By Naim A. Malak Physics Department An-Najah National University, Nablus, Palestine
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Transcript of By Naim A. Malak Physics Department An-Najah National University, Nablus, Palestine
The Magnetic Properties of the Anti-collinear Phase under the Effects of a Uniform External Magnetic Field in a Two Dimensional Square
Planar SystemBy
Naim A. MalakPhysics Department
An-Najah National University, Nablus, Palestine
7 -8 / May / 2007
Supervised by Dr. Abdel-Ruhman M. Abu-Labdeh
Outline
Aim
The Model in General Terms
Monte Carlo Method
Results
Summary
Aim
To investigate the magnetic properties of the Anti-collinear Phase under the effects of a
Uniform External Magnetic Field in an Anti-ferromagnetic Dipolar Planar System
The Model in General Terms
Where
a set of two dimensional classical vectors of unit magnitude g : the strength of the dipolar interaction h : the strength of uniform external magnetic field parallel to X-axis
J : the strength of the exchange interaction ( J< 0 )
)))((
3(})({53
ij
rr
ij
gErr
ijjiji
ji
jii
ii
jiji hRSRSJ
,
)()(
}{ i
Monte Carlo Method
• Constructing an infinite plane from replicas of a finite system
• Using the Ewald Summation Technique
• Using the slandered Metropolis Algorithm
Results
Spin Configurations at T=0.1,h=0.1Anti-collinear Phase
Spin Configurations Perpendicular to the applied Field ( Dipolar Anti-ferromagnetic Phase )
Spin Configurations at low T and high field Ferromagnetic Phase
( T=0.1, h=8.0 )
Summary
• The Phase Diagram Confirms The following results:
* First Order Transition from the Dipolar Anti-ferromagnetic Phase to Ferromagnetic Phase
* Second Order Transition from the Dipolar Anti-ferromagnetic Phase to Paramagnetic Phase
• Besides that, Simulation Results exhibit stable (pi/4) spin configurations at very low ( field & temperature
Acknowledgments
• My father
• Dr. Abdel-Ruhman M. Abu Labdeh for supervision
• My friends; for help