Magnetic relaxation in cyanide based single molecule magnets

Abstract

The present contribution is aimed at the elaboration of the model of magnetic relaxation in the cyano-bridged pentanuclear Mn(III) 2Mn(II) 3 cluster that belongs to a new family of single molecule magnets (SMM) containing ions with unquenched orbital angular momenta. We proceed from the energy pattern of the cluster formed by the trigonal component of the crystal field acting on the ground-state cubic terms 4 T 1 ( t 2 4 ) of the Mn(III)-ions, spin–orbital interaction and Heisenberg exchange between Mn(II) and Mn(III) ions. The ground state of the cluster possesses the total angular momentum projection ∣ M J ∣ = 15/2, while the energies of the excited states increase with decreasing ∣ M J ∣ values, thus giving rise to a barrier for the reversal of magnetization. The monophonon transitions between the states ∣ M J 〉 and ∣ M J ± 1〉, ∣ M J ± 2〉 induced by electron–vibrational interaction are shown to be allowed. The rates of all possible transitions between the states with 1/2 < ∣ M J ∣ < 15/2 are calculated in the temperature range 0.1 K < T < 3 K. With the purpose of calculation of the temperature dependence of the relaxation time of magnetization we solve the set of master equations for the populations n M J ( t ) of the ∣ M J 〉 states of the Mn(III) 2Mn(II) 3 clusters. The relaxation time is shown to diminish from 10 12s to 10 s with decrease in temperature from 1 K to 3 K for the cluster [Mn(III)(CN) 6] 2[Mn(II)(tmphen) 2] 3 (tmphen = 3,4,7,8-tetramethyl-1,10-phenanthroline) with the trigonal crystal field parameter Δ = −251 cm −1. The obtained values of the relaxation time are in qualitative agreement with the temperature dependence of the ac susceptibilities observed for this SMM. In order to reveal the possibility of enhancing the relaxation time of magnetization in the family of clusters Mn(III) 2Mn(II) 3 we vary the trigonal crystal field parameter ∣ Δ∣( Δ < 0) and demonstrate that increase in ∣ Δ∣ leads to a considerable growth of the relaxation time.