Antiferromagnetic resonance in the cubic iridium hexahalides $({\mathrm{NH}}_4{)}_2{\mathrm{IrCl}}_6$ and ${\mathrm{K}}_2{\mathrm{IrCl}}_6$

We report on high-field electron spin resonance studies of two iridium hexahalide compounds ${\left({\mathrm{NH}}_4\right)}_2{\mathrm{IrCl}}_6$ and ${\mathrm{K}}_2{\mathrm{IrCl}}_6$. In the paramagnetic state, our measurements reveal isotropic $g$ factors $g=1.79\left(1\right)$ for the ${\mathrm{Ir}}^{4+}$ ions, in agreement with their cubic symmetries. Most importantly, in the magnetically ordered state, we observe two magnon modes with zero-field gaps of 11.3 and 14.2 K for ${\left({\mathrm{NH}}_4\right)}_2{\mathrm{IrCl}}_6$ and ${\mathrm{K}}_2{\mathrm{IrCl}}_6$, respectively. Based on that and using linear spin-wave theory, we estimate the nearest-neighbor exchange couplings and anisotropic Kitaev interactions $J_1/k_B=10.3\mathrm{K},$ $K/k_B=0.7\mathrm{K}$ for ${\left({\mathrm{NH}}_4\right)}_2{\mathrm{IrCl}}_6,$ and $J_1/k_B=13.8\mathrm{K},$ $K/k_B=0.9\mathrm{K}$ for ${\mathrm{K}}_2{\mathrm{IrCl}}_6$, revealing the nearest-neighbor Heisenberg coupling as the leading interaction term, with only a weak Kitaev anisotropy.

Figure 1

(a) Schematic view of the type-III antiferromagnetic spin structure of the ${\mathrm{IrCl}}_6$ fcc lattice with four sublattices. Spins belonging to different sublattices are shown in red, green, blue, and orange colors. (b) Schematic representation of nearest-neighbor ${\mathrm{Cl}}^{-}$-mediated superexchange pathways across the parallel edges of the octahedra formed by chlorine atoms. The Ir ions are shown in gray while the Cl ions are in green color.

Figure 2

Normalized ESR spectra measured in single-crystalline ($H\parallel \left[111\right]$ and $H\perp \left[111\right]$) and powder samples of (a) ${\left({\mathrm{NH}}_4\right)}_2{\mathrm{IrCl}}_6$ and (b) ${\mathrm{K}}_2{\mathrm{IrCl}}_6$ at 50 K. The spectra are offset for clarity. Lorentzian fits to the powder sample are shown by the dashed red lines, while simulation of the single-crystal spectra are shown by the dashed blue lines.

Figure 3

(a) Temperature dependence of the resonance field (closed squares) and linewidth (open squares) measured in ${\left({\mathrm{NH}}_4\right)}_2{\mathrm{IrCl}}_6$ at 270 GHz. (b) Examples of normalized ESR spectra recorded at 270 GHz and different temperatures. The spectra are offset for clarity. Magnetic field is applied along the [111] direction.

Figure 4

(a) Temperature dependence of the resonance field (solid squares) and linewidth (open squares) measured in ${\mathrm{K}}_2{\mathrm{IrCl}}_6$ at 356 GHz. (b) Examples of normalized ESR spectra recorded at 356 GHz and different temperatures. The spectra are offset for clarity. Magnetic field is applied along the [111] direction.

Figure 5

Frequency-field diagram of ESR excitations in ${\left({\mathrm{NH}}_4\right)}_2{\mathrm{IrCl}}_6$ measured at 1.5 K with magnetic field applied parallel to the [111] direction. The dashed lines represent linear fits using Eq. (1).

Figure 6

Examples of normalized ESR spectra for ${\left({\mathrm{NH}}_4\right)}_2{\mathrm{IrCl}}_6$ at different frequencies and $T=1.5\mathrm{K}$ with $H\parallel \left[111\right]$. The spectra are offset for clarity.

Figure 7

Frequency-field diagram of ESR excitations in ${\mathrm{K}}_2{\mathrm{IrCl}}_6$ measured at 1.5 K with magnetic field applied parallel to the [111] direction. The dashed lines represent linear fits using Eq. (1). In the inset, examples of normalized ESR spectra for ${\mathrm{K}}_2{\mathrm{IrCl}}_6$ at different frequencies and $T=1.5\mathrm{K}$ with $H\parallel \left[111\right]$ are shown. The spectra are offset for clarity.