Many-spin effects in inelastic neutron scattering and electron paramagnetic resonance of molecular nanomagnets

Abstract

Many molecular magnetic clusters, such as single-molecule magnets, are characterized by spin ground states with defined total spin S exhibiting zero-field-splittings. In this work, the spectroscopic intensities of the transitions within the ground-state multiplet are analyzed. In particular, the effects of a mixing with higher-lying spin multiplets, which is produced by anisotropic interactions and is neglected in the standard single-spin description, are investigated systematically for the two experimental techniques of inelastic neutron scattering (INS) and electron paramagnetic resonance (EPR), with emphasis on the former technique. The spectroscopic transition intensities are calculated analytically by constructing corresponding effective spin operators perturbationally up to second order and consequently using irreducible tensor operator techniques. Three main effects of spin mixing are observed. Firstly, a pronounced dependence of the INS intensities on the momentum transfer Q, with a typical oscillatory behavior, emerges in first order, signaling the many-spin nature of the wave functions in exchange-coupled clusters. Secondly, as compared to the results of a first-order calculation, the intensities of the transitions within the spin multiplet are affected differently by spin mixing. This allows one, thirdly, to differentiate the higher-order contributions to the cluster magnetic anisotropy which come from the single-ion ligand-field terms and spin mixing, respectively. The analytical results are illustrated by means of the three examples of an antiferromagnetic heteronuclear dimer, the Mn-[3 × 3] grid molecule, and the single-molecule magnet Mn12.

Inelastic neutron scattering and frequency-domain magnetic resonance studies ofS=4andS=12Pieper1, Guidi2, Carretta3 et al. 2010Phys. Rev. B211160View full textAdd to dashboardCite

“…͑2͒. This situation is also encountered in other studied molecules, such as, for example, in Mn 12 , [32][33][34][35][36] in the Mn-͓3 ϫ 3͔ grid, 37,38 in Ni 4 , 39 and in V 15 , 33,35,40 where the detailed modeling of the experimental results has required the use of a multispin approach.…”

EPR Spectroscopy of a Family of CrIII7MII (M = Cd, Zn, Mn, Ni) “Wheels”: Studies of Isostructural Compounds with Different Spin Ground States

“…The problem of diagonalisation of very large spin-Hamiltonian matrices has been previously approached by use of ITO techniques, group theoretical treatments and the sparse matrix Lanczos diagonalisation algorithm. [5,[8][9][10] In addition, lower-dimension effective spin-Hamiltonian operators based on reduced spin model representations of the full systems have been employed to deal with the same problem. [6,11] We have recently developed a method for the interpretation of static thermodynamic and spectroscopic properties of large polymetallic systems based on the use of the Davidson numerical diagonalisation algorithm.…”

“…These experimental spectra provide rare examples of high nuclearity polymetallic systems where detailed information on the spin-Hamiltonian parameters of the ground and excited spin states is observed. We interpret the EPR spectra by use of restricted size effective subspaces obtained by the rigorous solution of spin-Hamiltonians of dimension up to 10 5 by use of the Davidson algorithm. We show that transferability of spin-Hamiltonian parameters across complexes of the Cr 7 M family is possible and that the spin-Hamiltonian parameters of Cr 7 M do not have sharply defined values, but are rather distributed around a mean value.…”

“…[12] The Davidson algorithm is an iterative subspace diagonalisation approach that allows the exact computation of a number of low-lying eigenstates of the full spin-Hamiltonian of the system starting from a set of, in principle arbitrarily chosen, guess vectors within realistic computation times and memory storage requirements. This approach, as with any other method which provides exact eigenstates numerically, [5,6,10,21] allows for any spin-Hamiltonian term to be included in the spin-Hamiltonian of the system and for all terms to be treated simultaneously and not in a sequential perturbation way. Thus, the methodology used allows for the simultaneous inclusion of single-ion and exchange anisotropy terms, as well as of any other relevant terms, in the spin-Hamiltonian without requiring that the total spin S is a good quantum number.…”

Studies of Finite Molecular Chains: Synthesis, Structural, Magnetic and Inelastic Neutron Scattering Studies of Hexa‐ and Heptanuclear Chromium Horseshoes

“…[36,37] The Q dependence of the INS intensity given by so-called interference factors of a certain transition bears information about the wavefunctions of the involved states. [36,38] Unfortunately, due to the incoherent scattering from the hydrogen atoms in our sample, the Q dependence could not be evaluated.…”