Coexisting Multiple Charge Orders and Magnetism in the Kagome Superconductor LaRu3Si2

Abstract

The Kagome lattice has emerged as a promising platform for hosting unconventional chiral charge orders at high temperatures. In the context of the correlated Kagome superconductor LaRu₃Si₂, a room-temperature charge-ordered state with a propagation vector of ( $\frac{1}{4}$ , 0, 0) is previously reported. However, understanding the interplay between this charge order and superconductivity, particularly with respect to time-reversal-symmetry breaking, remains elusive. In this study, we employ single-crystal X-ray diffraction, magnetotransport measurements, muon-spin rotation experiments, and first-principles calculations to investigate charge order and its electronic and magnetic responses in LaRu₃Si₂ across a wide temperature range, down to the superconducting state. These findings reveal the appearance of a charge order with a propagation vector of ( $\frac{1}{6}$ , 0, 0) below T_{co, 2} ≃ 80 K, which coexists with the previously identified room temperature primary charge order ( $\frac{1}{4}$ , 0, 0). The primary charge-ordered state exhibits zero magnetoresistance. In contrast, the appearance of the secondary charge order at T_{co, 2} is accompanied by a notable magnetoresistance response and a pronounced temperature-dependent Hall effect, which experiences a sign reversal, switching from positive to negative below T* ≃ 35 K. Intriguingly, a significant enhancement is observed in the internal field width sensed by the muon ensemble below T* ≃ 35 K. Moreover, the muon spin relaxation rate exhibits a substantial increase upon the application of an external magnetic field below T_{co, 2} ≃ 80 K. These results highlight the coexistence of two distinct types of charge order and magnetism in LaRu₃Si₂ within the correlated Kagome lattice, along with superconductivity. This study sheds light on the intricate electronic and magnetic phenomena occurring in Kagome superconductors, providing valuable insights into their unique properties and potential applications.

Keywords: Kagome lattice; charge order; muon‐spin rotation; superconductivity; time‐reversal symmetry‐breaking.

Figure 1

Charge order in LaRu₃Si₂. a) Schematic phase diagram as a function of temperature of LaRu₃Si₂. The arrows mark the structural phase transition temperature T _str from the high‐temperature hexagonal P6/mmm phase (SG No. 191) to the low‐temperature orthorhombic Cccm phase (SG No. 66), primary charge order transition temperature T _CO‐I and secondary charge order transition temperature T _CO‐II. b–i) Reconstructed reciprocal space along the (h k 1) direction, performed at various temperatures above and below the superconducting transition temperature. Green, blue, and red circles mark the Bragg peak, primary charge order CO‐I peak, and secondary charge order CO‐II peak, respectively. Red arrows in panel (h) indicate the diffuse scattering at 1/6 periodicity, which is clustered into sharp diffraction spots at lower temperatures.

Figure 2

Different optimized structures of LaRu₃Si₂. a) Experimental determination of CO‐I structure. b) CO‐I (SG No. 51) is moved from the $\mathrm{a}\times 2\sqrt{3}$×2c supercell of SG No. 191 structure. c) Experimental determination of CO‐II structure. d) Co‐II (SG No. 55) is moved from the $\mathrm{a}\times 3\sqrt{3}$×2c supercell of SG No. 191 structure. The arrows represent in‐plane movements of Si atoms, the dots(crosses) represent upward (downward) movements of Ru atoms along c direction. e) Phonon spectrum of SG No. 191 structure with experimental lattice constants a = 5.688Å and c = 3.567Å. f) Movements of the atoms corresponding to the imaginary phonon modes of SG No. 191 structure. The purple (red and black) arrows correspond to the mode marked by purple (orange) dot in e. The red and black colors indicate α and β modes respectively.

Figure 3

Calculated electronic structures for LaRu₃Si₂. a) The folded energy spectrum of SG No. 191 structure. b–c) The unfolded energy spectrum of CO‐I (SG No. 51) and CO‐II (SG No. 55) structures. The main difference of the spectrum near the Fermi level are pointed by blue arrows. d) The DOS of CO‐I, CO‐II, SG No. 191, and SG No. 193 structures.

Figure 4

Weakly anisotropic superconducting properties of LaRu₃Si₂. The temperature dependence of the electrical resistivity of a single crystal of LaRu₃Si₂, measured under various magnetic fields applied perpendicular to the c‐axis (a) and parallel to the c‐axis (b). c) the magnetic field‐temperature phase diagram is derived from the data shown in panels a and b.

Figure 5

Magnetic and transport anomalies in LaRu₃Si₂. a) The temperature dependence of magnetic susceptibility, measured under the magnetic field of 1 T, applied parallel and perpendicular to c‐axis. b) Temperature dependence of the normal state longitudinal resistance ρ _xx and its first derivative. Vertical grey lines mark three characteristic temperatures T*, T _{co, I} and T _{co, II}.

Figure 6

Magnetotransport characteristics for LaRu₃Si₂. a) The magnetoresistance measured at various temperatures across the charge ordering temperature T _{co, 2} ≃ 80 K. Black solid lines represent fits to the data by means of the following equation: Δρ/ρ _{H = 0} = α + β(µ₀ H) ⁿ . b) The temperature dependence of the value of magnetoresistance at 9 T and the power exponent n. c) Kohler plot, Δρ/ρ _{H = 0} versus (µ₀ H/ρ _{H = 0})², of the magnetoresistance, plotted from field‐sweeps at various temperatures. d) The temperature dependence of the value of the Hall resistance ρ _xy at 9 T. Inset shows the Hall resistance, measured at various temperatures between 10 and 300 K.

Figure 7

Magnetic response of the charge order in zero‐field and applying external magnetic fields in LaRu₃Si₂. a) The ZF µSR time spectra, obtained at T = 10 K and 300 K, all above the superconducting transition temperature T _c. The solid black curves in panel a represent fits to the recorded time spectra, using the simple exponential function. Error bars are the standard error of the mean (s.e.m.) in about 10⁶ events. b) The temperature dependences of the zero‐field muon spin relaxation rate Γ _ZF , obtained in a wide temperature range. The error bars represent the standard deviation of the fit parameters. c) Fourier transform of the µSR asymmetry spectra for the single crystal of LaRu₃Si₂ at 5 K in the presence of an applied field of µ₀ H = 8T. The solid line is a two‐component signal fit. The peaks marked by the arrows denote the external and internal fields, determined as the mean values of the field distribution from the silver sample holder and from the sample, respectively. The short‐time‐window apodization function was used in the Fourier transform amplitude plot. d) Temperature dependence of the high transverse field muon spin relaxation rate λ_HTF for the single crystal of LaRu₃Si₂, measured under different c‐axis magnetic fields. The vertical grey line marks the transition temperature below which field effect was observed. The error bars represent the standard deviation of the fit parameters.