Statistical mechanics of the square lattice planar rotator model and metamagnetism in bilayer strontium ruthenate $Sr_3Ru_2O_7$

Robson, Matthew (2018). Statistical mechanics of the square lattice planar rotator model and metamagnetism in bilayer strontium ruthenate $Sr_3Ru_2O_7$ . University of Birmingham. Ph.D.

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Abstract

We have investigated the thermodynamics of the square lattice planar rotator model. By calculating a variety of thermodynamic quantities for the planar rotator model on a sequence of one-dimensional geometries using transfer functions, we find evidence that the square lattice model exhibits an ordinary thermodynamic phase transition, with power-law singularities in the thermodynamics described by the usual set of critical exponents. This is in contrast to the widely-held view that the phase transition in the model should be of the Kosterlitz-Thouless type.

We have constructed a Hubbard-type model of bilayer strontium ruthenate $Sr_3Ru_20_7$ . We find that the HartreeFock mean field solution of our model can be made to exhibit a metamagnetic jump that matches that seen in $Sr_3Ru_20_7$ , and this is clearly associated with a certain quasi one-dimensional feature in the electronic structure. We therefore suggest that this is the origin of the metamagnetism in $Sr_3Ru_20_7$ . The metamagnetism in our modelling is associated with a phase-separated mixture of low- and high-magnetisation solutions, which we suggest corresponds to the nematic phase in $Sr_3Ru_20_7$ .