Monte-Carlo Simulations of Magnetic Ising Models for Sodium Cobaltate

Sodium cobaltate is a material whose physical properties depend strongly on the concentration of sodium. It is unique because it acts as a thermoelectric material, and a superconductor at different concentrations of sodium. The sodium ions move within layers sandwiched between CoO₂ layers. The sodium ions can occupy two different types of site; one low energy and one high energy. These sites neighbor each other, and by representing the two sites as pseudospin vectors pointing to the occupied site, we can study the ordering of sodium ions by simulating how the pseudospins interact with each other via the Ising Hamiltonian. This is done with the use of a Monte-Carlo Metropolis simulation with the results being presented here. The code is used to study the lowest energy structure of sodium cobaltate at different sodium concentrations.