Theory of partial quantum disorder in the stuffed honeycomb Heisenberg antiferromagnet

Recent numerical results [Gonzalez et al., Phys. Rev. Lett. 122, 017201 (2019); Shimada et al., J. Phys. Conf. Ser. 969, 012126 (2018)] point to the existence of a partial-disorder ground state for a spin-1/2 antiferromagnet on the stuffed honeycomb lattice, with 2/3 of the local moments ordering in an antiferromagnetic Ned pattern, while the remaining 1/3 of the sites display short-range correlations only, akin to a quantum spin liquid. We derive an effective model for this disordered subsystem, by integrating out fluctuations of the ordered local moments, which yield couplings in a formal 1/S expansion, with S being the spin amplitude. The result is an effective triangular-lattice XXZ model, with planar ferromagnetic order for large S and a stripe-ordered Ising ground state for small S, the latter being the result of frustrated Ising interactions. Within the semiclassical analysis, the transition point between the two orders is located at S-c = 0.646, being very close to the relevant case S = 1/2. Near S = S-c quantum fluctuations tend to destabilize magnetic order. We conjecture that this applies to S = 1/2, thus explaining the observed partial-disorder state.