Single-component molecular material hosting antiferromagnetic and spin-gapped Mott subsystems

We investigated a system based solely on a single molecular species, $\text{Cu}({\mathrm{tmdt})}_2$, accommodating $d$ and $\pi$ orbitals within the molecule. ${}^{13}\mathrm{C}$ nuclear magnetic resonance measurements captured singlet-triplet excitations of $\pi$ spins indicating the existence of a $\pi$-electron-based spin-gapped Mott insulating subsystem, which has been hidden by the large magnetic susceptibility exhibited by the $d$ spins forming antiferromagnetic chains. The present results demonstrate a unique hybrid Mott insulator composed of antiferromagnetic and spin-singlet Mott subsystems with distinctive dimensionalities.

Figure 1

Structural, orbital, and magnetic properties of $\mathrm{Cu}{\left(\mathrm{tmdt}\right)}_2$. (a) Molecular structure of $\mathrm{Cu}{\left(\mathrm{tmdt}\right)}_2$. Selectively enriched ${}^{13}\mathrm{C}$ isotopes are labeled in the outers of the double-bonded carbons in the center of the tmdt ligands. (b) Crystal structure of $\mathrm{Cu}{\left(\mathrm{tmdt}\right)}_2$. The $dp\sigma$ orbital is populated on the central ${\mathrm{CuS}}_4$ (yellow-colored part) and the $p\pi$ orbital is mainly populated in the blue-colored region in the tmdt ligand. (c) Energy levels of the $p\pi$ and $dp\sigma$ orbitals in $\mathrm{Ni}{\left(\mathrm{tmdt}\right)}_2$ and $\mathrm{Cu}{\left(\mathrm{tmdt}\right)}_2$. [10, 11] (d) Temperature dependence of the spin susceptibility, which is obtained by subtracting a low-$T$ Curie term from the raw data [17]. The blue line indicates the Bonner-Fischer-type fitting curve. The deviation of measured data from the fitted curves for $T>250$ K is indicated as the blue region in both the main panel and the inset.

Figure 2

${}^{13}\mathrm{C}$ nuclear magnetic resonance spectra and their analysis for $\mathrm{Cu}{\left(\mathrm{tmdt}\right)}_2$. (a) ${}^{13}\mathrm{C}$ NMR spectra of $\mathrm{Cu}{\left(\mathrm{tmdt}\right)}_2$ and the $p\pi$ electron conductor $\mathrm{Ni}{\left(\mathrm{tmdt}\right)}_2$ at room temperature. The ${}^{13}\mathrm{C}$ NMR spectrum of nonmagnetic $\mathrm{Zn}{\left(\mathrm{tmdt}\right)}_2$ at 51 K used for reference to the isotropic part of the chemical shift (a gray dashed line), ${\sigma }_{\mathrm{iso}}$ $\left(=126\mathrm{ppm}\right)$, is also shown. (b) Temperature dependence of the ${}^{13}\mathrm{C}$ NMR spectra for $\mathrm{Cu}{\left(\mathrm{tmdt}\right)}_2$. The colored regions in the spectra are used to determine the isotropic component of the Knight shift because tails without color are considered to originate from impurity phases. (c) Temperature dependence of the isotropic part of the ${}^{13}\mathrm{C}$ NMR shift, $K_{\mathrm{iso}}$. The value of $K_{\mathrm{iso}}$ is determined by subtracting ${\sigma }_{\mathrm{iso}}$ from that of the measured NMR shift, ${\delta }_{\mathrm{iso}}$. The error bar is defined by the inhomogeneous width obtained in the spectral fitting (see Supplemental Material [21]). The solid curve is the magnetic susceptibility scaled to the shift values for $T<140$ K. The colored region indicates the deviation of $K_{\mathrm{iso}}$ from the scaled magnetic susceptibility, $\mathrm{\Delta }{K}_{\mathrm{iso}}$, for temperatures above 150 K, which can be attributed to the singlet-triplet excitations of the $p\pi$ spins.

Figure 3

Nuclear spin-lattice relaxation rate, $T_1^{-1}$, for $\mathrm{Cu}{\left(\mathrm{tmdt}\right)}_2$. The green triangles and the red circles indicate $T_1^{-1}$ at the ${}^{13}\mathrm{C}$ and ${}^1\mathrm{H}$ sites (denoted as ${}^{13}T_1^{-1}$ and ${}^{1}T_1^{-1}$, respectively, in the main text). ${}^{1}T_1^{-1}$ data are from Ref. [18]. ${}^{13}T_1^{-1}$ and ${}^{1}T_1^{-1}$ are plotted so that they coincide with each other at $T=J_d$ $(=169$ K). The deviation of ${}^{13}T_1^{-1}$ from ${}^{1}T_1^{-1}$ normalized to ${}^{13}T_1^{-1}$ at $T=J_d$, (denoted as ${}^{\pi }{T}_1^{-1}$ in the text) for temperatures above 200 K, represented by the colored region, is plotted using blue squares.

Figure 4

NMR evidence for a spin gap and its structural reasoning for $\mathrm{Cu}{\left(\mathrm{tmdt}\right)}_2$. Activation plots for the $p\pi$-spin part of (a) ${}^{13}\mathrm{C}$ relaxation rate, ${}^{\pi }{T}_1^{-1}$, and (b) the isotropic component of ${}^{13}\mathrm{C}$ NMR shift multiplied by temperature, $\mathrm{\Delta }{K}_{\mathrm{iso}}T$. The inset of (a) is the activation plot of ${{(}^{\pi }{T}_{1}T)}^{-1}$. (c) The two-dimensional network of tmdt ligands in the $ab$ plane. Bonds between the tmdt ligands with significant transfer integrals are indicated as A: $\left[100\right]$, B: $\left[111\right]$, and Q: $\left[001\right]$; the transfer integrals are $t_{\mathrm{A}}=-90\mathrm{meV},t_{\mathrm{B}}=250\mathrm{meV}$, and $t_{\mathrm{Q}}=134\mathrm{meV}$ [19]. The thickness of the bonding lines is proportional to the values of the transfer integrals. (d) Spin model for the $p\pi$ electrons localized on the tmdt ligands corresponding to (c). The bonding lines are drawn such that their thickness is proportional to the exchange interaction $J_i=4t_i^2/U_{p\pi }$ $(i=$ A, B, and Q) with the on-site Coulomb repulsive energy $U_{p\pi }$.