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An Effective-field Theoretical Study on Ising Metamagnet

Author: GengJiaJia
Tutor: WeiGuoZhu
School: Northeastern University
Course: Theoretical Physics
Keywords: Ising metamagnet effective-field theory Gibbs free energy first-order phase transition phase diagram re-entrant phenomenon fourth-order critical point
CLC: TB34
Type: Master's thesis
Year: 2008
Downloads: 43
Quote: 0
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Abstract


Recently, more attention has been paid on the study of magnetic material, which can be theoretically well described by a two-sublattice Ising model. So far as we know, the magnetic property of metamagnet material in transverse fields within the effective-field theory has yet not been theoretically studied.In this paper, the phase diagrams of two-sublattice Ising metamagnet in external field are studied within the effective-field theory approach. The phase ground state diagrams with a mixed longitudinal and transverse magnetic field, the phase diagrams at finite temperature with longitudinal crystal field and the phase diagrams at finite temperature with a mixed longitudinal and transverse magnetic field are discussed, respectively. The main results are as follows.(1) The ground state magnetic properties of a two-sublattice Ising metamegnet in a mixed longitudinal hz and transverse magnetic field hx are studied within the effective-field theory. A parameter v=J2/J1 is introduced, which reflects the strength ratio of spin coupling between adjacent planes and in each plane. The ground state phase diagrams in hx-hz and magnetization curves are presented. The results show that when -1000≤v<0 the phase transition of the system is always first-order forO<hx< 2.751, and it is always second-order forhx>4.36. The reentrant phenomenon occurs in the range ofv<-11.89,hx>14.71. There is no fourth-order critical point in the phase diagrams given by using effective-field theory as found by using mean-field theory.(2) The phase diagrams and magnetization curves of a two-sublattice Ising metamagnet at finite temperature with longitudinal crystal field hz are investigated by the use of an effective-field theory with correlations. The results show that the phase transitions between these phases are the first-order for low temperatures and high longitudinal fields, and the phase transitions are the second-order for high temperatures and low longitudinal fields, being separated by the tricritical point. In region (0<t<3.1233) the phase transition of the system is always first-order and the tricritical point does not exist. Besides, we find that there is no fourth-order critical point or reentrant phenomenon in the phase diagrams given by using EFT as found by using MFT. Especially a method to calculate the Gibbs free energy numerically within the effective-field theory at finite temperature is presented, so that the entire phase diagrams and the stable solution of magnetization-temperature curve can be obtained.(3) The projection of the tricritical line and the phase diagrams of a two-sublattice Ising metamagnet at finite temperature. in a mixed longitudinal hz and transverse magnetic field hx are investigated by the use of an effective-field theory with correlations. The results show that for a given v, the critical transverse field hx decreases with the temperature t increasing. Furthermore, only one kind of phase diagram is obtained by using effective-field theory while three kinds of phase diagram are obtained by using mean-field theory, which indicates that only the first one of the three kinds of phase diagrams obtained by using mean-field theory is reliable. The reason is that while the mean-field theory totally neglects the correlations of spin fluctuations, the effective-field theory partly considers the correlations of spin fluctuations. For a given hz, three kinds of phase diagrams are obtained by using effective-field theory and by using mean-field theory respectively. Furthermore, by using effective-field theory, two kinds of t-hz curves are obtained when hx≠0,while only one kind of t-hz curves is obtained when hx=0.

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