Experimental Estimates of Dephasing Time in Molecular Magnets

Muon spin relaxation measurements in isotropic molecular magnets (MM) with a spin value $S$ ranging from $7/2$ to $27/2$ are used to determine the magnitude and origin of dephasing time ${\tau }_{\varphi }$ of molecular magnets. It is found that ${\tau }_{\varphi }\sim 10\mathrm{nsec}$ with no $S$ or ligand dependence. This indicates a nuclear origin for the stochastic field. Since ${\tau }_{\varphi }$ is a property of the environment, we argue that it is a number common to similar types of MM. Therefore, ${\tau }_{\varphi }$ is shorter than the Zener and tunneling times of anisotropic MM such as ${\mathrm{Fe}}_8$ or ${\mathrm{Mn}}_4$ for standard laboratory sweep rates. Our findings call for a stochastic Landau-Zener theory in this particular case.

Figure 1

The muon spin lattice relaxation rate $1/T_1$ as a function of temperature and field in the ${\mathrm{CrNi}}_2$ ($S=7/2$) high spin molecular magnet. Inset: the solid lines show the instantaneous energy levels as a function of time in the Landau-Zener problem. Dashed line is a schematic representation of a path the spin can take when tunneling from the low energy state to the high energy state at time $t^{\prime }/t_Z$.

Figure 2

Muon $T_1$ at 100 mK vs field squared for all molecules including three from Ref. 14. The solid lines are linear fits.

Figure 3

Dephasing rate ${\tau }_{\varphi }^{-1}$ extracted from the muon relaxation data as a function of spin value $S$ of the various magnetic molecules. The solid lines are fits to power laws as indicated in the figure. $\chi$ represent the quality of the fit.