Clock transitions and Dynamical Decoupling in Molecular Nanomagnets and Glass Defects

In spin systems, clock transitions (CTs), where the transition is insensitive to the decohering effects of fluctuating magnetic fields, can give rise to an enhancement of quantum coherence times [1,2]. The basic physics underlying this effect is the flatness of spin energy levels to changes in magnetic field in the vicinity of an avoided level crossing. The resulting transition frequency stability gives rise to phase stability that can substantially prolong T₂, the phase coherence time. Molecular nanomagnets provide fertile ground for exploring CT-enhanced coherence because various system parameters, such as anisotropy and hyperfine coupling, can be chemically engineered to achieve desirable properties. We studied the Cr₇Mn nanomagnet in a homemade electron-spin resonance spectrometer at frequencies of ~4 GHz and a temperature as low as 1.8 K [3]. In this system at zero magnetic field, we observe a CT-enhanced T₂ of ~1 μs that can be further enhanced to ~2.8 μs through use of the dynamical decoupling CPMG pulse sequence. When the system is tuned away from the CT, electron-spin-echo envelope modulation (ESEEM) oscillations are observed resulting from hyperfine coupling to nearby protons in the molecule and its environment. Interestingly, judiciously timed CPMG pulses can suppress these oscillations and lead to T₂ values ~3.6 μs, suggesting that ESEEM dynamics can help achieve a form of decoupling of the spin from environmental noise. CTs have also been unexpectedly found in borosilicate and aluminosilicate glasses. In these systems, we find coherence times at the zero-field CT of up to 5 μs, which can be extended to 25 μs with CPMG. The microscopic nature of these CTs remains somewhat mysterious but our observations suggest they originate from boron-vacancy (or aluminum-vacancy) centers within these glass materials.

[1] M. Shiddiq, et al., Nature 531, 348–351 (2016).

[2] C. Collett, et al., Magnetochemistry 5, 1 (2019).

[3] G. Joshi, et al., Rev. Sci. Instrum. 91, 023104 (2020).