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A 9.2-GHz clock transition in a Lu(II) molecular spin qubit arising from a 3,467-MHz hyperfine interaction

Nature Chemistry volume 14, pages 392–397 (2022)Cite this article

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Abstract

Spins in molecules are particularly attractive targets for next-generation quantum technologies, enabling chemically programmable qubits and potential for scale-up via self-assembly. Here we report the observation of one of the largest hyperfine interactions for a molecular system, Aiso = 3,467 ± 50 MHz, as well as a very large associated clock transition. This is achieved through chemical control of the degree of s-orbital mixing into the spin-bearing d orbital associated with a series of spin-½ La(II) and Lu(II) complexes. Increased s-orbital character reduces spin–orbit coupling and enhances the electron–nuclear Fermi contact interaction. Both outcomes are advantageous for quantum applications. The former reduces spin–lattice relaxation, and the latter maximizes the hyperfine interaction, which, in turn, generates a 9-GHz clock transition, leading to an increase in phase memory time from 1.0 ± 0.4 to 12 ± 1 μs for one of the Lu(II) complexes. These findings suggest strategies for the development of molecular quantum technologies, akin to trapped ion systems.

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Fig. 1: Clock transition and [Lu(OAr*)3]– structure.
Fig. 2: [Lu(OAr*)3]− Zeeman diagrams.
Fig. 3: ESE-detected W-band spectra.
Fig. 4: [Lu(OAr*)3]− ESE-detected X-band spectra.
Fig. 5: [Lu(OAr*)3]− relaxation measurements.

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Data availability

All data that support the findings of this study are available via the Open Science Framework (OSF, https://osf.io/jr3dq/) with the identifier https://doi.org/10.17605/OSF.IO/JR3DQ55. These data include the EPR results presented in the main paper, the optimized coordinate files from the computational studies, as well as the X-ray, 1H/13C NMR, infrared and UV–vis spectra in the Supplementary Information. The available crystallographic data have also been deposited at the Cambridge Crystallographic Data Centre under the following deposition numbers: [K(crypt)]+[LuII(OAr*)3]−, compound 4, CCDC 2074946 and LuIII(OAr*)3, CCDC 2074947. Copies of the data can be obtained free of charge via https://www.ccdc.cam.ac.uk/structures/. Source data are provided with this paper.

Code availability

All computer codes employed in this study are available in the cited references.

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Acknowledgements

We thank the US National Science Foundation (NSF; CHE-1855328 to W.J.E. and CHE-1800431 and CHE-2102568 to F.F.) and the Department of Energy (DE-SC0020260 to S.H.) for support of this research. Work performed at the NHMFL is supported by the NSF (DMR-1644779) and by the State of Florida. J.M.Y. acknowledges support of the NSF Graduate Research Fellowship Program (DGE-1839285). We also thank the Eddleman Quantum Institute for promoting this collaborative project.

Author information

Authors and Affiliations

  1. National High Magnetic Field Laboratory, Florida State University, Tallahassee, FL, USA

    Krishnendu Kundu & Stephen Hill

  2. Department of Chemistry, University of California, Irvine, CA, USA

    Jessica R. K. White, Samuel A. Moehring, Jason M. Yu, Joseph W. Ziller, Filipp Furche & William J. Evans

  3. Department of Physics, Florida State University, Tallahassee, FL, USA

    Stephen Hill

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Contributions

W.J.E., F.F. and S.H. conceived the research. J.R.K.W. and S.A.M. prepared the samples, S.H. and K.K. designed the experiments. K.K. performed the measurements. K.K. and S.H. analysed the EPR results, J.W.Z. performed the X-ray structural analysis. J.M.Y. and F.F. formulated and executed the computational analysis. All authors contributed to the writing of the manuscript.

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Correspondence to Filipp Furche, William J. Evans or Stephen Hill.

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Extended data

Extended Data Fig. 1 EPR spectral lineshapes.

(a) Qualitative simulations of the ESE intensity patterns observed for compounds 2 and 4. The full spectra (in purple) were generated by summing individual hyperfine components – the eight colored curves above each summed spectrum, labeled according to the associated nuclear projection, mI. The asymmetric lineshapes of the individual components are dictated by the \(\overleftrightarrow g\)-tensor anisotropy and the spacing by the hyperfine and nuclear quadrupole interactions. These simulations capture the main features observed in the experimental spectra, particularly the staircase increase in intensity on the low-field side of the spectrum for 2. The pink oval highlights the region of the spectrum shown in (b). (b) Zoomed region of the experimental spectrum of 4, from Fig. 3c, showing the feature that is very sensitive to the NQI. Superimposed are simulations for different values of Qzz, from which the optimum value of 100 ± 20 MHz is deduced (Table 1). We note that the qualitative simulations in (a) do not explicitly take into account the NQI, whereas the exact simulations in (b) do; for further details, see Supplementary Information Section 3.

