Prevailing orbital excitations in paramagnetic kagome superconductor Cs(V$_{0.95}$Ti$_{0.05}$)$_3$Sb$_5$

Abstract

Using the muon as a sensitive local magnetic probe, we investigated the layered kagome superconductor Cs(V$_{0.95}$Ti$_{0.05}$)$_3$Sb$_5$, a material notably devoid of both static magnetic moments and long-range charge order. Our transverse-field $μ$SR measurements reveal that the local magnetic susceptibility, obtained via the muon Knight shift, is dominated by orbital excitations with a split energy levels around 20 meV. Meanwhile, the persistence of itinerant electron paramagnetism down to 5 K and 7 T confirms the absence of static magnetism within this regime. In addition, zero-field (ZF) $μ$SR experiments detect a significant increase in the inhomogeneous nuclear dipolar field distribution below a featured temperature at 70 K. We attribute this ZF-$μ$SR feature to the emergence of local lattice distortions at low temperatures, potentially arising from orbital ordering. Significantly, our study establishes that orbital excitations constitute an intrinsic property of the layered V-Sb kagome lattice. Despite its small magnitude, spin-orbit coupling plays a crucial role in governing the lattice dynamics, potentially driving the emergence of novel phenomena such as phonon carrying angular momentum in crystals with non-chiral point groups.

Figures (4)

• Figure 1: (a) Schematic representation of the atomic structure of the Cs(V$_{0.95}$Ti$_{0.05}$)$_3$Sb$_5$ crystal, with atoms labeled; (b) Electronic phase diagram of CsV$_3$Sb$_5$ as a function of Ti doping adapted from Ref. yang_titanium_2022Huang_Revealing_2025; (c) Inverse magnetic susceptibility of Ti doped ($x=0.05$) Cs(V$_{0.95}$Ti$_{0.05}$)$_3$Sb$_5$ measured on a single crystal. The compound displays a Curie-Weiss behavior with the addition of paramagnetic contributions at higher temperatures. Insets: Low-temperature susceptibility data. The deviation from Curie-Weiss behavior indicates the impact of the crystal electric field on the magnetic susceptibility. Note, for comparison the magnetic susceptibility data for different applied magnetic fields have been multiplied by different scaling factors.
• Figure 2: $\mu$SR spectra taken from Ti ($x=0.05$) doped Cs(V$_{0.95}$Ti$_{0.05}$)$_3$Sb$_5$ single crystals: (a) in a weak applied transverse field (wTF) of 30 Oe at 5 K and 290 K. Note: a small initial phase shift of the spectra between the two measurements in (a) is due to the different initial muon spin angle settings; (b) in a varies of small applied longitudinal fields (LF) at 5 K. Solid lines are fits to the experimental data as described in the text; (c) ZF-$\mu$SR spectra of the Ti ($x=0.05$) doped sample. The experimental data marked in green and blue are the measured muon spin depolarization rate along the muon spin projection direction within the crystal $ab-$plane and $c-$axis, respectively.
• Figure 3: Results of the muon knight shift experiment: (a) temperature dependence of the muon Knight shifts ($K$) for magnetic fields $H=$ 5 T applied parallel to the $c-$axis ($H{\parallel}c$) of the Ti ($x=0.05$) doped Cs(V$_{0.95}$Ti$_{0.05}$)$_3$Sb$_5$ single crystal. The solid curve is a simulation of the local magnetic susceptibility of a two-level transition with a gap size of 20 meV. Inset: illustration of the V-Sb octahedron and the V split orbitals in a crystal field. (b) Plot of $K$ vs. the bulk magnetic susceptibility ($\chi$) for $H{\parallel}c$. The dashed curve is a guide to the eyes.
• Figure 4: Magnetic field dependent local magnetic broadening: (a) FFT of the TF muon spectra with $H = 5$ T, the linewidth is fitted using a Gaussian lineshape as depicted in Equ. 3. (b) Temperature-dependent TF-$\mu$SR depolarization rates measured under high magnetic fields between 1 T and 5 T. The horizontal lines are guided to the eyes. (c) Change of the local magnetic field broadening comparison of the relative changes based on the TF muon depolarization data shown.