Temperature-driven sodium-ion dynamical-to-static crossover in the zig-zag ordered phase of Na${}_{0.5}$CoO${}_2$

Abstract

We employ polarization-resolved Raman spectroscopy combined with first-principles calculations to study the sodium-ion lattice dynamics in a sodium zig-zag ordered cobaltate compound Na${}_{0.5}$CoO${}_2$. We detect two sodium phonon modes for the first time, and their mode frequencies are consistent with first-principles phonon calculations based on an orthorhombic unit cell. We find that they appear below around $T^{\ast }\sim 300\pm 50$K with large linewidth broadening, much lower than the sodium zig-zag ordering temperature $T_{\text{S}}\sim 460$K, and then narrow at lower temperatures. We interpret the sodium-phonon anomalies occurring at $T^{\ast }$ as a dynamical-to-static crossover involving mainly the motion of sodium ions. Our results suggest that the gradual freezing of the sodium ions and the well-defined static sodium-zigzag order below $T^{\ast }$ set the stage for the emergent electronic and magnetic orders in the CoO${}_2$ layer of Na${}_{0.5}$CoO${}_2$.

17 pages, 12 figures, to appear in Physical Review B

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