Zoology of Altermagnetic-type Non-collinear Magnets on the Maple Leaf Lattice

We define unconventional non-collinear magnetic ground states on the maple leaf lattice (MLL) distinguished by the selective breaking or preservation of time reversal ($\mathcal{T}$) and parity ($\mathcal{P}$). Depending on the nature of $\mathcal{P}\mathcal{T}$-breaking, linear spin-wave theory reveals momentum-dependent non-relativistic magnon spin splitting at different high symmetry points in the Brillouin zone. From a mean-field analysis of the Hubbard model at weak coupling, we reveal itinerant $\mathcal{P}$-preserving $q=0$ altermagnetic (A$l$M)-type order, while we expect $\mathcal{P}$-broken canted-$120^\circ$ A$l$M-type order at strong coupling. Our findings establish the MLL as a prime platform for exploring phase transitions and frustration phenomena emanating from competing non-collinear A$l$M-type orders.