Spin excitations in the quasi-two-dimensional charge-ordered insulator $\alpha$-(BEDT-TTF)${}_2$I${}_3$ probed via ${}^{13}$C NMR

The spin excitations from the nonmagnetic charge-ordered insulating state of $\alpha$-(BEDT-TTF)${}_2$I${}_3$ at ambient pressure have been investigated by probing the static and low-frequency dynamic spin susceptibilities via site-selective nuclear magnetic resonance at ${}^{13}$C sites. The site-dependent values of the shift and the spin-lattice relaxation rate $1\mathrm{/}{T}_1$ below the charge-ordering transition temperature ($T_{CO}\approx$ 135 K) demonstrate a spin density imbalance in the unit cell, in accord with the charge-density ratio reported earlier. The shift and $1\mathrm{/}{T}_1$ show activated temperature dependence with a static (shift) gap ${\mathrm{\Delta }}_S\approx$ 47-52 meV and a dynamic ($1\mathrm{/}{T}_1$) gap ${\mathrm{\Delta }}_R\approx$ 40 meV. The sizes of the gaps are well described in terms of a localized spin model, where spin one-half antiferromagnetic dimer chains are weakly coupled with each other.