Spin dynamics in mesoscopic size magnetic systems:AHtNMR1study in rings of iron (III) ions

Abstract

Two magnetic molecular clusters containing almost coplanar rings of iron (III) ions with spin S=5/2 have been investigated by $^{1}\mathrm{H}$ NMR and relaxation measurements. The first system, which will be referred to as Fe6, is a molecule of general formula [${\mathrm{NaFe}}_{6}$(${\mathrm{OCH}}_{3}$${)}_{12}$(${\mathrm{C}}_{17}$${\mathrm{O}}_{4}$${\mathrm{H}}_{15}$${)}_{6}$${]}^{+}$${\mathrm{ClO}}_{4}^{\mathrm{\ensuremath{-}}}$ or [${\mathrm{NaFe}}_{6}$(${\mathrm{OCH}}_{3}$${)}_{12}$(${\mathrm{C}}_{15}$${\mathrm{H}}_{11}$${\mathrm{O}}_{2}$${)}_{6}$${]}^{+}$${\mathrm{ClO}}_{4}^{\mathrm{\ensuremath{-}}}$ or [${\mathrm{LiFe}}_{6}$(${\mathrm{OCH}}_{3}$${)}_{12}$(${\mathrm{C}}_{15}$${\mathrm{H}}_{11}$${\mathrm{O}}_{2}$${)}_{6}$${]}^{+}$${\mathrm{ClO}}_{4}^{\mathrm{\ensuremath{-}}}$ while the second type of ring, denoted Fe10, corresponds to the molecule [${\mathrm{Fe}}_{10}$(${\mathrm{OCH}}_{3}$${)}_{20}$(${\mathrm{C}}_{2}$${\mathrm{H}}_{2}$${\mathrm{O}}_{2}$Cl${)}_{10}$]. The $^{1}\mathrm{H}$ NMR linewidth is broadened by the nuclear dipolar interaction and by the dipolar coupling of the protons with the iron (III) paramagnetic moment. It is found that the nuclear spin-lattice relaxation rate, ${\mathrm{T}}_{1}^{\mathrm{\ensuremath{-}}1}$, of the proton is a sensitive probe of the Fe spin dynamics. In both clusters, ${\mathrm{T}}_{1}^{\mathrm{\ensuremath{-}}1}$ decreases with decreasing temperatures from room temperature, goes through a peak just below about 30 K in Fe6 and 10 K in Fe10, and it drops exponentially to very small values at helium temperature. The temperature dependence of the relaxation rate is discussed in terms of the fluctuations of the local spins within the allowed total spin configurations in the framework of the weak collision theory to describe the nuclear relaxation. We use the calculated energy levels for the Fe6 ring based on a Heisenberg Hamiltonian and the value of J obtained from the fit of the magnetic susceptibility to describe semiquantitatively the behavior of ${\mathrm{T}}_{1}^{\mathrm{\ensuremath{-}}1}$ vs T. The exponential drop of ${\mathrm{T}}_{1}^{\mathrm{\ensuremath{-}}1}$ at low temperature is consistent with a nonmagnetic singlet ground state separated by an energy gap from the first excited triplet state. The values obtained for the gap energies are ${\mathrm{E}}_{\mathrm{T}}$/k=12 K for Fe10 and ${\mathrm{E}}_{\mathrm{T}}$/k=38 K for Fe6 which are almost twice as big as the values deduced from susceptibility measurements. At all temperatures the relaxation rate decreases with increasing magnetic field, i.e., NMR resonance frequency. This effect could be related to the long time persistence of the spin correlation functions typical of diffusive modes in low dimensional magnetic systems. It is argued that the data presented are a direct experimental study of spin dynamics in mesoscopic spin rings and should afford a test for exact analytical and/or numerical solutions.