Bridging frustrated-spin-chain and spin-ladder physics: Quasi-one-dimensional magnetism of BiCu₂PO₆

We derive and investigate the microscopic model of the quantum magnet BiCu₂PO₆ using band-structure calculations, magnetic susceptibility and high-field magnetization measurements, as well as exact diagonalization (ED) and density-matrix renormalization group (DMRG) techniques. The resulting quasi-one-dimensional spin model is a two-leg antiferromagnetic ladder with frustrating next-nearest-neighbor couplings along the legs. The individual couplings are estimated from band-structure calculations and by fitting the magnetic susceptibility with theoretical predictions, obtained using full diagonalizations. The nearest-neighbor leg coupling J₁, the rung coupling J₄, and one of the next-nearest-neighbor couplings J₂ amount to 120-150 K while the second next-nearest-neighbor coupling is J'₂ similar or equal to J₂/2. The spin ladders do not match the structural chains, and although the next-nearest-neighbor interactions J₂ and J'₂ have very similar superexchange pathways, they differ substantially in magnitude due to a tiny difference in the O-O distances and in the arrangement of nonmagnetic PO₄ tetrahedra. An extensive ED study of the proposed model provides the low-energy excitation spectrum and shows that the system is in the strong rung coupling regime. The strong frustration by the next-nearest-neighbor couplings leads to a triplon branch with an incommensurate minimum. This is further corroborated by a strong-coupling expansion up to second order in the inter-rung coupling. Based on high-field magnetization measurements, we estimate the spin gap of Delta-32 K and suggest the likely presence of antisymmetric Dzyaloshinskii-Moriya anisotropy and interladder coupling J(3). We also provide a tentative description of the physics of BiCu₂PO₆ in magnetic field, in the light of the low-energy excitation spectra and numerical calculations based on ED and DMRG. In particular, we raise the possibility for a rich interplay between one- and two-component Luttinger liquid phases and a magnetization plateau at 1/2 of the saturation value.