#### Abstract

We derive and investigate the microscopic model of the quantum magnet ${\text{BiCu}}_{2}{\text{PO}}_{6}$ 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 ${J}_{1}$, the rung coupling ${J}_{4}$, and one of the next-nearest-neighbor couplings ${J}_{2}$ amount to 120–150 K while the second next-nearest-neighbor coupling is ${J}_{2}^{\prime}\simeq {J}_{2}/2$. The spin ladders do not match the structural chains, and although the next-nearest-neighbor interactions ${J}_{2}$ and ${J}_{2}^{\prime}$ 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 ${\text{PO}}_{4}$ 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 $\Delta \simeq 32\text{\hspace{0.5em}}\text{K}$ 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 ${\text{BiCu}}_{2}{\text{PO}}_{6}$ 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.

- Received 12 July 2010

DOI:https://doi.org/10.1103/PhysRevB.82.144426

©2010 American Physical Society