The geometrically frustrated spin-1/2 Ising-Heisenberg model on triangulated Husimi lattices is exactly solved by combining the generalized star-triangle transformation with the method of exact recursion relations. The ground-state and finite-tempera
ture phase diagrams are rigorously calculated along with both sublattice magnetizations of the Ising and Heisenberg spins. It is evidenced that the Ising-Heisenberg model on triangulated Husimi lattices with two or three inter-connected triangles-in-triangles units displays in a highly frustrated region a quantum disorder irrespective of temperature, whereas the same model on triangulated Husimi lattices with a greater connectivity of triangles-in-triangles units exhibits at low enough temperatures an outstanding quantum order due to the order-by-disorder mechanism. The quantum reduction of both sublattice magnetizations in the peculiar quantum ordered state gradually diminishes with increasing the coordination number of underlying Husimi lattice.
The magnetization process of the spin-1 Heisenberg dimer model with axial and rhombic single-ion anisotropy terms is particularly investigated in connection with recent experimental high-field measurements performed on the single-crystal sample of th
e homodinuclear nickel(II) compound [Ni2(Medpt)2(ox)(H2O)2](ClO4)2.2H2O (Medpt=methyl-bis(3-aminopropyl)amine). The results obtained from the exact numerical diagonalization reveal a striking magnetization process with a marked spatial dependence on the applied magnetic field for arbitrary but non-zero single-ion anisotropy. It is demonstrated that the field range, which corresponds to an intermediate magnetization plateau emerging at a half of the saturation magnetization, basically depends on single-ion anisotropy terms as well as a spatial orientation of the applied field. The breakdown of the intermediate magnetization plateau is discussed at length in relation to the single-ion anisotropy strength.
