A review is given of the differential operator technique in the Ising spin systems. The theoretical frameworks of the various models are discussed on the basis of the Ising spin identities. These can be applied to examine the magnetic properties in a variety of magnetic materials.
The magnetic properties of a diluted spin-2 and spin-5/2 ferrimagnetic Ising system are investigated on the basis of the effective-field theory with correlations. In particular, the effect of a positive single-ion anisotropy D on the compensation temperature in a pure system with D only on spin-5/2 atoms is investigated, in order to clarify the characteristic feature of the temperature dependence of the total magnetization M observed in a molecular-based magnetic material, . The influences of D and the concentrations of magnetic atoms on the properties of the system on a honeycomb lattice are examined. The results show that several (two or three) compensation points are possible in the diluted system with special values of D and concentrations of magnetic atoms.
Magnetic properties (phase diagram and magnetization) of a cylindrical Ising nanowire or nanotube are investigated by the use of the effective-field theory with correlations. Particular emphasis is given to the effects of the surface and its dilution on them. Much attention is paid to the thermal variation of the magnetization when the spins at the surface are coupled antiferromagnetically to the ferromagnetic core spins by the negative shell coupling. The effects of dilution at the surface, the surface exchange interaction, and the shell coupling on the magnetization profiles are investigated. We find a number of characteristic phenomena for them.
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