Unveiling unconventional magnetism at the surface of Sr₂RuO₄

The study investigates whether the normal state of Sr₂RuO₄ (SRO214) hosts an intrinsic magnetic phase at its surface that breaks time-reversal symmetry (TRS). In reduced dimensional and layered perovskite systems, enhanced electronic correlations can stabilize exotic orders. Although superconducting TRS breaking in Sr₂RuO₄ remains debated, understanding its normal state is crucial for elucidating pairing mechanisms. Prior works reported bulk spin fluctuations and pressure-induced magnetism, and theories suggested surface ferromagnetism tied to RuO₆ octahedral rotations, but direct, surface-selective evidence of magnetism has been lacking. Using depth-resolved, highly sensitive low-energy muon spin rotation/relaxation (LE-μSR), the authors probe for surface-localized magnetism, its temperature onset, depth profile, and static versus dynamic character. They further hypothesize that any observed unconventional magnetism may stem from orbital loop currents stabilized by surface reconstruction and spin–orbital entanglement.

- Two-dimensional and layered systems can host nontrivial orders and topological transitions without conventional long-range order (Kosterlitz–Thouless). Layered oxide perovskites often show exotic phases such as high-Tc superconductivity, metal–insulator transitions, and multiferroicity. - In Sr₂RuO₄, extensive efforts have focused on superconducting symmetry and indications of spin fluctuations or magnetism under uniaxial stress in the bulk. Theoretical work proposed surface ferromagnetism stabilized by surface RuO₆ rotations; ARPES shows surface states but a definitive link to magnetism is lacking; scanning SQUID set strict upper bounds on spontaneous surface currents. - NMR Knight shift studies under strain revealed enhanced paramagnetism near a Van Hove singularity, but such conditions differ from the unstrained surface studied here. - Prior reports of orbital loop current phases in cuprates, iridates, and ladder cuprates suggest TRS-breaking orders without net magnetization, though experimental consensus is mixed, and alternative orders can mimic signatures. This motivates exploration of loop-current-like phases in Sr₂RuO₄’s surface environment where inversion symmetry is broken.

Experimental approach: - Samples: High-purity Sr₂RuO₄ single crystals grown by floating-zone method; Tc ~1.45 K; residual resistivity ratio >200. Characterized by X-ray diffraction and transport. - Surface preparation: Cleaving with non-magnetic ZrO₂ blade; mosaics (~2 cm diameter) mounted on Ni-coated Al plate to match muon beam footprint. - LE-μSR configurations: External field B_ext applied along c-axis (out of plane) for transverse-field (TF) with initial muon spin S_μ ⟂ B_ext, and longitudinal-field (LF) with S_μ ∥ B_ext; zero-field (ZF) also performed. Muon implantation energies E varied to control stopping depth; depth profiles simulated with TrimSP. Typical E included 3, 6, 14–16 keV, corresponding to average depths from ~15 nm to >50 nm. - Measurement protocols: Temperature scans (T-scans) after zero-field cooling; TF typically at B_ext = 100 G to assess Δλ(T) and at B_ext = 1500 G to probe ΔB_loc(T) and Δλ(T) at varying depths. Energy scans (E-scans) compared signals between T = 5 K and T ≈ T_on. - Signal analysis: TF asymmetry A_s(t) modeled as A_0 exp(−λ t) cos(γ_μ B_loc t + φ), with global fitting across T at fixed E assuming T-independent A_0 and φ. Exponential relaxation used due to broad depth distributions in LE-μSR; Δλ(T) defined relative to λ at high T to remove systematic background. LF/ZF data analyzed with exponential/Lorentzian Kubo–Toyabe functions to distinguish static fields from spin fluctuations via field decoupling behavior. - Complementary probes: LEED on in-situ-cleaved surfaces (10 K, UHV) confirmed surface reconstruction (rotated RuO₆); scanning SQUID magnetometry/susceptometry mapped local flux and placed bounds on ferromagnetic impurities or SrRuO₃ inclusions; four-probe transport and high-resolution XRD provided sample quality metrics. Theoretical modeling: - Tight-binding model including Ru d-orbitals (d_xy, d_xz, d_yz) and planar O p-orbitals with ab initio hopping parameters; includes d–p and p–p Coulomb interactions. Spin–orbit coupling lifts degeneracy of loop-current configurations. - Surface inversion symmetry breaking constrains allowed loop-current patterns to asymmetric intra-plaquette currents that generate staggered magnetic flux without net current flow, compatible with metallicity and surface reconstruction. - Two loop-current states considered: LC⁺ (same sign flux in xy and z orbital sectors) and LC⁻ (opposite sign). Free energy E(φ) − E(0) computed versus order parameter φ and interaction U at T = 50 K to determine stability. Magnetic fields from loop currents estimated via Biot–Savart using measured magnetic permeability μ and computed bond currents to compare with LE-μSR B_loc (~5–15 G expected).

