Intercalant-mediated Kitaev exchange in ${\mathrm{Ag}}_3{\mathrm{LiIr}}_2{\mathrm{O}}_6$

The recently synthesized ${\mathrm{Ag}}_3{\mathrm{LiIr}}_2{\mathrm{O}}_6$ has been proposed as a Kitaev magnet in proximity to the quantum spin liquid phase. We explore its microscopic Hamiltonian and magnetic ground state using many-body quantum chemistry methods and exact diagonalization techniques. Our calculations establish a dominant bond dependent ferromagnetic Kitaev exchange between Ir sites and find that the inclusion of Ag $4d$ orbitals in the configuration interaction calculations strikingly enhances the Kitaev exchange. Furthermore, using exact diagonalization of the nearest-neighbor fully anisotropic $J\text{−}K\text{−}\mathrm{\Gamma }$ Hamiltonian, we obtain the magnetic phase diagram as a function of further neighbor couplings. We find that the antiferromagnetic off-diagonal coupling stabilizes long range order, but the structure factor calculations suggest that the material is very close to the quantum spin liquid phase and the ordered state can easily collapse into a liquid by small perturbations such as structural distortion or bond disorder.

Figure 1

Honeycomb network formed by edge sharing ${\mathrm{IrO}}_6$ octahedra in ${\mathrm{Ag}}_3{\mathrm{LiIr}}_2{\mathrm{O}}_6$. The ${\mathrm{Ag}}^{+}$ ions are located in such a way that an interlayer connectivity is realized through linear O-Ag-O chains [23].

Figure 2

Magnetic phase diagram in the ${\mathrm{\Gamma }}_{xy}-{\mathrm{\Gamma }}_{yz}$ plane for $J=-0.3$ meV, $K=-11.2$ meV, $J_2=J_3=0$ meV. Possible magnetic phases are shown along with schematic drawings of spin configurations.

Figure 3

(a) Brilluion zone, smaller hexagon being the first BZ; Structure factor plots for (b) ${\mathrm{Ag}}_3{\mathrm{LiIr}}_2{\mathrm{O}}_6$, (c) ${\mathrm{Na}}_2{\mathrm{IrO}}_3$ [32], and (d)-(f) the Kitaev-Heisenberg model with parameters (in meV) as indicated; (g), (h) Static structure factor $S(Q_x=0,Q_y)$ for (b), (d)-(f).