Dysprosium-based experimental representatives of an Ising-Heisenberg chain and a decorated Ising ring

Abstract

It is shown that the bond-decorated Ising model is a realistic model for certain real magnetic compounds containing lanthanide ions. The lanthanide ion plays the role of Ising spin. The required conditions on the crystal-field spectrum of the lanthanide ion for the model to be valid are discussed and found to be in agreement with several recent ab initio calculations on ${\text{Dy}}^{3+}$ centers. Similarities and differences between the spectra of the simple Ising chain and the decorated Ising chain are discussed and illustrated, with attention to level crossings in a magnetic field. The magnetic properties of two actual examples (a ${[\text{DyCuMoCu}]}_{\ensuremath{\infty}}$ chain and a ${\text{Dy}}_{4}{\text{Cr}}_{4}$ ring) are obtained by a transfer-matrix solution of the decorated Ising model. $g$-factors of the metal ions are directly imported from ab initio results, while exchange coupling constants are fitted to experiment. Agreement with experiment is found to be satisfactory, provided one includes a correction (from ab initio results) for susceptibility and magnetization to account for the presence of excited Kramers doublets on ${\text{Dy}}^{3+}$.