Transfer function approaches to the one-dimensional thermodynamics of classical magnets, and the long-range dipole interaction in rare-earth pyrochlores

Mason, Richard (2015). Transfer function approaches to the one-dimensional thermodynamics of classical magnets, and the long-range dipole interaction in rare-earth pyrochlores. University of Birmingham. Ph.D.

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Abstract

We will use the transfer function technique to solve the plane rotator with nearest neighbour interactions and a magnetic field, and the Heisenberg model with nearest and next nearest neighbour interactions, all exactly. For the plane rotator model and the Heisenberg, we find that the models with nearest and next nearest neighbour interactions are thermodynamically equivalent to models with nearest neighbour interactions and a magnetic field. We investigate the zero temperature phase transition in all models. For the case of the plane rotator and Heisenberg models, this is between a pure antiferromagnet and a spiral state, and for the continuous Ising model it is between a ferromagnet and an antiferromagnet. We investigate the thermal effects on the phase transition, and find a fluctuation driven crossover (rather than transition due to the dimensionality) which stabalises collinear states. We also investigate magnetisation of the models as well, and find that the continuous spin Ising model (particularly) exhibits strong field dependence, staying magnetised well beyond the associated temperature of the field. We also work on long range dipole interactions on the pyrochlore lattice, specifically are-earth pyrochlores.

Type of Work:

Thesis (Doctorates > Ph.D.)

Award Type:

Doctorates > Ph.D.

Supervisor(s):