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.