Scientific Challenge

A solid-state spin can act as a qubit only for as long as it holds quantum phase information, and what destroys that information is the environment around it: the fluctuating magnetic field of neighbouring spins, coupled to the central spin through the hyperfine interaction. In a clean, ordered host this environment is fixed. But the most promising spin centres are often those generated by the host’s own chemistry — a vacancy, a reduced site, a native defect — and chemistry of this kind is intrinsically disordered. The spacing of the spin centres, their mutual exchange, and the local hyperfine environment all depend on where the defects sit and how they cluster. The question that organises our work here is therefore the same one that runs through the rest of the group, in a new setting: given a spin centre created by native defect chemistry, what does the surrounding disorder do to the couplings that ultimately set its coherence? Coherence is the macroscopic target; the control variables are the concentration and geometry of disorder.

Our Approach

The route to a coherence time runs through a connected chain, and we work along the same pipeline the group uses for disordered magnets — electronic structure, to couplings, to dynamics — applied here to the spin bath. First-principles calculations fix the electronic structure of the defect centre and its magnetic ground state; all-electron reconstruction of the spin density at the nucleus yields the hyperfine tensors that quantify how strongly the central spin feels its environment; and these tensors are the direct numerical input to coherence-time modelling through the cluster-correlation expansion.

Treating the strongly correlated electrons of the defect correctly is a prerequisite, so the on-site interaction is fixed from first principles rather than fitted. And because the object of study is disorder, the calculations are designed to vary one thing at a time: contrasting clustered against dispersed defect arrangements at fixed concentration isolates the effect of geometry, while varying concentration at fixed geometry isolates the effect of crowding. Cerium dioxide — where removing a lattice oxygen creates a shielded rare-earth Ce³⁺ spin centre by intrinsic stoichiometry — serves as a clean realisation of this design, but the framing is general: a spin centre that the host chemistry generates and the defect geometry tunes.

Key Insights & Achievements

• A concentration scale where the single-site picture fails. The isotropic hyperfine coupling of the defect spin is nearly constant and only weakly geometry-dependent while the centres are dilute, but collapses sharply once they are crowded together — locating the concentration at which neighbouring spin densities begin to overlap and the clean single-site description breaks down.
• Structural control over inter-spin exchange. At fixed concentration, the magnetic ground state switches between ferromagnetic and antiferromagnetic order purely as a function of how the defects are arranged — direct evidence that the geometry of disorder, not just its amount, controls the exchange between spin centres.
• A geometric fingerprint in the hyperfine environment. The anisotropic part of the weak ligand hyperfine couplings carries a distinctive, geometry-dependent signature, suggesting that distinct defect-cluster arrangements could be told apart spectroscopically — a handle on the disorder that would otherwise be hidden.

Taken together, these results characterise how the concentration and geometry of native defects reshape the hyperfine and exchange couplings that govern coherence — the quantitative input that a first-principles coherence-time calculation requires. They extend the group’s central question, of how disorder bridges local electronic structure and collective response, from finite-temperature magnetism into the physics of spin coherence.

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