Quantum interference oscillations of the superparamagnetic blocking in an Fe8 molecular nanomagnet

Observation of Cooperative Electronic Quantum Tunneling: Increasing Accessible Nuclear States in a Molecular Qudit

As an extension of two-level quantum bits (qubits), multilevel systems, so-called qu dits, where d represents the Hilbert space dimension, have been predicted to reduce the number of iterations in quantum-computation algorithms. This has been tested in the well-known [TbPc₂]⁰ single-molecule magnet (SMM), which allowed implementation of the Grover algorithm in a single molecular unit. In the quest for molecular systems possessing an increased number of accessible nuclear spin states, we explore herein a dimeric Tb₂-SMM via single-crystal μ-SQUID measurements at sub-Kelvin temperatures. We observe ferromagnetic interactions between the Tb^III ions and cooperative quantum tunneling of the electronic spins with spin ground state | J _z = ±6⟩. Strong hyperfine coupling with the Tb^III nuclear spins leads to a multitude of spin-reversal paths, leading to seven strong hyperfine-driven tunneling steps in the hysteresis loops. Our results show the possibility of reading out the Tb^III nuclear spin states via cooperative tunneling of the electronic spins, making the dimeric Tb₂-SMM an excellent nuclear spin qu dit candidate with d = 16.

Exact Mapping from Many-Spin Hamiltonians to Giant-Spin Hamiltonians

Thermodynamic and spectroscopic data of exchange-coupled molecular spin clusters (e.g. single-molecule magnets) are routinely interpreted in terms of two different models: the many-spin Hamiltonian (MSH) explicitly considers couplings between individual spin centers, while the giant-spin Hamiltonian (GSH) treats the system as a single collective spin. When isotropic exchange coupling is weak, the physical compatibility between both spin Hamiltonian models becomes a serious concern, due to mixing of spin multiplets by local zero-field splitting (ZFS) interactions ('S-mixing'). Until now, this effect, which makes the mapping MSH→GSH ('spin projection') non-trivial, had only been treated perturbationally (up to third order), with obvious limitations. Here, based on exact diagonalization of the MSH, canonical effective Hamiltonian theory is applied to construct a GSH that exactly matches the energies of the relevant (2S+1) states comprising an effective spin multiplet. For comparison, a recently developed strategy for the unique derivation of effective ('pseudospin') Hamiltonians, now routinely employed in ab initio calculations of mononuclear systems, is adapted to the problem of spin projection. Expansion of the zero-field Hamiltonian and the magnetic moment in terms of irreducible tensor operators (or Stevens operators) yields terms of all ranks k (up to k=2S) in the effective spin. Calculations employing published MSH parameters illustrate exact spin projection for the well-investigated [Ni(hmp)(dmb)Cl]₄ ('Ni₄ ') single-molecule magnet, which displays weak isotropic exchange (dmb=3,3-dimethyl-1-butanol, hmp^- is the anion of 2-hydroxymethylpyridine). The performance of the resulting GSH in finite field is assessed in terms of EPR resonances and diabolical points. The large tunnel splitting in the M=± 4 ground doublet of the S=4 multiplet, responsible for fast tunneling in Ni₄ , is attributed to a Stevens operator with eightfold rotational symmetry, marking the first quantification of a k=8 term in a spin cluster. The unique and exact mapping MSH→GSH should be of general importance for weakly-coupled systems; it represents a mandatory ultimate step for comparing theoretical predictions (e.g. from quantum-chemical calculations) to ZFS, hyperfine or g-tensors from spectral fittings.