- Surface-localized magnetism in normal state: LE-μSR detects enhanced muon depolarization rate Δλ upon cooling with an onset temperature T_on between ~50 and 75 K, strongest for shallow implantation (E = 3 keV, z ≈ 15 nm), indicating a surface origin. - Depth profile: Energy scans show the magnetic signal strength (Δλ and ΔB_loc) increases for E < ~4 keV, corresponding to an average depth range of ~10–20 nm from the surface; deeper muons register delayed/weak response, confirming surface confinement. - Field response: At B_ext = 1500 G, B_loc increases with cooling for both shallow and deeper depths, diverging below ~25 K with a positive shift at E = 3 keV relative to E = 14 keV, consistent with enhanced surface susceptibility; ΔB_loc reaches ~0.65 G (~0.45% of B_ext) near the surface in 1500 G, while any shift at 100 G is below noise. - Static nature: ZF/LF measurements at 5 K show decoupling of asymmetry damping with modest longitudinal fields (10–100 G), evidencing static local dipolar fields of order ~10 G rather than dynamic spin fluctuations. - Moment size: Using muon stopping near O sites and Ru–O bond lengths (~2 Å), the static fields (~10 G) correspond to a very small average moment <0.01 μ_B per Ru atom. - Homogeneity and symmetry: The in-plane field distribution is monomodal and consistent with a homogeneous, translation-symmetric source within unit-cell length scales; scanning SQUID detects only sparse extrinsic spots (<1% area), placing strong bounds on ferromagnetic inclusions. - Exclusions: Conventional surface ferromagnetism from RuO₆ rotations (which would yield ~1 μ_B/Ru) is incompatible with the small measured moments; antiferromagnetic orders, spin textures with canceling moments, and impurity-mediated magnetism are also inconsistent with T_on, depth localization, and field magnitudes. - Mechanism: A surface TRS-breaking orbital loop current phase is proposed. Calculations find loop-current states (LC⁻ favored over LC⁺) with free-energy gain ~20–30 meV (matching T_on scale). Predicted B_loc from LC⁻ currents is ~5–15 G, matching LE-μSR. The phase yields staggered flux with zero net current, compatible with metallic SRO214 surface. - Implications: The surface TRSB phase may influence superconductivity (possible pair-density-wave reconstruction or suppression of uniform SC), and fields comparable to H_c1 (~10 G at 0 K) could foster a vortex liquid, potentially explaining bulk μSR TRSB signals.

The LE-μSR evidence establishes a TRS-breaking magnetic phase confined to the first ~10–20 nm of the Sr₂RuO₄ surface with an onset between 50 and 75 K, static dipolar fields ~10 G, and extremely small effective moments (<0.01 μ_B/Ru). These features and the homogeneous in-plane distribution rule out conventional ferromagnetism, impurity-driven magnetism, and simple antiferromagnetism. Depth and field dependences further corroborate a surface-confined, intrinsic order. Theoretical analysis shows that asymmetric orbital loop currents stabilized by surface inversion-symmetry breaking and spin–orbit coupling can form an energetically favorable LC⁻ state with a free-energy scale (20–30 meV) consistent with T_on and generate local fields of the correct magnitude. This provides a microscopic mechanism for the unconventional magnetism and reconciles the absence of macroscopic ferromagnetism with TRSB. The findings address the central question by pinpointing an intrinsic, surface-normal-state TRSB order grounded in electronic structure and correlations. These results are significant for the ongoing debate on superconducting symmetry in Sr₂RuO₄. A pre-existing normal-state TRSB surface phase can interact with superconductivity, possibly leading to reconstruction of the order parameter near the surface (e.g., pair-density wave) or competition that suppresses uniform superconductivity locally. Surface dipolar fields comparable to H_c1 could nucleate a vortex liquid, offering a route to interpret previous bulk μSR TRSB observations. More broadly, the work suggests that orbital loop current phases may be a general motif in correlated oxides, with implications for pairing mechanisms involving broken TRS and chirality.

The study demonstrates an unconventional, intrinsic magnetic phase at the surface of Sr₂RuO₄ in its normal state: static, weak dipolar fields (~10 G), onset at 50–75 K, confined to ~10–20 nm depth, and associated with moments <0.01 μ_B/Ru. Depth-resolved LE-μSR and complementary probes rule out conventional ferromagnetism and impurity-related magnetism. A microscopic mechanism based on asymmetric orbital loop currents (LC⁻) stabilized by surface inversion-symmetry breaking and spin–orbit coupling quantitatively accounts for the observed fields and energy scales. This discovery provides a framework for identifying similar TRSB electronic phases in other correlated materials and points to a potential electronic route for chiral pairing interactions in Sr₂RuO₄. Future work should elucidate how this surface TRSB phase interacts with superconductivity—whether it suppresses or reconstructs the superconducting order (e.g., via pair-density waves), its evolution below Tc, and whether it can extend deeper into the bulk. Systematic studies varying strain, surface reconstruction, and magnetic field could tune the loop-current phase and clarify its role in superconducting TRSB.

- LE-μSR depth profiles are broad at fixed implantation energy, necessitating exponential relaxation modeling and limiting spatial resolution along depth. - Field-induced shifts at low B_ext (~100 G) are near the detection noise floor; higher fields (beyond 1500 G) and controlled uniaxial strain—key to quantitative comparisons with NMR Knight shift studies—are not accessible in the current setup. - Scanning SQUID detects occasional small extrinsic magnetic spots likely from cleaving; although they occupy <1% area and cannot explain the uniform LE-μSR response, they represent surface inhomogeneities. - Direct discrimination among alternative subtle TRSB orders (e.g., other intra-unit-cell orders) relies on modeling and symmetry arguments; complementary momentum-resolved probes (e.g., spin-polarized neutron scattering) at the required surface sensitivity are challenging. - Comparison to strain-tuned Knight shift is qualitative due to different probe sites (μ⁺ vs ¹⁷O), field strengths, and absence of strain in LE-μSR.