Kondo effect in binuclear metal-organic complexes with weakly interacting spins

We report a combined experimental and theoretical study of the Kondo effect in a series of binuclear metal-organic complexes of the form $\left[{\left(\mathrm{Me}\right(\mathrm{hfacac})}_2{)}_2\left(\mathrm{bpym}\right)\right]{}^0$, with Me = nickel (II), manganese (II), zinc (II); hfacac = hexafluoroacetylacetonate, and bpym = bipyrimidine, adsorbed on Cu(100) surface. While Kondo features did not appear in the scanning tunneling spectroscopy spectra of nonmagnetic ${\mathrm{Zn}}_2$, a zero bias resonance was resolved in magnetic ${\mathrm{Mn}}_2$ and ${\mathrm{Ni}}_2$ complexes. The case of ${\mathrm{Ni}}_2$ is particularly interesting as the experiments indicate two adsorption geometries with very different properties. For ${\mathrm{Ni}}_2$ complexes we have employed density functional theory to further elucidate the situation. Our simulations show that one geometry with relatively large Kondo temperatures $T_{\mathrm{K}}\sim 10$ K can be attributed to distorted ${\mathrm{Ni}}_2$ complexes, which are chemically bound to the surface via the bipyrimidine unit. The second geometry we assign to molecular fragmentation: we suggest that the original binuclear molecule decomposes into two pieces, including Ni(hexafluoroacetylacetonate)${}_2$, when brought into contact with the Cu substrate. For both geometries our calculations support a picture of the $\left(S=1\right)$-type Kondo effect emerging due to open $3d$ shells of the individual ${\mathrm{Ni}}^{2+}$ ions.

Figure 1

Structure of the ${\left(\mathrm{Me}\right(\mathrm{hfacac})}_2{)}_2\left(\mathrm{bpym}\right)$ complex. Each metal ion ${\mathrm{Me}}^{2+}$ is linked with two hexafluoroacetylacetonate (hfacac) ligands by Me-O bonds. By forming N-Me bonds the aromatic 2,2'-bipyrimidine (bpym) ligand coordinates as bidentate chelate with two of the Me(hfacac)${}_2$ components.

Figure 2

Topography of (a) ${\mathrm{Mn}}_2\text{−}\gamma$, (b) ${\mathrm{Ni}}_2\text{−}\alpha$, (c) ${\mathrm{Ni}}_2\text{−}\beta$, (d) ${\mathrm{Zn}}_2\text{−}\alpha$, and (e) ${\mathrm{Zn}}_2\text{−}\gamma$. [Images (a)–(e) are squares of side length of 3.7, 2.8, 2.5, 2,9, and 3.3 nm, respectively. Feedback conditions are 100 mV and 1 nA, 200 mV and 200 pA, $-10$ mV and 200 pA, 15 mV and 1 nA, 100 mV and 1 nA, respectively.] The orientation of $\beta$ and $\gamma$ configuration follows [001] and [011] direction of the substrate, respectively, while the orientation of $\alpha$ configuration seems to be random. The differential conductance $dI/dU$ near the Fermi level is shown in (f). The black dots are experimental data which were fitted with Fano functions (red lines). The STM images and STS were measured at 4.2 K. The spectra are normalized and a linear background was considered to obtain reasonable fitting result.

Figure 3

Topography of ${\mathrm{Ni}}_2\text{−}\alpha$ (a) and ${\mathrm{Ni}}_2\text{−}\beta$ (b). STS on different position of the ${\mathrm{Ni}}_2\text{−}\alpha$ is shown in (c) ($T=1$ K, feedback conditions: $U=10$ mV, $I=20$ nA, $200\mu \mathrm{V}$ modulation). STS $(dI/dU)$ map of ${\mathrm{Ni}}_2\text{−}\beta$ is shown in (d). White areas indicate large differential conduction, black low ($T=5$ K, feedback conditions $U=10$ mV, $I=10$ nA). An intuitive assumption for the adsorption configurations of ${\mathrm{Ni}}_2\text{−}\alpha$ and ${\mathrm{Ni}}_2\text{−}\beta$ (front view) on the Cu(100) substrate is shown in (e) and (f), respectively.

