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arXiv:1008.1771 · Physical Review B

Bridging frustrated-spin-chain and spin-ladder physics: Quasi-one-dimensional magnetism of BiCu 2 PO 6

Alexander A. Tsirlin, Ioannis Rousochatzakis, Deepa Kasinathan, Oleg Janson, R. Nath, Franziska Weickert, C. Geibel, Andreas Martin Läuchli, Helge Rosner

Published Oct 18, 2010• 62 citations
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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 ${J}_{2}^{\ensuremath{'}}\ensuremath{\simeq}{J}_{2}/2$. The spin ladders do not match the structural chains, and although the next-nearest-neighbor interactions ${J}_{2}$ and ${J}_{2}^{\ensuremath{'}}$ 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 $\ensuremath{\Delta}\ensuremath{\simeq}32\text{ }\text{K}$ 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.

DOI
10.1103/physrevb.82.144426

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The quantum phase transitions induced by a magnetic field are theoretically studied in a frustrated two-leg spin ladder. Using the density-matrix renormalization-group method, we find some magnetic phase transitions and plateaux in two different cases of strong and weak rung couplings. With the strong rung coupling, the three magnetization plateaux are found at 1/3, 1/2, and 2/3 due to the frustration. Those can be understood in terms of a quasi-spinon reconstructed from the singlet and the triplets of spins on a rung. The plateau at 1/2 corresponds to the valence bond solid of the quasispinons, while the plateaux at 1/3 and 2/3 can be associated with the array of quasi-spinons such as soliton lattice. This is different from the usual Bose-Einstein-condensation picture of triplons. Our results will be useful to understand magnetization curves in BiCu2_{2}2​PO6_{6}6​.