Exact Mapping from Many‐Spin Hamiltonians to Giant‐Spin Hamiltonians
Exchange‐coupled molecular spin clusters (e.g. single‐molecule magnets) are routinely described in terms of a many‐spin Hamiltonian (MSH) that considers individual spins, or a giant‐spin Hamiltonian (GSH) that treats the system as a collective spin. When isotropic coupling is weak, the mapping MSH → GSH ('spin projection'), becomes non‐trivial due to mixing of spin multiplets by anisotropic terms, an effect crucial for generating transverse magnetic anisotropy. Going beyond perturbational spin‐projection schemes, based on exact diagonalization and canonical effective Hamiltonian theory, we construct a GSH that exactly matches the energies of the relevant (2S+1) states. For comparison, we adapt a recently developed strategy for the unique definition of effective ('pseudospin') Hamiltonians of mononuclear systems, through adiabatic connection to a high‐symmetry point in parameter space. The developed exact MSH → GSH mapping is of importance for various weakly‐coupled systems. An application to a Ni4 single‐molecule magnet (S = 4) attributes the large tunnel splitting in the M = ± 4 ground doublet, responsible for fast magnetization tunneling, to a Stevens operator with eightfold rotational symmetry.
Shadan Ghassemi Tabrizi, Alexei V Arbuznikov, Martin Kaupp
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