Controlled vapor crystal growth of $\mathrm{N}{\mathrm{a}}_4\mathrm{I}{\mathrm{r}}_3{\mathrm{O}}_8$: A three-dimensional quantum spin liquid candidate

We report the successful bulk single-crystal growth of the hyperkagome lattice iridate $\mathrm{N}{\mathrm{a}}_4\mathrm{I}{\mathrm{r}}_3{\mathrm{O}}_8$ (Na438) by vapor transport using a sealed aluminum oxide tube as a container. Crystals were characterized by magnetization, x-ray diffraction, and energy-dispersive x-ray measurements, confirming their identity and properties. Single-crystal x-ray diffraction experiments revealed superlattice peaks indexed on a propagation vector $q=(1/3,1/3,1/3)$ based on the cubic substructure with cell parameter $a=8.986\left(1\right)\AA$. This superlattice is three-dimensional and fully coherent. Polarization analysis rules out spin and/or orbital order as the underlying origin of the modulation and points to long-range ordering of Na ions at the notionally disordered Na sites as a plausible origin for the observed superlattice.

Figure 1

(a) Crystals grown along the inside surface of the alumina tube (inset: sealed alumina tubes prior to crystal growth). (b) An as-grown $\mathrm{N}{\mathrm{a}}_4\mathrm{I}{\mathrm{r}}_3{\mathrm{O}}_8$ single crystal (top) and $\mathrm{N}{\mathrm{a}}_2\mathrm{Ir}{\mathrm{O}}_3$ crystals (bottom). (c) $HK0$ plane of $\mathrm{N}{\mathrm{a}}_4\mathrm{I}{\mathrm{r}}_3{\mathrm{O}}_8$.

Figure 2

Rietveld refinement of laboratory powder x-ray diffraction pattern of pulverized Na438 single crystals. Crosses, data; solid green line, calculated fit; tick marks, expected reflection positions; solid blue line, difference $l_{\mathrm{obs}}-l_{\mathrm{calc}}$.

Figure 3

EDX measurement. Squares show as-measured composition, and green triangles are the $\mathrm{N}{\mathrm{a}}_2\mathrm{Ir}{\mathrm{O}}_3,\mathrm{N}{\mathrm{a}}_{4-x}\mathrm{I}{\mathrm{r}}_3{\mathrm{O}}_8$, and $\mathrm{N}{\mathrm{a}}_3\mathrm{I}{\mathrm{r}}_3{\mathrm{O}}_8$ compositions after correction. Inset: magnetic susceptibility measured on the same samples.

Figure 4

Magnetic susceptibility measured on warming at 0.2 T after field cooling (inset: low-temperature region of curve $a)$.

Figure 5

(a) Section of the (1/3,$K,L)$ plane showing several superlattice reflections at 200 K. (b) A representative $(H,K)$ map of scattering about the (1/3,1/3,1/3) satellite peaks at the (6,6,1) zone center. The $L$ value is 1.33. (c) $H$ scan through the (6.33,6.33,1.33) satellite in both the σ-σ and σ-π scattering channels. (d) Energy scan conducted while sittingσ at $Q=(6.33,6.33,1.33)$. Parts (b)–(d) were collected at 1.8 K.