDW order to uniaxial pressure is consistent with the behavior of the CDW order previously observed in x-ray scattering experiments under similar conditions. This indicates a direct coupling between CDW and SDW orders, supporting the existence of a charge-spin stripe arrangement in LSCO. The integrated intensity of the Q_SDW peak at ambient pressure is roughly twice that of the Q_SDW peak, consistent with the expected 2:1 ratio for a charge-spin stripe state, where CDW incommensurability is double that of SDW incommensurability.

The results provide direct experimental evidence for a single-Q magnetic structure in LSCO, and that application of pressure along the Cu-O bond direction favors domains aligned perpendicular to the pressure direction. The observation of single-domain charge-spin stripe order under uniaxial pressure strongly supports a strong coupling picture where stripe order arises from local correlations. In this scenario, holes reside at antiphase SDW domain boundaries to minimize kinetic energy, establishing a clear link between charge and spin order. The findings are less consistent with a weak coupling picture based on Fermi surface nesting, which would require substantial and anisotropic Fermi-surface distortions to account for the unidirectional charge and spin domain states observed under pressure. The unchanged magnetic correlation length, SDW onset temperature, and CDW-superconductivity coupling under pressure suggest a deep intertwining of charge-spin stripe order and unconventional superconductivity in LSCO. This contrasts with observations in La_2-xBa_xCuO₄ (LBCO), where uniaxial pressure along a different direction exhibits direct competition between superconductivity and magnetic order, highlighting the material-specific nature of this interplay.

This study demonstrates that uniaxial pressure effectively tunes the charge-spin stripe order in LSCO, leading to a single-domain state. The findings provide strong evidence for a direct coupling between CDW and SDW orders, supporting a strong-coupling model for the underlying stripe arrangement. Further research using uniaxial pressure on other cuprates along different crystallographic directions will provide valuable insights into the connection between stripe order and unconventional superconductivity. The development of new techniques has allowed exploration of the impacts of uniaxial pressure on other strongly correlated systems.

The study focuses on a specific doping level (x=0.12) in LSCO. Extending the investigations to other doping levels is essential to gain a broader understanding of the pressure-induced domain repopulation across the phase diagram. The sample size limitations, while overcome by advanced instrumentation, might still impose constraints on the precision of certain measurements. Future experiments with larger samples could allow for more accurate determinations of the wave vector changes and correlation lengths under applied pressure.