Engineering of Magnetic Coupling in Nanographene

Nanographenes with sublattice imbalance host a net spin according to Lieb’s theorem for bipartite lattices. Here, we report the on-surface synthesis of atomically precise nanographenes and their atomic-scale characterization on a gold substrate by using low-temperature noncontact atomic force microscopy and scanning tunneling spectroscopy. Our results clearly confirm individual nanographenes host a single spin of $S=1/2$ via the Kondo effect. In covalently linked nanographene dimers, two spins are antiferromagnetically coupled with each other as revealed by inelastic spin-flip excitation spectroscopy. The magnetic exchange interaction in dimers can be well engineered by tuning the local spin density distribution near the connection region, consistent with mean-field Hubbard model calculations. Our work clearly reveals the emergence of magnetism in nanographenes and provides an efficient way to further explore the carbon-based magnetism.

Figure 1

(a) Chemical structure of achieved nanographene with an embedded five-membered ring. The presence of the five-membered ring breaks the bipartite character of graphene honeycomb lattice. (b) Nc-AFM frequency shift image of an f-NG ($f_0=26\mathrm{KHz}$, oscillation amplitude of 80 pm). (c) Constant-height current image (bias voltage: 1 mV). (d) Calculated singly occupied molecular orbital shape. (e) Mean-field Hubbard model calculated energy spectrum. Left:$U=0\mathrm{eV}$; right:$U=3.5\mathrm{eV}$. (f) Calculated spin density distribution of f-NG by mean-field Hubbard model. Numbers denote spin density values. (g) Calculated spin density distribution by spin-polarized DFT. The spin delocalizes at the side without the embedded five-membered ring. Blue and red isosurfaces denote spin-up and spin-down density. Scale bars: 0.3 nm.

Figure 2

(a) $dI/dV$ spectra taken at the positions marked by colored numbers in the inset current image (Bias: 1 mV). A Kondo resonance is observed as manifested by a zero-energy peak in $dI/dV$ spectra. The peak intensity is proportional to the spatial spin density intensity. (b) Out-of-plane magnetic field dependence of the Kondo resonance. All $dI/dV$ spectra were taken at the same position. (c) Temperature dependence of the Kondo resonance. All $dI/dV$ spectra were taken at the same position. The dotted lines are simulated curves using a Frota function. (d) The full peak width at half maximum as a function of temperature. A Kondo temperature of 16 K is obtained.

Figure 3

(a) The magnetic exchange interaction $J$ as a function of the distance between two carbon atoms with the strongest spin density in each unit [the carbon atom No. 8 in (b)]. Inset: spin density distribution of six different f-NG dimers. All dimers exhibit a singlet ground state. Blue and red isosurfaces denote spin up and spin down density. (b) Chemical structure with numbered carbon atoms. The orange and blue solid circles depict sublattice $A$ and $B$. The red $C\text{−}C$ bond breaks the bipartite nature of graphene honeycomb lattice. (c) Left: spin density distributions with the $C\text{−}C$ bond length of 1.43 Å; right: with the $C\text{−}C$ bond compressed by 5%. (d) Spin density intensity at the carbon atom 2 and 28 as a function of hopping integral $t$. (e) Magnetic exchange interaction as a function of hopping integral. From left to right: $C1/C2$, $C3/C4$, and $C5/C6$.

Figure 4

(a)–(d) Experimental observed four configurations of f-NG dimers named as $C1\text{−}C4$. Left, nc-AFM frequency shift image ($f_0=26\mathrm{KHz}$ oscillation amplitude: 80 pm); middle, constant-height current image (bias: 1 mV), and right, simulated STM image. (e) $dI/dV$ spectra taken at the positions marked in (a)–(d). The $C1$ shows a Kondo resonance at both units, suggesting no magnetic coupling at 5 K. The $C2$ shows a magnetic exchange interaction of 2 mV due to the reduced bond length of the $C\text{−}C$ bond in embedded five-membered rings, revealing that magnetic exchange energy can be engineered by varying the tilted angle between neighboring units. The $C3$ and $C4$ show a magnetic exchange interaction of 3 and 3.85 meV, confirming that magnetic exchange energy can be engineered by changing the positions of embedded five-membered ring positions. (f) Magnetic exchange energy in $C1\text{−}C4$. Scale bars: 0.3 nm.