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 TCDW\!≈\!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 TCO\!≈\!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 νQ 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 TCO. 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.