Isotropic and anisotropic spin-spin interactions and a quantum phase transition in a dinuclear Cu(II) compound

Abstract

We report electron-paramagnetic resonance (EPR) studies at $\ensuremath{\sim}9.5\text{ }\text{GHz}$ ($X$ band) and $\ensuremath{\sim}34\text{ }\text{GHz}$ ($Q$ band) of powder and single-crystal samples of the compound ${\text{Cu}}_{2}{[\text{TzTs}]}_{4}$ [$N$-thiazol-2-yl-toluenesulfonamidatecopper(II)], ${\text{C}}_{40}{\text{H}}_{36}{\text{Cu}}_{2}{\text{N}}_{8}{\text{O}}_{8}{\text{S}}_{8}$, having copper(II) ions in dinuclear units. Our data allow determining an antiferromagnetic interaction ${J}_{0}=(\ensuremath{-}113\ifmmode\pm\else\textpm\fi{}1)\phantom{\rule{0.3em}{0ex}}{\text{cm}}^{\ensuremath{-}1}$ $({\mathcal{H}}_{\text{ex}}=\ensuremath{-}{J}_{0}{\mathbf{S}}_{\mathbf{1}}\ensuremath{\cdot}{\mathbf{S}}_{\mathbf{2}})$ between Cu(II) ions in the dinuclear unit and the anisotropic contributions to the spin-spin coupling matrix $\mathcal{D}\phantom{\rule{0.3em}{0ex}}({\mathcal{H}}_{\text{ani}}={\mathbf{S}}_{1}\ensuremath{\cdot}\mathcal{D}\ensuremath{\cdot}{\mathbf{S}}_{2})$, a traceless symmetric matrix with principal values $\mathcal{D}/4=(0.198\ifmmode\pm\else\textpm\fi{}0.003)\phantom{\rule{0.3em}{0ex}}{\text{cm}}^{\ensuremath{-}1}$ and $\mathcal{E}/4=(0.001\ifmmode\pm\else\textpm\fi{}0.003)\phantom{\rule{0.3em}{0ex}}{\text{cm}}^{\ensuremath{-}1}$ arising from magnetic dipole-dipole and anisotropic exchange couplings within the units. In addition, the single-crystal EPR measurements allow detecting and estimating very weak exchange couplings between neighbor dinuclear units, with an estimated magnitude $|{J}^{\ensuremath{'}}|=(0.060\ifmmode\pm\else\textpm\fi{}0.015)\phantom{\rule{0.3em}{0ex}}{\text{cm}}^{\ensuremath{-}1}$. The interactions between a dinuclear unit and the ``environment'' of similar units in the structure of the compound produce a spin dynamics that averages out the intradinuclear dipolar interactions. This coupling with the environment leads to decoherence, a quantum phase transition that collapses the dipolar interaction when the isotropic exchange coupling with neighbor dinuclear units equals the magnitude of the intradinuclear dipolar coupling. Our EPR experiments provide a new procedure to follow the classical exchange-narrowing process as a shift and collapse of the line structure (not only as a change of the resonance width), which is described with general (but otherwise simple) theories of magnetic resonance. Using complementary procedures, our EPR measurements in powder and single-crystal samples allow measuring simultaneously three types of interactions differing by more than three orders of magnitude (between $113\phantom{\rule{0.3em}{0ex}}{\text{cm}}^{\ensuremath{-}1}$ and $0.060\phantom{\rule{0.3em}{0ex}}{\text{cm}}^{\ensuremath{-}1}$).