Classical phase diagram of the stuffed honeycomb lattice

We investigate the classical phase diagram of the stuffed honeycomb Heisenberg lattice, which consists of a honeycomb lattice with a superimposed triangular lattice formed by sites at the center of each hexagon. This lattice encompasses and interpolates between the honeycomb, triangular, and dice lattices, preserving the hexagonal symmetry while expanding the phase space for potential spin liquids. We use a combination of iterative minimization, classical Monte Carlo, and analytical techniques to determine the complete ground state phase diagram. It is quite rich, with a variety of noncoplanar and noncollinear phases not found in the previously studied limits. In particular, our analysis reveals the triangular lattice critical point to be a multicritical point with two new phases vanishing via second order transitions at the critical point. We analyze these phases within linear spin wave theory and discuss consequences for the S=1/2 spin liquid.