Fig. 2

(a) Pie charts show the dominance of the ground states of the \(\text {Fe}^{3+}\) complex described by the Hamiltonian (1) in the \((J_2, B)\) parameter space, assuming \(J_1 = 42.2\, \text {cm}^{-1}\) and four different values of \(J_3\). Different ground states are represented by distinct colors, with the corresponding magnetization values labeled on each chart. The magnetization values (\(M/M_\textrm{s}\)) are indicated on each slice, with purple for 0, light blue for \(\frac{1}{3}\), yellow for \(\frac{2}{3}\), and brown for 1. (b) Ground-state phase diagram in the \(B-J_3\) plane for fixed values of \(J_1 = 42.2\, \text {cm}^{-1}\) and \(J_2 = 34.2\, \text {cm}^{-1}\). (c) Ground-state phase diagram in the \(B-J_2\) plane, assuming \(J_1 = 42.2\, \text {cm}^{-1}\) and \(J_3 = 0.015\, \text {cm}^{-1}\). (d) Magnetization as a function of the magnetic field B for various fixed temperatures T. Experimental data from  ¹⁹ are shown as black circles, while theoretical magnetization curves are represented by lines. The blue solid line corresponds to the best-fit magnetization curve, obtained using the parameter set \(J_1 = 42.2\, \text {cm}^{-1}\), \(J_2 = 34.2\, \text {cm}^{-1}\), and \(J_3 = 0.015\, \text {cm}^{-1}\), as reported in  ¹⁹.