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hysteresis.py generates a hysteresis loop of a ferroelectric material according to Garrity et al 2014.

Requires Numpy, Scipy, Matplotlib, PyYAML.

To generate hysteresis loop, first, create YAML file with values for

  • cell_dims: dimensions of unit cell in bohr.
  • energy_data: path to text file containing space-delimited table. Column 1 contains values of effective coordinate Q (normalised between -1 and 1) expressing an atomic configuration in a 3N-dimensional space between the 2 relaxed ferroelectric configurations. Column 2 contains corresponding values of the energy per unit cell in hartrees.
  • chi_data: path to text file containing space-delimited table. Column 1 contains values of effective coordinate Q (normalised between -1 and 1) expressing an atomic configuration in a 3N-dimensional space between the 2 relaxed ferroelectric configurations. Column 2 contains corresponding values of the electronic contribution to the linear polarizability (in cgs units).
  • remnant_polarisation: remnant polarisation of ferroelectric in uC/cm2.
  • Emax: maximum external field at which to calculate equilibrium polarization in kV/cm.
  • Esamples: number of electric field values between -Emax and +Emax at which polarization will be calculated.
  • debug: int indicating whether contributions to free energy should be printed during minimizations.
    • 0: never output;
    • 1: output after minimization;
    • 2: output at each free energy evaluation during minimization.

See ferro_scripts/example_params.yaml for an example.

Then cd into the ferro_scripts directory and run python hysteresis.py <path to params YAML file>.

Troubleshooting

  1. Hysteresis loop contains fewer points than expected. The electric field values specified through Emax and Esamples may be too large, which leads to most free energy curves having minima outside $Q\in[-1,1]$. Try reducing Emax and/or increasing Esamples.

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