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### Interplay of metallicity, ferroelectricity and layer charges in SmNiO3/BaTiO3
superlattices
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E. Simmen, N.A. Spaldin
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#### Abstract:
Using density-functional theory, we demonstrate that the formal layer charges of the metallic samarium nickelate electrode influence the spontaneous ferroelectric polarization of the barium titanate in SmNiO3/BaTiO3 capacitors. We find that, despite the metallic screening of SmNiO3, the spontaneous polarization of BaTiO3 always aligns with the layer polarization of the SmNiO3 formal charges. We also find zero critical thickness for the ferroelectricity in BaTiO3 in this orientation. The opposite polarization direction is highly disfavored for thin BaTiO3 slabs but becomes less unstable with increasing slab thickness. We construct a simple electrostatic model that allows us both to study the behavior for thicker BaTiO3 and SmNiO3 slabs and to extract the influence of various material parameters on the behavior. We mimic a metal-insulator transition in the SmNiO3 by varying the metallic screening length, which we find influences the stability of the ferroelectric polarization. Our results show that layer charges in the metal electrodes strongly influence the properties of ferroelectric capacitors and can even provide new ways to control them.
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All calculations were performed with VASP and the PBEsol functional with the Ba_sv, Ti_sv, Ni_pv, and Sm_3 pseudopotentials (v54). Relaxations were performed with a VASP version compiled so that only the out-of-plane lattice parameter can change. The phonon calculations were performed with atomate2 and phonopy (2.22.1). The Python code used to generate the publication figures can be found at https://github.com/materialstheory/metSNO-BTO-superlattices.

The directories contain the necessary input files (INCAR, POSCAR, KPOINTS) to reproduce the calculations and the output files to reproduce the figures. For structure relaxations, the POSCARs for a first relaxation run and a subsequent second one (starting from the results of run 1) are provided.

Clarification for the folder structure:  
- bulk: DFT calculations performed on the bulk (for BaTiO3 and SmNiO3)  
  - the results from the phonon calculations are given as a JSON dictionary. They can be read using the loads function from bson.json_util (see GitHub for an example)  
- with_rots / no_rots: DFT calculations for the superlattices containing SmNiO3 with active/disabled rotations  
  - subdirectories are ordered by BTO and SNO thickness  
  - not_relax: static calculation of the energy and the DOS without any prior relaxation of the superlattice  
  - bto_relax: relaxation of only the BaTiO3 slab; SmNiO3 atoms are fixed  
  - full_relax: starting from the result of bto_relax, full relaxation of all atoms in the superlattice and the cell  
  - unhappy: relaxation of the superlattice in the unhappy orientation. Any "unhappy" relaxations are performed with 3 BaTiO3 layers fixed to the unhappy orientation  
  - soft_mode: calculations of the energy as a function of the BaTiO3 polarization. A fraction of 1 corresponds to the full BaTiO3 bulk polarization in the happy orientation, 0 to paraelectric BaTiO3, and -1 to BaTiO3 with full bulk polarization in the unhappy orientation  
- elstat_model: output from the electrostatic model. See the elstat_model_best_parameters.ipynb on GitHub for more details on how they were produced  
  - files in this directory are the results for the fitted parameters. "opt_energy_landscape" contains the entire energy landscape as a function of P_sno and P_bto for different slab thicknesses, "opt_energy_double_well" is a cut of the landscape for P_sno = 0, and "opt_results" contains the minimum-energy P_sno and P_bto as a function of thickness for the happy ("hp") and unhappy ("uhp") orientations  
  - 4_uc_sno: results from the electrostatic model with ("depANDsc" in name) and without ("nsc" in name) electron-hole excitation across the band gap for different factors lambda^2/epsilon_r ("factor") and different band gaps ("eg")