Will Spin-Relaxation Times in Molecular Magnets Permit Quantum Information Processing?

Using $X$-band pulsed electron-spin resonance, we report the intrinsic spin-lattice ($T_1$) and phase-coherence ($T_2$) relaxation times in molecular nanomagnets for the first time. In ${\mathrm{Cr}}_{7}M$ heterometallic wheels, with $M=\mathrm{Ni}$ and Mn, phase-coherence relaxation is dominated by the coupling of the electron spin to protons within the molecule. In deuterated samples $T_2$ reaches $3\mu \mathrm{s}$ at low temperatures, which is several orders of magnitude longer than the duration of spin manipulations, satisfying a prerequisite for the deployment of molecular nanomagnets in quantum information applications.

Figure 1

$X$-band echo-detected ESR as a function of magnetic field for (a) ${\mathrm{Cr}}_7\mathrm{Ni}$ and (b) ${\mathrm{Cr}}_7\mathrm{Mn}$ measured at 4.5 K (blue), and the simulated powder spectrum for a species with $S=1$, $g=2$, $D=21\mathrm{GHz}$, $E=1.9\mathrm{GHz}$ (green). In this experiment, the intensity of a Hahn-echo signal with short ($\tau =300\mathrm{ns}$) delays is measured as a function of the applied magnetic field. Selective pulses, of 64 ns for a $\pi /2$ pulse and 128 ns for a $\pi$ pulse, ensure that only spins within a window of about 0.3 mT are excited. Using a broad integration window suppresses ${}^1\mathrm{H}$ ESEEM effects. The echo intensity is proportional to the ESR excitation spectrum. The fine structure in the data close to 0.33 T is an artifact of the cavity.

Figure 2

(a) Decay of the Hahn-echo intensity in ${\mathrm{Cr}}_7\mathrm{Ni}$ as a function of delay time for long, selective pulses (64 ns $\pi /2$ pulse, 128 ns $\pi$ pulse, blue) and for short broadband pulses (16 ns $\pi /2$ pulse, 32 ns $\pi$ pulse, cyan). (b) Decay of the Hahn-echo intensity for long, selective pulses in perdeuterated ${\mathrm{Cr}}_7\mathrm{Ni}$. Dashed green lines indicate fits to the data. The fit in (b) assumes that the ESEEM effect is dominated by a single harmonic at the ${}^2\mathrm{D}$ Zeeman frequency [31]. (Note the different horizontal axis scales.)

Figure 3

(a) $T_1$ as a function of temperature in ${\mathrm{Cr}}_7\mathrm{Ni}$ (blue open circles) and ${\mathrm{Cr}}_7\mathrm{Mn}$ (red open squares). (b) $T_2$ as a function of temperature for ${\mathrm{Cr}}_7\mathrm{Ni}$ (blue open circles), ${\mathrm{Cr}}_7\mathrm{Mn}$ (red open squares), and perdeuterated ${\mathrm{Cr}}_7\mathrm{Ni}$ (blue filled circles).