Maximized $K/J$ ratio and cubiclike $j_{\text{eff}}=\frac{1}{2}$ moments in a noncubic environment in $\alpha \text{−}{\mathrm{RuCl}}_3$ under pressure

Maximization of the ratio between Kitaev and residual Heisenberg interactions is a major goal in the current research on Kitaev-Heisenberg magnets. Here we investigate Kitaev-Heisenberg exchange in a recently discovered crystalline phase of $\alpha \text{−}{\mathrm{RuCl}}_3$ under pressure—it displays unusually high symmetry, with only one type of Ru-Ru links and uniform Ru-Cl-Ru bond angles of $\approx {93}^{\circ }$. Using quantum chemical calculations, we find a very small nearest-neighbor Heisenberg $J$, which yields a $K/J$ ratio between Kitaev and Heisenberg exchange as large as $\sim 100$. We also find that this is associated with vanishingly small $d$-shell trigonal splittings, i.e., minimal departure from ideal $j_{\mathrm{eff}}=1/2$ moments. This reconfirms ${\mathrm{RuCl}}_3$ as a most promising platform for materializing the much sought-after Kitaev spin-liquid phase and should stimulate further experiments under strain and pressure.

Figure 1

(a) Unit cell of $\alpha \text{−}{\mathrm{RuCl}}_3$ for $p=1.26$ GPa [5]. (b) Hexagonal ring of edge-sharing ${\mathrm{RuCl}}_6$ octahedra. Gray and green spheres represent Ru and Cl ions, respectively.

Figure 2

(a) Generic phase diagram for variable off-diagonal couplings $\mathrm{\Gamma }$ and ${\mathrm{\Gamma }}^{\prime }$ in units of the ferromagnetic Kitaev interaction parameter $\left|K\right|$. Inset: spin structure factor illustrating the proximate Kitaev spin liquid [28] in the QSL2 region. (b) Phase diagram for variable $\mathrm{\Gamma }$ and third-neighbor Heisenberg coupling $J_3$; $K$ and ${\mathrm{\Gamma }}^{\prime }/\mathrm{\Gamma }$ are set to –1 and 2/5, respectively. Inset: phase boundaries for additional ${\mathrm{\Gamma }}^{\prime }/\mathrm{\Gamma }$ ratios.