Figure 4

(a) Ni(hfacac)${}_2$ moiety bound to a Cu(001) surface via a Ni atom placed at the hollow site. (b) Estimated dependence of the binding energy of Ni(hfacac)${}_2$ to Cu (001) surface, including contributions due to vdW forces [62], on the angle that fixes the orientation of the moiety's mirror planes vs the [001] direction of the fcc (001) surface. (c) Experimentally recorded topographic ${\mathrm{Ni}}_2\text{−}\alpha$ STM image (reproduced from Fig. 2), where color coding is identical to Fig. 4. (d) Simulated image of Ni(hfacac)${}_2$, computed employing vasp package [63]: different colors refer to isosurfaces of the space-resolved (local) density of states (DOS) at the Fermi level. (e) Simulated image of Ni(hfacac)${}_2$, computed employing aitranss package [64, 65]: selected three-dimensional isosurface of the space-resolved DOS (above the molecule) integrated over the energy window 0.1 eV around the Fermi level is shown, where color coding refers to the distance $\mathrm{\Delta }z$ to the Cu surface. Consistent with experimental STM image, simulated images obey two mirror planes and outermost contours with a butterfly shape.

Figure 5

Upper plot: spin dependent local density of states projected on Ni atom of the Ni(hfacac)${}_2$ on Cu(001). Red and blue lines highlight contributions to the LDOS associated with Ni $d_{z^2}$ and $d_{xy}$ orbitals. Lower plots: corresponding Kohn-Sham wave functions of the free standing molecule.

Figure 6

Experimentally recorded (a), (b) ${\mathrm{Ni}}_2\text{−}\beta$ and simulated STM images of the ${\mathrm{Ni}}_2$ complex, with partially weakened chemical bonds, bound to Cu(001) via the bpym moiety [see lower plot (g)]. Theoretical images are computed with vasp [63] (c),(d) and AITRANSS [65] (e),(f). Images (c) and (e) are obtained assuming symmetry constrains within the DFT relaxation procedure, while images (d) and (f) correspond to the relaxed structure without constrains (see text for further details). Lower plot (g) shows distorted ${\mathrm{Ni}}_2$ complex with partially weakened chemical bonds bound to Cu(001) via (bpym) moiety.

Figure 7

Upper plot: spin-dependent local density of states projected on one of the Ni atoms of the distorted ${\mathrm{Ni}}_2$ complex deposited on Cu(001) [for a geometrical arrangement, see Fig. 6]. Middle (zoomed in) plot shows majority (up-) spin spectral function below the Fermi level, where contributions are highlighted arising from four orbitals ($a$, $b$, $a^{\prime }$, and $b^{\prime }$), each carrying one unpaired spin. Corresponding wave functions are presented below. There $a$ and $b$ are localized on the left-hand side, while $a^{\prime }$ and $b^{\prime }$ are localized on the right-hand side of the molecular complex.

Figure 8

Differential conductance $dI/dU$ of ${\mathrm{Ni}}_2\text{−}\beta$ measured at different temperatures. Sidebands at 30 mV are surrounding the Kondo resonance at zero bias. Feedback conditions: $U=50$ mV, $I=1$ nA, 2 mV modulation.

Figure 9

(a) and (b) Kohn-Sham spectral function of ${\mathrm{Ni}}_2$ complex at Cu surface in the minority spin channel: (a) ${\mathrm{Ni}}_2$ complex with local $C_{2v}$ symmetry; (b) ${\mathrm{Ni}}_2$ complex relaxed at surface without symmetry constrains. Lower plot (c) shows frontier (minority-spin) unoccupied molecular orbitals.

Figure 10

Dimensionless electron-phonon (el-ph) coupling constants (a) between the “Kondo-active” molecular orbital ${\psi }_K$ shown in (b) and low-energy vibrational eigenmodes, which are forced to be localized in the vicinity of ${\mathrm{Ni}}^{2+}$ ion at the right-hand side of the molecule (see text for details). Plot (c) is a visual representation of the mode (atomic displacements are scaled by $\times 10$) with energy $\hslash {\omega }_1=25.1$ meV exhibiting the largest el-ph coupling constant $\approx 0.75$.