Two types of alternating spin- 1 2 chains and their field-induced transitions in ɛ − LiVOPO 4

Thermodynamic properties, $^{31}\mathrm{P}$ nuclear magnetic resonance (NMR) measurements, and density-functional band-structure calculations for $\ensuremath{\varepsilon}\text{\ensuremath{-}}{\mathrm{LiVOPO}}_{4}$ are reported. This quantum magnet features a singlet ground state and comprises two types of alternating spin-$\frac{1}{2}$ chains that manifest themselves by the double maxima in the susceptibility and magnetic specific heat, and by the two-step magnetization process with an intermediate $\frac{1}{2}$-plateau. From thermodynamic data and band-structure calculations, we estimate the leading couplings of ${J}_{1}\ensuremath{\simeq}20$ K and ${J}_{2}\ensuremath{\simeq}60$ K and the alternation ratios of ${\ensuremath{\alpha}}_{1}={J}_{1}^{\ensuremath{'}}/{J}_{1}\ensuremath{\simeq}0.6$ and ${\ensuremath{\alpha}}_{2}={J}_{2}^{\ensuremath{'}}/{J}_{2}\ensuremath{\simeq}0.3$ within the two chains, respectively. The zero-field spin gap ${\mathrm{\ensuremath{\Delta}}}_{0}/{k}_{\mathrm{B}}\ensuremath{\simeq}7.3$ K probed by thermodynamic and NMR measurements is caused by the ${J}_{1}\text{\ensuremath{-}}{J}_{1}^{\ensuremath{'}}$ spin chains and can be closed in the applied field of ${\ensuremath{\mu}}_{0}{H}_{\mathrm{c}1}\ensuremath{\simeq}5.6$ T, giving rise to a field-induced long-range order. The NMR data reveal predominant three-dimensional spin-spin correlations at low temperatures. Field-induced magnetic ordering transition observed above ${H}_{\text{c}1}$ is attributed to the Bose-Einstein condensation of triplons in the sublattice formed by the ${J}_{1}\text{\ensuremath{-}}{J}_{1}^{\ensuremath{'}}$ chains with weaker exchange couplings.