Resolution of zigzag magnetic correlations in Na-deficient NaxIrO3 without long-range ordering

Abstract

The materials search for Kitaev quantum spin liquids led to the discovery of many honeycomb lattice materials. Much attention has been paid to materials without magnetic order down to the lowest temperatures. The newly synthesized Na-deficient ${\mathrm{Na}}_{x}{\mathrm{IrO}}_{3}$ has been found to bear no sign of long-range magnetic order above 1 K from physical property measurements. In this paper, we report momentum- and energy-resolved excitation spectra in Na-deficient ${\mathrm{Na}}_{x}{\mathrm{IrO}}_{3}$ measured using a resonant inelastic x-ray scattering spectrometer. Orbital excitation spectra show that the octahedral and trigonal crystal field splittings are larger in ${\mathrm{Na}}_{x}{\mathrm{IrO}}_{3}$ than in ${\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}$. On the other hand, the low-energy spectrum at low temperature shows a wave-vector dispersion and a spectral weight distribution that are similar to those of ${\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}$, revealing that the two-dimensional zigzag magnetic correlations in ${\mathrm{Na}}_{x}{\mathrm{IrO}}_{3}$ are similar to those in ${\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}$ in terms of the ordered magnetic moment direction and three dynamically fluctuating zigzag orders. The azimuth angle dependence of the low-energy spectrum corroborates these results. The two-dimensional zigzag magnetic correlations rapidly weaken until 50 K. At high temperatures, the spectral weight distribution of the low-energy excitation resembles that of the pure Kitaev model, indicating that the Kitaev interaction dominates the dynamic magnetic response at high temperature. We suggest that the larger crystal field and distortion and the weakened longer-range Heisenberg exchange interactions due to the Na deficiency in ${\mathrm{Na}}_{x}{\mathrm{IrO}}_{3}$ contribute to bring ${\mathrm{Na}}_{x}{\mathrm{IrO}}_{3}$ away from the zigzag long-range magnetic order phase.