Magnetism and spin dynamics in the cluster compound [ Cr 4 S ( O 2 CCH 3 ) 8 ( H 2 O ) 4 ] ( N O 3 ) 2 ⋅ H 2 O

The magnetism and spin dynamics of $[{\mathrm{Cr}}_{4}{\mathrm{S}(\mathrm{O}}_{2}{\mathrm{CCH}}_{3}{)}_{8}{(\mathrm{H}}_{2}{\mathrm{O})}_{4}{](\mathrm{N}\mathrm{O}}_{3}{)}_{2}{\mathrm{\ensuremath{\cdot}}\mathrm{H}}_{2}\mathrm{O}$ have been investigated by magnetic susceptibility and proton NMR measurements and by theoretical calculations. The proton-spin lattice relaxation rate ${1/T}_{1},$ as a function of the temperature T and external magnetic field B, provides a very useful probe of the dynamical behavior of the four ${\mathrm{Cr}}^{+3}$ (spins $s=\frac{3}{2})$ paramagnetic ions which are ferromagnetically coupled via isotropic Heisenberg exchange interaction. From our derived formulas for the two-ion time correlation functions, we find that ${1/T}_{1}$ may be expressed as a function of the single scaling variable ${\ensuremath{\mu}}_{B}{B/(k}_{B}T),$ where ${\ensuremath{\mu}}_{B}$ is the Bohr magneton and ${k}_{B}$ is Boltzmann's constant, for the regime of our measurements. Our experimental data are in good agreement with this prediction and our derived form of the scaling function.