Theoretical Investigation On The Phase Transition Of Ising Metamagnet In The Transverse Field

Recently, with the development of magnetic material in apply field, the new type magnetic material has attracted the attention. Specially, many kinds of metamagnet material have been studied both theoretically and experimentally. According our investigation, the magnetic property of metamagnet material in transverse fields is not studied theoretically.In this paper, the phase diagram and the multicritical behavior of two-sublattice Ising metamagnet in both external longitudinal and transverse fields are studied within the mean-field approach. Many different types of phase diagrams in the longitudinal field-temperature plane and in the transverse field-temperature plane are determined, respectively. The effects of the transverse field on the phase transitions and the multicritical behavior are discussed. The main results are as follow:(1) The ground state magnetic properties of a two-sublattice Ising metamegnet in both external longitudinal and transverse field are studied within the mean-field approach. A parameter a is introduced, which reflects the strength ration of spin coupling in the plane and in adjacent planes. Whenα=0 andα≠0 the ground state energy, the longitudinal staggered magnetization, the longitudinal total magnetization and the transverse total magnetization are calculated. The ground state phase diagrams inΩ-h andΩ-αplane are presented, respectively. The results show that whenα=0 the position of the tricritical point at ht= 0.3578,Ωt= 0.7156. Whenα≠0, the fourth-order critical point can occur in the phase diagrams. The position of the fourth order critical point isα=-0.500,Ω= 0.354, h=0.707. Whenα≠0 andΩis given, the longitudinal critical magnetic field increases with a decreasing; the phase transition changes always from first-order to second-order with the increasing of the longitudinal magnetic field h or the decreasing ofα; the reentrant phenomenon occurs in the range ofα≤-0.66,Ω≤0.21,h≥0.78.(2) At the finite temperatures the phase diagrams and the thermodynamics properties of the two-sublattice Ising metamagnet in the transverse fieldΩand the longitudinal field h are studied by using the mean-field theory whenα=0. We calculate the internal energy, the specific heat, the staggered magnetization, the longitudinal total magnetization, the transverse total magnetization and plot the finite temperature phase diagrams in theΩ-t plane and in the h-t plane, respectively. The results show that the tricritical points can occur in a certain region of the external longitudinal and transverse fields, the temperature of the tricritical point monotone increases as decreasing the transverse magnetic fieldΩand increasing the longitudinal magnetic field h. In region [0.7156＜Ω＜1,0＜h＜0.3578] the phase transition is always the second-order. In region [0＜Ω＜0.4470,0.4390＜h＜0.5] the phase transition is always the first-order. In these two regions, the tricritical point does not exist. The phase transitions change from the second-order to the first-order with increasingΩfrom 0 to 0.7156 for a given value of h in the region 0.3578＜h＜0.4390 or with increasing h from 0 to 0.5 for a given value ofΩin the region 0＜Ω＜0.7156. With the increasing of transverse fieldsΩthe internal energy, the temperature of transitions and the maximum value of specific heat decrease.(3) Within the mean-field approach based on Bogoliubov's inequality for the Gibbs free energy the two-sublattice Ising metamagnet in both external longitudinal and transverse fields is studied. We calculate the staggered magnetization, the longitudinal total magnetization, the transverse total magnetization, the free energy etc. and plot the finite temperature phase diagrams in theΩ-t plane forα= 0.1,α=-0.4,α=-0.6. The results show that the tricritical points can occur in a certain region of the external longitudinal and transverse fields, the temperature of the tricritical point monotone increases with decreasing the transverse magnetic fieldΩand increasing the longitudinal magnetic field h. Of most interest is the existence of the fourth-order critical point in the phase diagrams due to the existence of the transverse fieldΩ. We have found that the fourth order critical point appears in region-0.5≤α≤-0.25, and obtained the position of the fourth order critical point as a function ofα. In the phase diagrams there are various reentrant phenomena. The role of transverse fieldΩis to destroy the reentrant phenomenon. It is shown that the role of h is to generate the reentrant phenomenon. The internal energy and the specific heat are calculated when the longitudinal and transverse fields is a certain value forα= 0.1 andα=-0.4. The results show that with the increasing of transverse fieldsΩthe internal energy decreases without fourth-order critical points. When the tricritical point decomposes into a critical endpoint and a bicritical endpoint the problem becomes very complicated.