Electron-assisted magnetization tunneling in single spin systems

Magnetic excitations of single atoms on surfaces have been widely studied experimentally in the past decade. Lately, systems with unprecedented magnetic stability started to emerge. Here, we present a general theoretical investigation of the stability of rare-earth magnetic atoms exposed to crystal or ligand fields of various symmetry and to exchange scattering with an electron bath. By analyzing the properties of the atomic wave function, we show that certain combinations of symmetry and total angular momentum are inherently stable against first or even higher-order interactions with electrons. Further, we investigate the effect of an external magnetic field on the magnetic stability.

Figure 1

Classes and transitions in fivefold rotation-symmetric environments. (a), (c) Rotational classes for integer and half-integer $J$, respectively. Each circle indicates a set of $\left|m\right.〉$ acquiring the same phase under rotation by $2\pi /5$. Empty circles show classes protected against first-order transitions. (b), (d) Transition matrix elements between states belonging to particular doublets. Asterisks at certain $J$ values indicate that higher-order protection is valid only for coherent electron scattering.

Figure 2

Classes and transitions in two-, three-, four- and sixfold rotation-symmetric environments. Each circle indicates a set of $\left|m\right.〉$ acquiring the same phase under rotation by $2\pi /q$. Empty circles show classes protected against first-order transitions. Half-empty circles indicate classes protected only at low $J$. Asterisks at certain $J$ values indicate that higher-order protection is valid only for coherent electron scattering.