General scheme for stable single and multiatom nanomagnets according to symmetry selection rules

At low temperature, information can be stored in the orientation of the localized magnetic moment of an adatom. However, scattering of electrons and phonons with the nanomagnet leads its state to have incoherent classical dynamics and might cause fast loss of the encoded information. Recently, it has been understood that such scattering obeys certain selection rules due to the symmetries of the system. By analyzing the point-group symmetry of the surface, the time-reversal symmetry and the magnitude of the adatom effective spin, we identify which nanomagnet configurations are to be avoided and which are promising to encode a stable bit. A new tool of investigation is introduced and exploited: the quasispin quantum number. By means of this tool, our results are easily generalized to a broad class of bipartite cluster configurations where adatoms are coupled through Heisenberg-like interactions. Finally, to make contact with the experiments, numerical simulations have been performed to show how such stable configurations respond to typical scanning tunneling microscopy measurements.

Figure 1

(a)–(d) Atoms deposited on different surfaces with $C_{\chi v}$ symmetry. $\chi =2,3,4,\text{and}6$, respectively, for the adatoms (a), (b), (c), and (d). (Bottom right) Sketch of a scanning tunneling microscope current measurement to infer the total momentum of the adatom. The tip of the microscope (in grey) exchanges electrons with the surface through the adatom.

Figure 2

(a) Periodic Brillouin zones (BZs) for integer spin systems (top) and half-integer ones (bottom). To better visualize the periodicity of the BZs, their elements (the little circles) are placed at the complex eigenvalues of $R$ and the number they contain indicates the associated quasispin. Blue(red) arrows indicate SE transitions with transfer of positive(negative) quasispin. (b) Typical spectrum of a three-fold rotation symmetric system with small transversal anisotropy. On horizontal axis is the average magnetization along $z$ of the levels. The color code of the level indicates its quasispin according to the top left case in (a). All figures are adapted from Ref. [22].

Figure 3

Bias-dependent switching rate of a spin with $J=13/2...17/2$ in a sixfold rotational symmetric crystal ($\chi =6$). Other parameters are ${\kappa }^2/D=0.1,{\alpha }_6^6/D=5\times {10}^{-5}, kT/D=0.01$, and $P=0.1$ ($P$ is the tip polarization) and $\mathrm{\Delta }$ is the first excitation energy of the spin.

Figure 4

Zero-bias temperature dependency of the switching rate of a spin with $J=13/2,...,17/2$ in a sixfold rotational symmetric crystal ($\chi =6$). Other parameter as in in Fig. 3.

Figure 5

Magnetic field dependency of the switching rate of a spin with $J=13/2,7,\text{and}17/2$ in a sixfold symmetric crystal ($\chi =6$) for $eV/D=6$ and other parameters as in Fig. 3.

Figure 6

Bias-dependent switching rate of a dimer with spin magnitudes $J_1$ and $J_2$ in a sixfold symmetric crystal ($\chi =6$), at different strength of the exchange coupling $G_{12}$ (in unit of $D$). The tip is placed on top of the first atom, i.e., ${\kappa }_1^2/D=0.1$ and ${\kappa }_2^2/D=0$. Here, ${\alpha }_6^6/D=1·{10}^{-3}$, all other parameters are as in Fig. 3.

Figure 7

Same as in Fig. 6 but for a dimer with different spin magnitudes.