Evidence for a Reorientation Transition in the Phase Behaviour of a Two-Dimensional Dipolar

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. 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. Definitions • Magnetism results from the • Spin and orbital degrees of freedom of the electron • Magnetism is influenced by the •  Structure • Composition • Dimensionality of the system • Magnetic materials can be divided into • Bulk • Low-dimensional (Quasi-2D) • Ultra thin magnetic films • Layered magnetic compounds (e.g., REBa2Cu3O7-δ) • Arrays of micro or nano-magnetic dots 3

4. Motivation • Quasi-2D spin systems have received much greater attention due to • Their magnetic properties • 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. 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 (322 , 642 , 1042 ) Including • Antiferromagnetic Exchange interaction • Long-range dipolar interaction • Magnetic surface anisotropy 5

6. The Model in General Terms )1) where • {σi } 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. Monte Carlo Method • Constructing an infinite plane from replicasof a finite system • Using the Ewald summation technique • Using the standard Metropolis algorithm 7

8. Ground State At the Transition:

9. Definition of the Order Parameters

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

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

12. The Magnetic Phase Diagram: J= -l0g

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

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 phasewith increasing Applying an out-of-plane magnetic field causes this phase boundary to be at lower values of

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. Thank You