Theoretical Investigation On Magnetic Properties Of Ising Nanoislands

Ising model is very useful for study order-disorder phase transitions in modern statistical mechanics.Some rigorous analytic solutions have been given for Ising model of one-dimensional and two-dimensional lattices.Precise solution for Ising model of three-dimension and its various variants has been investigated extensively for many years.Ising model is of great academic value for study the properties of magnetic material in both fundamental magnetic physics and material science.In this paper,we study three kinds of Ising model:the magnetic property of the hexagonal lattice Ising nano-island with longitudinal magnetic field spin of 1/2,the magnetic property of the square lattice Ising nano-island with longitudinal magnetic field spin of 1/2,the magnetic properties of the tetragonal lattice Ising nano-islands with longitudinal magnetic field spin of 1/2.In this paper,based on the Ising model,The magnetizations and magnetic susceptibility with longitudinal magnetic field,transverse magnetic field and interlayer coupling in the transverse magnetic field and longitudinal magnetic field are examined by using the effective-field theory with correlations.The results show that the longitudinal magnetic field,surface exchange interaction,transverse magnetic field and interlayer coupling have different effects on the magnetizations and magnetic susceptibility.For hexagonal lattice Ising nano-island with spin of 1/2,The numerical results point out existence of two types of the total longitudinal magnetizations within certain parameters.One is that the total longitudinal magnetizations gradually decreases with increasing temperature;the other is that the total longitudinal magnetizations curve decreases to a small constant with increasing temperature and a small amplitude occurs.The total transverse magnetizations gradually decreases with increasing temperature.The phase transition temperature decreases with surface exchange interaction,?/?,?/Jincreases,and increases with the increase of interlayer coupling.For positive cubic lattice Ising nano-island with spin of 1/2,the total longitudinal magnetizations curve is similar to the hexagonal lattice under specific physical parameters.The total transverse magnetizations of the system decreases with the surface exchange interaction,?s,/?,and the longitudinal magnetic field increases.The total transverse magnetizations of the system increases with the interaction of the interlayer coupling and ?/Jincreases.The phase transition temperature decreases with the increase of the interlayer coupling,and increases with the surface exchange interaction,?s/?,and the longitudinal magnetic field.For tetragonal lattice Ising nano-island with spin of 1/2,the total longitudinal magnetizations curve is similar to a hexagonal lattice and a positive cubic lattice under specific physical parameters.The total transverse magnetizationst of the system decreases with the interaction of the interlayer exchange and the increase of the longitudinal magnetic field.The total transverse magnetizations of the system increases with the surface exchange interaction and the increase of ?s/? and ?/J.The phase transition temperature decreases with the increase of ?s/? and ?/J,and increases with the surface exchange interaction,the interlayer coupling,and the increase of the longitudinal magnetic field.