⁵¹V NMR evidence for interlayer-modulated charge order and a first-order low-temperature transition in CsV₃Sb₅

Charge order in the kagome superconductor CsV₃Sb₅ exhibits a complex three-dimensional organization and intermediate-temperature anomalies whose bulk character has remained unsettled.We use orientation-dependent ⁵¹V NMR as a site-selective probe to determine the stacking of the charge density wave (CDW) state and its thermal evolution. Below T_CDW≈94 K, the field-linear splitting of the ⁵¹V central transition together with the anisotropy of the Knight shift tensor identify an interlayer-modulated 3q CDW whose local environments are consistent with a four-layer 2 × 2 × 4 stacking with mixed trihexagonal/Star-of-David distortions, in agreement with synchrotron x-ray determinations. For comparison, RbV₃Sb₅ serves as a reference exhibiting a uniform trihexagonal 2 × 2 × 2 stacking, allowing us to isolate features unique to the 2 × 2 × 4 state in CsV₃Sb₅. With H₀ ‖ c, the ⁵¹V quadrupolar satellites through the intermediate temperature scale near T_CO≈65 K reorganize into two well-resolved electric-field-gradient manifolds that coexist over a finite interval; their relative spectral weights interchange on cooling while the total integrated satellite intensity remains conserved and ν_Q within each manifold is nearly temperature independent. The coexistence without critical broadening, together with conserved intensity, provides bulk evidence consistent with a first-order charge-order transition near T_CO. Our measurements do not resolve whether this lower-temperature transition corresponds to a distinct in-plane order or a reorganization of the 3q state; rather, they delimit this window and provide bulk, site-resolved constraints that connect prior reported anomalies to a thermodynamic first-order transition.