Molecular-based 2D S $=$ 1/2 Heisenberg Antiferromagnetic Layers and Ladders

Low dimensional Quantum Heisenberg Antiferromagnets (QHAF) have long provided materials [1] with which to examine the influence of dimensionality and exchange anisotropy on critical behavior of cooperative systems. Molecular-based QHAF have provided materials with low exchange strengths ($\approx $ 10 K), facilitating examination of the compounds up to the saturation fields using current facilities. This presentation will provide an overview of recent developments of two classes of molecular magnets: 2D QHAF and spin ladders. Recent specific heat studies of Cu(pz)$_{2}$(ClO$_{4})_{2}$ in fields up to 45 tesla have determined the (H,T) phase diagram for this quasi-2D QHAF; the results will be compared to the results of QMC simulations of the diagram as a function of the intralayer exchange $J$, the interlayer exchange $J'$, and the XY-exchange anisotropy parameter. Developments in the study of spin ladders include the discovery of Luttinger liquid behavior for two molecular-based spin layers: the strong-rung ladder BPCB, (piperidinium)$_{2}$CuBr$_{4}$ [2] and the strong-rail ladder DIMPY, (2,3-dimethypyridinium)$_{2}$CuBr$_{4}$ [3]. The properties of a new, isotropic spin ladder will be reported. \\[4pt] [1] L. J. de Jongh and A. R. Miedema, Adv. Phys. \textbf{50}, 947 (2001).\\[0pt] [2] M. Klanj\v{s}ek \textit{et al}, Phys. Rev. Lett. \textbf{101}, 137207 (2008); Ch. R\"{u}egg \textit{et al}, Phys. Rev. Lett. \textbf{101}, 247207 (2008).\\[0pt] [3] K. Ninios \textit{et al}, Phys. Rev. Lett. \textbf{108}, 097201 (2012); D. Schmidiger \textit{et al}, Phys. Rev. Lett. \textbf{108}, 167201 (2012).