A 54.6 GHz Clock Transition in Ho³⁺ Electron Spin Qubits Assembled into a Metal-Organic Framework

A high-symmetry assembly of molecular spin qubits has been achieved in the metal-organic framework (MOF) [Ho(pzdo)₄](ClO₄)₃ (1), where the eight-coordinate Ho³⁺ nodes are bridged by pyrazine-1,4-dioxide (pzdo) ligands. The approximate square-antiprismatic (D_4d) coordination of the Ho³⁺ ion leads to the stabilization of the m_J = ±4 ground-state doublet due to crystal-field splitting of the J = 8 total angular momentum state. Mixing of the m_J = +4 and m_J = -4 projection states opens a zero-field energy gap (Δ) resulting in the spin clock transition (SCT) evident in the EPR spectra of 1. The SCTs are known to protect qubits from the surrounding magnetic noise to first order, thus enhancing the coherence time of the superposition states crucial for quantum information processing. Frequency-dependent EPR studies reveal that the Ho³⁺ centers in 1 exhibit a high-frequency SCT with Δ_SCT = 54.6 GHz, which can be beneficial to minimizing second-order decoherence effects. The angular dependence of the resonance fields maps well onto the lattice symmetry, with two distinct orientations of the molecular anisotropy axes related to the tetragonal space group symmetry. All salient aspects of the magnetic and EPR measurements have been captured by a model that uses a new theoretical technique based on a constrained DFT derivation of the effective spin Hamiltonian. This work demonstrates the possibility of engineering SCTs in ordered arrays of molecular spin qubits, thus paving the way to scaling up molecular systems that are promising for applications in emerging quantum technologies.