1. 1 Evidence for a Reorientation Transition in the Phase Behaviour of a Two-Dimensional Dipolar Antiferromagnet By Abdel-Rahman M. Abu-Labdeh An-Najah National University, Palestine Collaborated by John Whitehead, MUN-Canada Keith De’Bell, UNB-Canada Allan MacIsaac, UWO-Canada Supported by MUN & NSERC of Canada May 8, 2007

2. 2 Outline 1. Introduction a. Definitions b. Motivation c. Aim 2. The Model in General Terms 3. Monte Carlo Method 4. Results 5. Summary 2

3. 3 Definitions  Magnetism results from the  Spin and orbital degrees of freedom of the electron  Magnetism is influenced by the 1. Structure 2. Composition 3. Dimensionality of the system  Magnetic materials can be divided into 1. Bulk 2. Low-dimensional (Quasi-2D) a. Ultra thin magnetic films b. Layered magnetic compounds (e.g., REBa 2 Cu 3 O 7-δ ) c. Arrays of micro or nano-magnetic dots 3

4. 4 Motivation  Quasi-2D spin systems have received much greater attention due to 1. Their magnetic properties 2. Their significant advances in technological applications such as a. Magnetic sensors b. Recording c. Storage media  Few systematic work have done on the quasi-2D antiferromagnetic systems. In particular, having  Exchange  Dipolar  Magnetic surface anisotropy 4

5. 5 Aim  Is to obtain a better understanding of the quasi­-2D antiferromagnetic systems  To achieve this aim  Results from Monte Carlo simulations are pre­ sented for a 2D classical Heisenberg system on a square lattice (32 2, 64 2, 104 2 ) Including  Antiferromagnetic Exchange interaction  Long-range dipolar interaction  Magnetic surface anisotropy 5

6. 6 The Model in General Terms )1) where  { σ i } is a set of three-dimensional classical vec­ tors of unit magnitude  g is the strength of the dipolar interaction  J is the strength of the exchange interaction  K, is the strength of the magnetic surface anisotropy. In this study  K≤ 0  J / 9 = -10 6

7. 7 Monte Carlo Method 1. Constructing an infinite plane from replicas of a finite system 2. Using the Ewald summation technique 3. Using the standard Metropolis algorithm 7

8. 8 Ground State At the Transition:

9. 9 Definition of the Order Parameters

10. 10 The Order Parameters: J= -l0g, L=I04

11. 11 The Heat Capacity: J= -l0g, L=104

12. 12 The Magnetic Phase Diagram: J= -l0g

13. 13 The Magnetic Phase Diagram: J= -lOg Hz=O, 10, 15g

14. 14 Summary  The T magnetic phase diagram is established for the 2D dipolar Heisenberg antiferromagnetic system on a square lattice for J = -l0g  This phase diagram shows A first-order reorientation transition from the parallel antiferromagnetic phase to the perpen­ dicular antiferromagnetic phase with increasing  Applying an out-of-plane magnetic field causes this phase boundary to be at lower values of

15. 15 Acknowledgements  MUN & NSERC for Financial Support  C3.ca for Access to Computational Resources at University of Calgary Memorial University of Newfoundland  An-Najah National University  Conference Organizing Committee

16. 16 Thank You