Heat Capacity of [Cr₄(OH)₆(en)₆](SO₄)₃·10H₂O from 1.4 to 200 K and Spin Interaction

Abstract

The heat capacity was measured between 1.4 and 200 K. The magnetic contribution was determined by subtracting the lattice contribution from the overall heat capacity with the aid of effective frequency distribution function. The magnetic heat capacity showed two peaks at 2.3 K and at about 20 K. These features are satisfactorily accounted for by assuming a spin Hamiltonian of the form, \(\mathscr{H}{=}-J(\textbf{\itshape S}_{1}{\cdot}\textbf{\itshape S}_{3})-j[(\textbf{\itshape S}_{1}{\cdot}\textbf{\itshape S}_{2})+(\textbf{\itshape S}_{2}{\cdot}\textbf{\itshape S}_{3})+(\textbf{\itshape S}_{3}{\cdot}\textbf{\itshape S}_{4})+(\textbf{\itshape S}_{4}{\cdot}\textbf{\itshape S}_{1})]-J_{24}(\textbf{\itshape S}_{2}{\cdot}\textbf{\itshape S}_{4})\). The closest agreement between theory and experiment was obtained for J =-42.6 k , j =-22.8 k and J 24 =-7.6 k . The sign of the parameters indicates that all the spin interactions are antiferromagnetic. It was concluded that one need not introduce any higher-order spin interactions to interpret the magnetic properties in the present system. To determine existing spin-interactions in a cluster, the complementary role of heat capacity and magnetic susceptibility measurements is emphasized. Also described in this paper is a new method to separate the magnetic heat capacity based on an effective frequency spectrum.