Abu-Labdeh, Abdel-Rahman Mustafa
(2004)
*Monte Carlo simulations for classical two-dimensional dipolar antiferromagnetic systems on a square lattice.*
Doctoral (PhD) thesis, Memorial University of Newfoundland.

[English]
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## Abstract

In this research, the phase behavior of a lattice-based model for a classical two dimensional dipolar antiferromagnet on a square lattice is determined using Monte Carlo simulations. Four different systems are investigated, with the magnetic phase diagram for each system being established for both zero and finite temperature. The results are compared to earlier theoretical and experimental results on low dimensional magnetic systems. -- The first model is the Heisenberg system in which the three-dimensional classical spins interact through both nearest-neighbor antiferromagnetic exchange and long-range dipolar interactions. The magnetic phase diagram for this system was determined as a function of both T/g and |J|/g, where T is the temperature in units of 1/κβ such that κβ is the Boltzmann constant, J is the strength of the antiferromagnetic exchange interaction, and g is the strength of the dipolar interaction. At low temperatures, this phase diagram shows a dipolar planar antiferromagnetic phase for low values of |J|/g, and a simple perpendicular antiferromagnetic phase for large values of |J|/g. The reorientation transition value of the exchange interaction, J r (T), on the phase boundary separating these two ordered phases, shows only a weak dependence on temperature. The data also indicate that the dipolar planar antiferromagnetic phase separates into two distinct phases in which the orientation of the spins depends on the value of the |J|/g. -- The second model is the plane rotator system in which the two-dimensional classical spin rotors are confined to the plane of the system and interact through both nearest-neighbor antiferromagnetic exchange and long-range dipolar interactions. The phase diagram of this system was constructed as a function of both T/g and |J|/g. The results for the plane rotator system are compared to the results obtained for the Heisenberg system. This comparison clarifies the role played by the out-of-plane degree of freedom of spins in determining the structure of the dipolar planar antiferromagnetic phase. -- The third model is the anisotropic Heisenberg system with fixed κ (where κ is the strength of the planar magnetic surface anisotropy). In this system, the three dimensional classical spins interact through nearest-neighbor antiferromagnetic exchange and long-range dipolar interactions, as well as by a weak planar magnetic surface anisotropy (i.e., κ = — 1.0g). Again, the magnetic phase diagram for this system was determined as a function of both T/g and |J|/g. This phase diagram shows similar behavior to that of the Heisenberg system, except that there exists a range of |J|/g in which the system exhibits a reorientation transition from the dipolar planar antiferromagnetic phase to the simple perpendicular antiferromagnetic phase with increasing temperature. -- Finally, the fourth model is the anisotropic Heisenberg system with fixed J. In this system, the three-dimensional classical spins interact through a short-range antiferromagnetic exchange interaction, a planar magnetic surface anisotropy and a long-range dipolar interaction. The simulations focus on the exchange-dominated regime in which the strength of the exchange interaction is significantly greater than both the dipolar interaction and the magnetic surface anisotropy. The magnetic phase diagram for this system was then established as a function of both T/g and |κ|/g, for a fixed value of the exchange constant (i.e., J = —10.0g). This phase diagram shows that there exists a range of the |κ|/g in which the system exhibits a reorientation transition from the simple planar antiferromagnetic phase to the simple perpendicular antiferromagnetic phase with increasing temperature. Finally, some implications of these findings are presented.

Item Type: | Thesis (Doctoral (PhD)) |
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URI: | http://research.library.mun.ca/id/eprint/9818 |

Item ID: | 9818 |

Additional Information: | Bibliography: leaves 188-210. |

Department(s): | Science, Faculty of > Physics and Physical Oceanography |

Date: | 2004 |

Date Type: | Submission |

Library of Congress Subject Heading: | Antiferromagnetism; Phase transformations (Statistical physics) |

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