Source data

Extended Data Fig. 2 Parallel and perpendicular mode X-band simulations.

(a) Perpendicular mode simulations using parameters from Table 1, but with Qzz = 0. The important thing to note is the absence of the weakly allowed 8 → 10 resonance that is clearly seen in the experimental spectra (Fig. 4). (b) The 8 → 10 resonance appears upon inclusion of the NQI in the perpendicular mode simulations, with Qzz = 100 MHz correctly reproducing the relative intensities of the 8 → 9 and 8 → 10 resonances, which are only seen in the perpendicular mode simulations. (c) Parallel mode simulations with full parameterization in Table 1. A frequency dependent mixture of perpendicular and parallel simulations is needed for the simulations in Fig. 4 (see Methods). Although the units are arbitrary, the three panels are presented in the same absolute scale, that is, the simulations have not been rescaled.

Source data

Extended Data Fig. 3 Spin-lattice (T1) relaxation measurements for 4.

ESE saturation recovery measurements at 310 (a), 410 (b) and 720 mT (c); the frequency was 9.16 GHz and the temperature 5 K. T1 times deduced from exponential fits are displayed in each panel; the uncertainties correspond to the standard errors. See Supplementary Information Section 4 for further details.

Source data

Extended Data Fig. 4 Spin density calculations.

Contours of the spin density (blue) computed with DFT for compounds 2 (a), 3 (b), and 4 (c), plotted at a contour value of 0.005. Hydrogen atoms have been omitted. Color codes: Grey = C, Red = O, Brown = Si, Teal = N, Pink = Ln.

Source data

Extended Data Fig. 5 Ellipsoid plots of the nuclear quadrupole moment tensor.

Visualization of the quadrupole tensors arising from the Ln nucleus computed with DFT for compounds 4 (a), 3 (b), and 2 (c). Because η is small, the ellipsoids are effectively spheroidal in all three cases. Scaling factors, s, of 5.5 × 103, 5.5 × 103, and 1.65 × 104 were applied in (a), (b), and (c), respectively; see Supplementary Information Section 5 for further details. Hydrogen atoms were omitted for clarity. Color codes: Grey = C, Red = O, Tan = Si, Blue = N, Teal = Ln.

Source data

Extended Data Fig. 6 Synthesis of [K(crypt)][Lu(OAr*)3], 4.

Potassium reduction of Lu(OAr*)3 in the presence of 2.2.2-cryptand yields [K(crypt)][Lu(OAr*)3].

Extended Data Table 1 Natural population analysis. Natural atomic populations [n(s), etc.] of the SOMO arising from Ln = La or Lu for compounds 2–4 (see Supplementary Information Section 5 for further details)
Full size table

Supplementary information

Supplementary Information

Supplementary Figs. 1–7, Tables 1–14 and discussion of structural characterization, synthetic details, EPR simulations, T1 measurements, computational details and crystallography (including relevant references).

Supplementary Data 1

Crystallographic file for Lu(III)(OAr*)3, CCDC 2074947.

Supplementary Data 2

Crystallographic file for [K(crypt)][Lu(II)(OAr*)3]·3Et2O, compound 4, CCDC 2074946.

Source data

Source Data Fig. 1a

Source curves (x, y values); further details in file; note that the structure in Fig. 1b is provided as a separate ChemDraw file.

Source Data Fig. 1b

Image of molecule made in Mercury for part (b) of Fig. 1.

Source Data Fig. 2

Source curves (x, y values) for each panel of the figure, including resonance positions; further details in file.

Source Data Fig. 3

Source curves (x, y values) for each panel of the figure, including data and simulations; further details in file.

Source Data Fig. 4

Matrix for 2D color map in panel (a), together with data and simulations (x, y & error values) for each panel of the figure; further details in file.

Source Data Fig. 5

Source data points and curves (x, y & error values) for each panel of the figure; further details in file.

Source Data Extended Data Fig. 1

Source curves (x, y values) for each panel of the figure; further details in file.

Source Data Extended Data Fig. 2

Source curves (x, y values) for each panel of the figure; further details in file.

Source Data Extended Data Fig. 3

Source data points and curves (x, y values) for each panel of the figure; further details in file.

Source Data Extended Data Fig. 4

Optimized atomic xyz coordinates for the compounds studied with electronic structure calculations.

Source Data Extended Data Fig. 5

Optimized atomic xyz coordinates for the compounds studied with electronic structure calculations.

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Kundu, K., White, J.R.K., Moehring, S.A. et al. A 9.2-GHz clock transition in a Lu(II) molecular spin qubit arising from a 3,467-MHz hyperfine interaction. Nat. Chem. 14, 392–397 (2022). https://doi.org/10.1038/s41557-022-00894-4

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