Electrical control over the Fe(II) spin crossover in a single molecule: Theory and experiment

We report on theoretical and experimental work involving a particular molecular switch, an [Fe${}^{\mathrm{II}}$(L)${}_2$]${}^{2+}$ complex, that utilizes a spin transition (“crossover”). The hallmark of this transition is a change of the spin of the metal ion, $S_{\mathrm{Fe}}=0$ to $S_{\mathrm{Fe}}=2$, at fixed oxidation state of the Fe ion. Combining density functional theory and first principles calculations, we demonstrate that within a single molecule this transition can be triggered by charging the ligands. In this process the total spin of the molecule, combining metal ion and ligands, crosses over from $S=0$ to $S=1$. Three-terminal transport through a single molecule shows indications of this transition induced by electric gating. Such an electric field control of the spin transition allows for a local, fast, and direct manipulation of molecular spins, an important prerequisite for molecular spintronics.

Figure 1

Schematic representation of the spin transition of octahedrally coordinated ${\mathrm{M}}^{\mathrm{II}}$ metal ions: two different $d^6$ electronic configurations with closed (low spin, LS) and open shell (high spin, HS) are accessible. The orbital population depends on the octahedral energy splitting ${\Delta }_{\mathrm{oct}}$, which is due to the electronic Coulomb repulsion and controlled by the ligand system.

Figure 2

Top: Atomic structure of the complexes 1 $([\mathrm{Fe}(\mathrm{bpp}{)}_2{]}^{2+})$, bpp—bispyrazolyl pyridine 2 $([\mathrm{Fe}(\mathrm{tpy}{)}_2{]}^{2+})$, tpy—terpyridine and 3 $([\mathrm{Ru}(\mathrm{bpp}{)}_2{]}^{2+})$. (The molecular complex used in the experiment has in addition to 1 pyridine anchor groups.) Colors: dark gray: carbon; cyan (light gray): nitrogen; red (gray): iron; magenta (gray): ruthenium; hydrogen atoms are not displayed. Bottom: model geometry of a single molecule transport measurement.[8, 13, 32, 33, 34] The surrounding cylinder models an electrolyte gate.

Figure 3

Metal-organic complex Fe${}^{\mathrm{II}}$(bpp)${}_2^{2+}$: Left: low spin (narrow) and high spin (wide) geometries (Fe${}^{\mathrm{II}}$: red (dark gray), C: gray, N: turquoise(light gray)). Right: Spin density of the molecule with two additional electrons. The plot highlights the antiferromagnetic couplings between the excess electrons (located on the ligands, red) and the high spin core (blue).

Figure 4

Schematic representation illustrating the dependency of the energy of the Fe${}^{\mathrm{II}}$ $(\mathrm{bpp}){}_2^{2+}$ complex on the geometry, here represented by the (averaged) distance between the Fe${}^{\mathrm{II}}$ ion and the ligand based N atoms. Black lines: the complex at $Q=+2$, no excess charge. Red lines: same complex with two extra electrons, $Q=0$.

Figure 5

Left: The spin transition complex together with the linker units that were employed in the experimental measurements: $[\mathrm{Fe}-(\mathrm{L}{)}_2{]}^{2+}]$ complex [$L=4^{\prime }-(4^{‴}-$pyridyl)$-1,2^{\prime }:6^{\prime }{1}^{″}$-bis-(pyrazolyl)pyridine]. Right: Schematic representation of the three-terminal molecular junction setup.

Figure 6

(a) Differential conductance of sample A vs source-drain ($V_{\mathrm{b}}$) and gate ($V_{\mathrm{g}}$) voltages. (b) Zoom of the differential conductance plot. The red (gray) arrows indicate the diagonal line discussed as an electrostatic shift in Sec. 3. (c) Differential conductance traces (from top to bottom) vs $V_{\mathrm{b}}$ taken at gates voltages of, respectively, 2, 2.4, 2.9, and 3.3 V. The black (red/gray) traces correspond to gates voltages on the left (right) hand side of the diagonal line.

Figure 7

(a) Differential conductance of sample B vs source-drain ($V_{\mathrm{b}}$) and gate ($V_{\mathrm{g}}$) voltages. (b) and (c) Zoom of the differential conductance plot. The red (gray) arrows indicate the diagonal line discussed as an electrostatic shift in Sec. 3. (d) Differential conductance traces (from a to e) vs $V_{\mathrm{b}}$ taken at gate voltages of, respectively, 0.8, 0.9, 1.15, 1.2, and 1.25 V. The black (red/gray) traces correspond to gates voltages on the left (right) hand side of the diagonal line. From the full width at half height of the trace a we estimate a Kondo temperature $T_{\mathrm{K}}^{\mathrm{B}}\approx 25$ K.

Figure 8

(a) and (b) Temperature dependence of differential conductance traces of sample A vs $V_{\mathrm{b}}$ taken, respectively, for $V_{\mathrm{g}}=2.2$ V and $V_{\mathrm{g}}=3.2$ V. (c) Temperature dependence of the zero bias conductance in (a) and (b). The red (light gray) and blue (dark gray) lines represent the fits obtained from the analytical fitting functions[29] of the form $G_S(T)=G(0)f_S(T/T_{\mathrm{K}})+G_{\mathrm{bg}}$. For $S=1/2$ the parameters are $G(0)=0.061e^2/h$, $T_{\mathrm{K}}=56$ K, and for $S=1$ they are $G(0)=0.064e^2/h$, $T_{\mathrm{K}}=73$ K, with $G_{\mathrm{bg}}=0.025e^2/h$ for both fits.

Figure 9

(a) Simulation of the differential conductance vs source-drain ($V_{\mathrm{b}}$) and gate ($V_{\mathrm{g}}$) voltages calculated for $T=4.2$ K. (b) Schematic representation of the double-dot system. T: transfer dot, S: spectator dot. (c) Schematic representation of molecule-electrode contacts realizing the double-dot system.

Figure 10

Two highest occupied molecular orbitals (HOMO-1 and HOMO) of [Fe${}^{\mathrm{II}}$(L)${}_2^{-}$]${}^0$. A green (light gray) dot represents a positive, point-like countercharge, 5.29 Å above the outermost pyridine ring.

Figure 11

Genealogy of the Kohn-Sham orbitals from DFT. Left column of a term scheme indicates five degenerate $3d$ orbitals of the free Fe(II) atom. Center column displays spectra of $[\mathrm{Fe}(\mathrm{bpp}{)}_2{]}^{2+}$ (left set) and $[\mathrm{Fe}(\mathrm{bpp}{)}^{-}{}_2]{}^0$ (two right sets). Right column indicates the frontier states of the complex $[\mathrm{Fe}(\mathrm{bpp}{)}_2]{}^Q$ after the replacement Fe(II)$\to$Mg(II) serving as the reference state for the ligand orbitals. The relative energies in a given term scheme, center and right column, have been obtained with the TPSSH functional. Colors: red (gray)/pink (light gray) orbitals are preferentially located on the ligands, blue (dark gray)/magenta (gray) orbitals on the metal core. Chemical potential ($E_F$) is placed in the middle of the HOMO-LUMO gap.

Figure 12

Schematic representation of the double-dot system in the external dot scenario.

Figure 13

Easy axis tilting geometry used in order to estimate the impact of molecular deformations on total energies and exchange couplings (Table ).