Temperature Dependence of the Effective Interdimeric Exchange Interaction in a Weakly Coupled Antiferromagnetic Dimeric Copper Compound

We report a variation with temperature ($T$) of the effective interdimeric interaction $J^\prime_{\mathrm{eff}}$ in the antiferromagnetic (AFM) copper dimeric organic compound Cu$_2$[TzTs]$_4$ [N-thiazol-2-yl-toluenesulfonamidate Cu$^\mathrm{II}$]. This $T$ dependence was obtained from measurements of the effects in the electron paramagnetic resonance (EPR) spectra of the proposed quantum phase transition associated to the exchange narrowing processes. Cu$_2$[TzTs]$_4$ contains exchange coupled pairs of Cu$^\mathrm{II}$ spins $\mathbf{S_\mathrm{A}}$ and $\mathbf{S_\mathrm{B}}$ ($S$ = 1/2), with intradimeric AFM exchange coupling $J_0$ = (-115$\pm$1) cm$^{-1}$ ($\mathcal{H}_\mathrm{ex} = -J_\mathrm{0} \mathbf{S_\mathrm{A}}\cdot \mathbf{S_\mathrm{B}}$). The variation of the EPR line width of single crystals with field orientation around a "magic angle" where the transitions intersect, as well as the integrated signal intensity of the so-called "U-peak" of the powder spectrum were measured as a function of $T$. Modeling these data using arguments of exchange narrowing in the adiabatic regime considering the angular variation of the single crystal spectra and a geometric description, we find that $|J^\prime_{\mathrm{eff}}|$ associated with the exchange frequency $\omega_{ex}$ is negligible for $T<<|J_\mathrm{0}/k_\mathrm{B}|$, when the units are uncoupled, and $|J^\prime_{\mathrm{eff}}|$ = (0.080 $\pm$ 0.005) cm$^{-1}$ ($|J^\prime_{\mathrm{eff}}/J_0|$ = 7.0$\times$10$^{-4}$) at 298 K. Within this $T$-interval, two ranges of $J^\prime_{\mathrm{eff}}$ with linear temperature variation but different slopes, with a kink at $\sim$80 K, are observed and discussed. This $T$-dependence arises from the growing population of the triplet state and its relevance in the properties of various arrays of DUs is discussed. Our experimental procedures and results are compared with those of previous works.