Direct Observation of Magnetic Anisotropy in an Individual ${\mathrm{Fe}}_4$ Single-Molecule Magnet

We study three-terminal charge transport through individual ${\mathrm{Fe}}_4$ single-molecule magnets. Magnetic anisotropy of the single molecule is directly observed by introducing a spectroscopic technique based on measuring the position of the degeneracy point as a function of gate voltage and applied magnetic field. A nonlinear field-dependence is observed which changes by rotating the sample and is, thus, a direct proof of magnetic anisotropy. The sensitivity of this method allows us to observe small changes in the orientation and magnitude of the anisotropy in different charge states. We find that the easy axes in adjacent states are (almost) collinear.

Figure 1

(a) Schematic drawing of a ${\mathrm{Fe}}_4$ single-molecule magnet in a three-terminal transistor geometry. A magnetic molecule bridges source and drain electrodes made by self-breaking electromigration of a gold nanowire. The gate electrode is used to access different redox states of the molecule. (b) $\Delta E$ vs $B$ calculated by numerical diagonalization of Eq. (3) for different values of $\theta ={\theta }_N={\theta }_{N+1}$. We assume $S_N=5$ and $S_{N+1}=9/2$. The anisotropy parameters are $D_N=D_{N+1}=56\mu \mathrm{eV}$ as found in bulk samples. A nonlinear dependence of $\Delta E$ upon $B$ can be observed for large values of $\theta$, which is a fingerprint of magnetic anisotropy.

Figure 2

(a) Color plot of $dI/dV$ vs $V$ and $V_g$ at $T=1.9\mathrm{K}$ and zero field. Left and right-hand blue areas (denoted by $N$ and $N+1$ to the left and right of the cross) are low differential conductance regions in which the charge state is stabilized within the ${\mathrm{Fe}}_4$. Red-dark lines (dark cross) define high-conductance regions in which single-electron transport takes place through the ${\mathrm{Fe}}_4$. The crossing point at zero bias indicates the ground state to ground state transition between two charge states. The inset shows $dI/dV$ curves as a function of $V_g$ at zero bias measured at $B=0$ and $B=8\mathrm{T}$. (b) $dI/dV$ color plot around the degeneracy point as a function of $B$ and $V_g$ measured at zero bias.

Figure 3

Coulomb peak position as a function of $B$ at two different angles ${\alpha }_1$ and ${\alpha }_2={\alpha }_1+90°$. A vertical offset of 0.1 meV is introduced for clarity. The solid lines are calculations of $\Delta E$ by numerical diagonalization of the spin Hamiltonian in Eq. (3). Fitting parameters are: $S_N=5$, $S_{N+1}=9/2$, $D_N=56\mu \mathrm{eV}$, $D_{N+1}=68\mu \mathrm{eV}$. For ${\alpha }_1$: ${\theta }_N=63°$ and ${\theta }_{N+1}=62°$. For ${\alpha }_2$: ${\theta }_N=87°$ and ${\theta }_{N+1}=85°$. Other measurements at intermediate angles $\alpha$ are shown in the Supplemental Material [17].

Figure 4

Coulomb peak position as a function of $B$ for a second sample of ${\mathrm{Fe}}_4$ measured at two different angles ${\alpha }_1$ and ${\alpha }_2={\alpha }_1+90°$. The solid lines are calculations of $\Delta E$ by numerical diagonalization of the spin Hamiltonian of the adjacent charge states. Fitting parameters are: $S_N=5$, $S_{N+1}=9/2$, $D_N=56\mu \mathrm{eV}$, and $D_{N+1}=54.5\mu \mathrm{eV}$. For ${\alpha }_1$: ${\theta }_N=90°$ and ${\theta }_{N+1}=89.5°$. For ${\alpha }_2$: ${\theta }_N=82°$ and ${\theta }_{N+1}=81°$. The inset shows the $dI/dV$ color plot around the degeneracy point as a function of $V_g$ and $B$ at ${\alpha }_1$.