Quantum magnetism on the Cairo pentagonal lattice

We present an extensive analytical and numerical study of the antiferromagnetic Heisenberg model on the Cairo pentagonal lattice, the dual of the Shastry-Sutherland lattice with a close realization in the $S=5/2$ compound Bi₂Fe₄O₉. We consider a model with two exchange couplings suggested by the symmetry of the lattice, and we investigate the nature of the ground state as a function of their ratio x and the spin S. After establishing the classical phase diagram, we switch on quantum mechanics in a gradual way that highlights the different role of quantum fluctuations on the two inequivalent sites of the lattice. The most important findings for $S=1/2$ include (i) a surprising interplay between a collinear and a four-sublattice orthogonal phase due to an underlying order-by-disorder mechanism at small x (related to an emergent J₁-J₂ effective model with J₂J₁), and (ii) a nonmagnetic and possibly spin-nematic phase with d-wave symmetry at intermediate x.