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