Unveiling unconventional magnetism at the surface of Sr2RuO4

Abstract

Materials with strongly correlated electrons often exhibit interesting physical properties. An example of these materials is the layered oxide perovskite Sr₂RuO₄, which has been intensively investigated due to its unusual properties. Whilst the debate on the symmetry of the superconducting state in Sr₂RuO₄ is still ongoing, a deeper understanding of the Sr₂RuO₄ normal state appears crucial as this is the background in which electron pairing occurs. Here, by using low-energy muon spin spectroscopy we discover the existence of surface magnetism in Sr₂RuO₄ in its normal state. We detect static weak dipolar fields yet manifesting at an onset temperature higher than 50 K. We ascribe this unconventional magnetism to orbital loop currents forming at the reconstructed Sr₂RuO₄ surface. Our observations set a reference for the discovery of the same magnetic phase in other materials and unveil an electronic ordering mechanism that can influence electron pairing with broken time reversal symmetry.

Fig. 1. Low-energy μSR setup for measurements on SRO₂₁₄ single crystals.

a SRO₂₁₄ crystals cleaved and glued onto a Ni-coated aluminium plate to form a mosaic for the LE-μSR measurements. The scale bar corresponds to a length of 2 cm. b Experimental LE-μSR setup with applied field vector B_ext perpendicular to the sample (i.e., along the c-axis of SRO₂₁₄ coinciding with the axis z of our orthonormal reference-axes system) and arrays of positron detectors used to count muon decay events. The schematic cut-out allows viewing the sample inside the detectors. c LE-μSR measurement configurations for different orientations of the initial muon spin polarization vector S_μ+: S_μ+ perpendicular to the applied field vector B_ext and precessing in the xy-plane of our reference-axes system as indicated by the shadowed red circle (transverse field, top) or S_μ+ collinear to B_ext (longitudinal field or zero fields with B_ext = 0, bottom). d Muon implantation profiles in SRO₂₁₄ simulated for a few representative implantation energies.

Fig. 2. Temperature dependence of magnetism in SRO₂₁₄ at different implantation depths.

Shift in the muon depolarization rate, Δλ, from the λ value measured at T = 270 K as a function of temperature T measured in a TF setup (inset) with applied field amplitude B_ext = 100 G at different implantation energy E values: E = 3 keV (red symbols with error bars), E = 6 keV (orange symbols with error bars) and E = 16 keV (blue symbols with error bars). The solid grey line serves as a guide to the eye and marks the T range (grey shaded region) where Δλ changes slope for E = 3 keV, which we identify as the onset temperature T_on of the magnetism in SRO₂₁₄. The inset shows the relative orientation of the applied field B_ext with respect to the muon spin polarization S_μ+ in our orthonormal reference-axes system for the TF configuration.

Fig. 3. Magnetic field response and depth profile of magnetism in SRO₂₁₄.

a, b, Temperature dependence of the local field amplitude B_loc (a) and of the shift in the depolarization rate, Δλ, from the λ value measured at T = 200 K (b) measured in TF with amplitude of the external field B_ext = 1500 G at E = 3 keV (red symbols with error bars) and E = 14 keV (blue symbols with error bars). Error bars in (a) are within the symbols. The inset schematic in (a) shows the relative orientation of the applied field B_ext with respect to the muon spin polarization S_μ+ in our orthonormal reference-axes system for the TF configuration. The Δλ values in (b) are different from those shown in Fig. 2, as they are measured at a different stage of the experiment after warming the samples to room T, degaussing the magnet and zero-field cooling the samples again before applying B_ext. c, d Shift in the local field amplitude ΔB_loc (c) and in Δλ (d) between T = 100 K > T_on and T = 5 K < T_on measured in TF as a function of E for B_ext = 100 G (green symbols with error bars) and B_ext = 1500 G (purple symbols with error bars). The top axes are the corresponding muon average stopping depth $\overline{z}$ values determined from the simulated muon stopping distributions in Fig. 1d. Dashed lines in (b) to (d) are guides to the eye.

Fig. 4. Static nature of magnetism in SRO₂₁₄.

Asymmetry signal measured at $T$ =  5 K in ZF/LF for parallel (angle = 90°) and antiparallel (angle = −90°) alignments of the applied field B_ext and the muon spin polarization S_μ+ with different B_ext amplitude values: B_ext = 0 G (red symbols with error bars), B_ext = 10 G (blue symbols with error bars) and B_ext = 100 G (green symbols with error bars). The inset schematic shows the relative orientation of B_ext and S_μ+ in our orthonormal reference-axes system for the ZF/LF setup.

Fig. 5. Magnetism due to orbital loop currents in SRO₂₁₄.

a Illustration of the RuO₄ plaquette and of the corresponding d-orbitals for the Ru atoms (red box) and p-orbitals for the O atoms (light blue box) with asymmetric loop current distributions generating magnetic flux pointing inward (yellow triangle with ‘−’ symbol) or outward (grey triangle with ‘+’ symbol) the RuO₄ plane. b Possible orbital loop currents for a given RuO₄ plaquette associated with the Ru–O hybridization of the d_xy orbitals (top) and of the (d_xz, d_yz) orbitals (bottom). c Loop current states with equal (LC⁺ state) and opposite sign (LC⁻ state) of the magnetic flux associated with the xy- and z-orbital sectors of the RuO plaquettes in the SRO₂₁₄ supercell. d, Free energy E(ϕ)−E(0) of the LC⁺ (dashed lines) and LC⁻ states (solid lines) calculated at T = 50 K for different values of the d–p Coulomb interaction $U$ ($U$ values given in eV units are specified in the figure legend) as a function of the order parameter ϕ which sets the amplitude of the bond current.