Strongly correlated electron materials often exhibit fascinating physical properties, and Sr₂RuO₄, a layered oxide perovskite, is a prime example. While the debate about the symmetry of its superconducting state continues, understanding its normal state is crucial because it's the backdrop for electron pairing. Reduced dimensionality systems like 2D materials exhibit increased quantum fluctuations compared to 3D systems, leading to unique symmetry-breaking phase transitions and quantum orders. Layered 3D crystals, like Sr₂RuO₄, represent a 3D analogue of 2D materials, where in-plane electronic correlations dominate. Sr₂RuO₄ is situated near various electronic instabilities, potentially further stabilized by surface asymmetry caused by structural reorganization of surface RuO₆ octahedra. Although extensive research focuses on the nature of its superconducting state, evidence of spin fluctuations or magnetism under uniaxial pressure in the normal state exists but lacks surface-specific information. Theoretical predictions suggest the emergence of conventional ferromagnetic ordering at the surface due to the rotation of RuO₆ octahedra, but conclusive experimental evidence has been lacking. This study aims to resolve this using low-energy muon spin spectroscopy (LE-µSR), which offers high sensitivity to magnetic fields and nanometer depth resolution.

Previous studies on Sr₂RuO₄ have reported evidence for spin fluctuations and magnetism under uniaxial pressure in the normal state. However, these investigations focused primarily on bulk properties. Theoretical work suggested that conventional ferromagnetic ordering could emerge at the Sr₂RuO₄ surface, potentially stabilized by the rotation of surface RuO₆ octahedra. However, experimental evidence supporting surface magnetism remained elusive, even with techniques like scanning superconducting quantum interference device (SQUID) magnetometry. While Angle-resolved photoemission spectroscopy (ARPES) measurements revealed surface states, their correlation with magnetism wasn't conclusive. This paper addresses the gap in knowledge by employing LE-µSR to investigate the surface magnetic properties of Sr₂RuO₄.

Low-energy muon spin spectroscopy (LE-µSR) was employed to investigate the surface magnetism of Sr₂RuO₄ single crystals grown by the floating zone method. The crystals were cleaved using a non-magnetic ZrO₂ razor blade to avoid magnetic impurity contamination. Cleaved crystal pieces were arranged to form a mosaic to maximize the LE-µSR signal. Measurements were performed with an external magnetic field (Bext) applied both in-plane and out-of-plane. The LE-µSR data were collected in transverse-field (TF) and longitudinal-field (LF) configurations, along with zero-field (ZF) measurements. Temperature scans (T-scans) in the TF configuration were conducted at various implantation energies (E), each corresponding to a different muon implantation depth. The asymmetry signal (As(t)) was modeled using an exponential relaxation function considering the finite width of the muon implantation profiles. Global fits were performed to extract temperature-dependent parameters like the muon spin depolarization rate (λ) and local field amplitude (Bloc). Energy scans (E-scans) were also conducted to investigate the depth dependence of magnetic signals at different temperatures and magnetic field strengths. Measurements in LF/ZF configurations were performed to determine the static or dynamic nature of the magnetism. The analysis involved fitting the LF/ZF asymmetry data to an exponential/Lorentzian Kubo-Toyabe function.

The LE-µSR measurements revealed unambiguous evidence for an unconventional magnetic phase near the Sr₂RuO₄ surface. This phase is characterized by: a high-temperature onset (Ton) between 50 and 75 K; a small magnetic moment (<0.01 µB/Ru atom); a homogeneous distribution of magnetic sources within the ab-plane; and a decay in magnetic signal intensity over a length scale of ~10–20 nm. These characteristics rule out conventional ferromagnetism. Temperature scans revealed an increase in the muon depolarization rate (Δλ) as the temperature decreased, indicating enhanced magnetism closer to the surface at lower temperatures. Energy scans showed that the magnetic signal is strongest within ~20 nm of the surface. Further analysis using higher external magnetic fields (Bext = 1500 G) showed a positive shift in Bloc, akin to a Knight shift, consistent with enhanced susceptibility near the surface. Zero-field/longitudinal-field (ZF/LF) measurements demonstrated the static nature of the observed magnetism, ruling out spin fluctuations as the origin. The measured local magnetic dipolar fields (~10 G) translate to a magnetic moment significantly smaller than 0.01 µB/Ru atom.

The small magnetic moment and high Ton indicate that the surface magnetism is not due to conventional ferromagnetism. Calculations suggested that the magnetism arises from orbital loop currents with staggered magnetic flux, a result of electronic instabilities at the Fermi level and spin-orbit coupling. This unconventional phase is consistent with the measured magnetic field strength and temperature dependence. The results rule out other potential explanations, such as spin textures with canceling moments, correlations between magnetic impurities, and antiferromagnetic ordering. The study links the surface magnetism to previous observations of strain-induced magnetism and spin fluctuations in the bulk. The interplay between the normal-state time-reversal symmetry breaking (TRSB) phase and the TRSB superconductivity is discussed, suggesting that fluctuations of the chiral loop currents could contribute to the formation of Cooper pairs with intrinsic chirality. The possibility of surface superconducting order parameter reconstruction due to the loop current phase is also considered.

This study presents definitive evidence for an unconventional magnetic phase at the surface of Sr₂RuO₄, attributed to orbital loop currents. This finding offers insights into the electronic mechanisms influencing unconventional superconductivity and provides a benchmark for similar investigations in other materials. Future research should focus on the detailed interplay between the surface magnetism and the bulk superconducting state, including the possibility of a vortex liquid phase formation and the role of surface strain.

The study focuses on the surface region of Sr₂RuO₄ and might not fully capture the bulk behavior. The interpretation of the magnetic moment relies on estimations and assumptions about muon implantation sites and interactions. Further theoretical work could refine the model to account for all observed features. The current study provides experimental evidence for an orbital loop current model, but additional direct observations, such as imaging techniques, would strengthen the conclusions.