Incommensurate Spin-Density Waves in a Frustrated Maple-Leaf Lattice Ferromagnet

Abstract

We study how ferromagnetism breaks down in the spin-$\frac{1}{2}$ nearest-neighbor Heisenberg model on the maple-leaf lattice with ferromagnetic $J_t,J_d$ and antiferromagnetic $J_h$, motivated by the mixed ferro-antiferromagnetic interactions in Na${}_2$Mn${}_3$O${}_7$. Exact diagonalization shows that the ferromagnetic boundary does not feature a zero-field spin-nematic phase on the clusters studied here, but an extended regime of incommensurate spin-density-wave correlations with continuously evolving ordering vector. The phase diagram also contains collinear Néel, canted $120^{\circ }$, and hexagonal-singlet regimes, separated by regions that remain difficult to classify from exact diagonalization alone. Variational tests of fully symmetric Gutzwiller-projected Abrikosov-fermion U(1) and ${\mathbb{Z}}_2$ states find no competitive spin-liquid description of the interior unresolved regions. By contrast, on the ruby-lattice boundary we identify a point between the collinear Néel and hexagonal-singlet phases where a projected ${\mathbb{Z}}_2$ Ansatz reproduces the finite-size energy and spin correlations with good accuracy.

16 pages, 9 figures, comments welcome!