Theory of Single-Spin Inelastic Tunneling Spectroscopy

I show that recent experiments of inelastic scanning tunneling spectroscopy of single and a few magnetic atoms are modeled with a phenomenological spin-assisted tunneling Hamiltonian so that the inelastic $dI/dV$ line shape is related to the spin spectral weight of the magnetic atom. This accounts for the spin selection rules and $dI/dV$ spectra observed experimentally for single Fe and Mn atoms deposited on ${\mathrm{Cu}}_2\mathrm{N}$. In the case of chains of Mn atoms it is found necessary to include both first and second-neighbor exchange interactions as well as single-ion anisotropy.

Figure 1

(a) Differential conductance for single Fe atom with magnetic field along the $z$ axis. (b) The same with magnetic field along the $x$ axis. (c) Scheme of the $B=0$ energy levels of Eq. (8) and the tunneling induced transitions.

Figure 2

(a) $dI/dV$ for $B=0$, $k_{B}T=0.6\mathrm{K}$ for chains of $N$ Mn atoms, $\mathcal{N}=1$, 2, 3, 4. Solid circles represent the atom underneath the tip. (b) Evolution of the $dI/dV$ for $\mathcal{N}=2$ for 3 values of $B$. (c) Evolution of the corresponding excitations. (d) Evolution of the $dI/dV$ for $\mathcal{N}=3$ for 3 values of $B$. In all the cases $\overrightarrow{B}$ lies in plane, ${55}^{°}$ from the chain.