Chemical and hydrostatic-pressure effects on the Kitaev honeycomb material ${\mathrm{Na}}_2{\mathrm{IrO}}_3$

The low-temperature magnetic properties of polycrystalline ${\mathrm{Na}}_2{\mathrm{IrO}}_3$, a candidate material for the realization of a quantum spin-liquid state, were investigated by means of muon-spin relaxation and nuclear magnetic resonance methods under chemical and hydrostatic pressure. The Li-for-Na chemical substitution promotes an inhomogeneous magnetic order, whereas hydrostatic pressure (up to 3.9 GPa) results in an enhancement of the ordering temperature $T_{\mathrm{N}}$. In the first case, the inhomogeneous magnetic order suggests either short- or long-range correlations of broadly distributed $j=$½ ${\mathrm{Ir}}^{4+}$ magnetic moments, reflecting local disorder. The increase of $T_{\mathrm{N}}$ under applied pressure points at an increased strength of three-dimensional interactions arising from interlayer compression.

Figure 1

Schematic sketch of the honeycomb layer in ${\mathrm{Na}}_2{\mathrm{IrO}}_3$. The effective spin-$\frac{1}{2}5d^5{\mathrm{Ir}}^{4+}$ ions (at the center of oxygen octahedra) interact via three distinct NN (nearest neighbor) exchange couplings, here denoted by $\alpha$, $\beta$, and $\gamma$. The $J$ and $K$ parameters in Eq. (1) represent the Heisenberg- and Kitaev exchange integrals, respectively, taken over all the NN links in the honeycomb.

Figure 2

Paramagnetic fraction as a function of temperature for samples with different Li-substitution levels (a) and for ${\mathrm{Na}}_2{\mathrm{IrO}}_3$ measured at different pressures (b), as obtained from the $\mu \mathrm{SR}$ experiments. Lines represent fits using Eq. (2).

Figure 3

Best-fit values as extracted from fits of wTF-$\mu \mathrm{SR}$ data with Eq. (2) for different pressures (left) and Li-substitution levels (right). Symbols correspond to the measurements reported in Fig. 2. Lines are guides to the eye.

Figure 4

Time-domain muon-decay asymmetries for various temperatures as observed in ${\mathrm{Na}}_2{\mathrm{IrO}}_3$ (a) and in ${\mathrm{Na}}_{1.85}{\mathrm{Li}}_{0.15}{\mathrm{IrO}}_3$ (b). Note the lack of oscillations in the second case.

Figure 5

Muon-decay asymmetry as a function of time at 2 K in the Li-substituted ${\mathrm{Na}}_2{\mathrm{IrO}}_3$ series. For clarity, the datasets are vertically offset by 0.5 units.

Figure 6

Oscillating asymmetry $F_{\mathrm{osc}}$ as obtained from fits using Eq. (3). In the case of Li substitution we observe a clear decrease with increasing $x$ (a). Since no oscillations are observed in the $x=0.15$ case, the fast relaxing component of the asymmetry, $F_{\mathrm{fast}}$, is plotted, which corresponds to the static part of the sample. Oscillating asymmetry vs temperature for ${\mathrm{Na}}_2{\mathrm{IrO}}_3$, measured at ambient pressure and at $p=2.51$ GPa (b). The triangles indicate the transition temperatures as obtained from transverse-field measurements. Lines are guides to the eye.

Figure 7

Temperature dependence of the internal magnetic fields vs temperature for the Li-substituted samples where oscillations could be clearly identified (a) and as a function of applied pressure for the pure ${\mathrm{Na}}_2{\mathrm{IrO}}_3$ (b). Triangles denote the transition temperatures as obtained from weak transverse field measurements. Lines are guides to the eye.

Figure 8

Shifts (a) and FWHM widths (b) of the ${}^{23}\mathrm{Na}$ NMR lines in ${\mathrm{Na}}_2{\mathrm{IrO}}_3$, measured at 7.057 T and $p=0$ GPa from 4 to 295 K. Insets highlight the drop in shift and the increase in line width occurring at $T_{\mathrm{N}}$. Uncertainties are of the order of the marker size.

Figure 9

${\mathrm{Na}}_2{\mathrm{IrO}}_{3}1/T_1\left(T\right)$ relaxation rates from 4 to 25 K, measured at the central transition of the ${}^{23}\mathrm{Na}$ NMR lines in 7.057 T, at ambient- and at three applied hydrostatic pressures (1, 2.4, and 3.9 GPa). Inset: $\beta \left(T\right)$ variation across $T_{\mathrm{N}}$, as resulting from ambient-pressure $T_1$ measurements.

Figure 10

$T_{\mathrm{N}}$ variation upon increasing pressure. The gradient and intercept value, as determined from a straight-line fit, are shown.

Figure 11

Normalized lattice constants for different Li substitution levels. The lattice constants for $x=0$ were taken from Ref. [12].

Figure 12

The decoupling of muon spins in an applied longitudinal field indicates static magnetic moments in ${\mathrm{Na}}_{1.85}{\mathrm{Li}}_{0.15}{\mathrm{IrO}}_3$. To highlight the recovery of asymmetry, a data binning of 50 ns was chosen, exceeding that of the rest of the figures.

Figure 13

${}^{23}\mathrm{Na}$ NMR lines in ${\mathrm{Na}}_2{\mathrm{IrO}}_3$ from 4 to 295 K, measured at 7.057 T. The vertical dashed line indicates the Larmor frequency.

Figure 14

Magnetization measurements of ${\mathrm{Na}}_2{\mathrm{IrO}}_3$ in an applied field of 3 mT. The molar magnetic susceptibility vs temperature exhibits a clear change before (red line) and after the preliminary NMR measurements (blue line), reflecting a sample degradation during handling. This required a constant sample handling under Ar flow. As explained in the literature [43], the onset of magnetic order occurs at the inflection point between the minimum and the maximum, here at $\sim 15\mathrm{K}$. The dotted vertical line shows the $T_{\mathrm{N}}$ value as obtained from NMR data. Further details about the uncertainty in identifying $T_{\mathrm{N}}$ are given in the discussion section.