M. Miura, B. Maiorov, T. Kato, T. Shimode, K. Wada, S. Adachi, and K. Tanabe, Strongly enhanced flux pinning in one-step deposition of (Equation presented) superconductor films with uniformly dispersed (Equation presented) nanoparticles, Nat. Commun. 4, 2499 (2013) 10.1038/ncomms3499.
D. Pergolesi, E. Fabbri, A. D'Epifanio, E. Di Bartolomeo, A. Tebano, S. Sanna, S. Licoccia, G. Balestrino, and E. Traversa, High proton conduction in grain-boundary-free yttrium-doped barium zirconate films grown by pulsed laser deposition, Nat. Mater. 9, 846 (2010) 10.1038/nmat2837.
P. S. Dobal, A. Dixit, R. S. Katiyar, Z. Yu, R. Guo, and A. S. Bhalla, Micro-Raman scattering and dielectric investigations of phase transition behavior in the (Equation presented) system, J. Appl. Phys. 89, 8085 (2001) 10.1063/1.1369399.
M. Acosta, N. Novak, V. Rojas, S. Patel, R. Vaish, J. Koruza, G. A. Rossetti Jr., and J. Rödel, (Equation presented)-based piezoelectrics: Fundamentals, current status, and perspectives, Appl. Phys. Rev. 4, 041305 (2017) 10.1063/1.4990046.
H. D. Megaw, Origin of ferroelectricity in barium titanate and other perovskite-Type crystals, Acta Cryst. 5, 739 (1952) 10.1107/S0365110X52002069.
Y. L. Li and L. Q. Chen, Temperature-strain phase diagram for (Equation presented) thin films, Appl. Phys. Lett. 88, 072905 (2006) 10.1063/1.2172744.
R. E. Cohen and H. Krakauer, Lattice dynamics and origin of ferroelectricity in (Equation presented): Linearized-Augmented-plane-wave total-energy calculations, Phys. Rev. B 42, 6416 (1990) 10.1103/PhysRevB.42.6416.
R. A. Evarestov and A. V. Bandura, First-principles calculations on the four phases of (Equation presented), J. Comput. Chem. 33, 1123 (2012) 10.1002/jcc.22942.
R. Raffaele, Ab initio simulation of the properties of ferroelectric materials, Modelling Simul. Mater. Sci. Eng. 11, R69 (2003) 10.1088/0965-0393/11/4/201.
Y. Zhang, J. Hong, B. Liu, and D. Fang, Strain effect on ferroelectric behaviors of (Equation presented) nanowires: A molecular dynamics study, Nanotechnology 21, 015701 (2010) 10.1088/0957-4484/21/1/015701.
Z. Ma, L. Xi, H. Liu, F. Zheng, H. Gao, Z. Chen, and H. Chen, Ferroelectric phase transition of (Equation presented) single crystal based on a tenth order Landau-Devonshire potential, Comput. Mater. Sci. 135, 109 (2017) 10.1016/j.commatsci.2017.04.011.
Y. L. Li, L. E. Cross, and L. Q. Chen, A phenomenological thermodynamic potential for (Equation presented) single crystals, J. Appl. Phys. 98, 064101 (2005) 10.1063/1.2042528.
W. Zhong, D. Vanderbilt, and K. M. Rabe, Phase transitions in (Equation presented) from first principles, Phys. Rev. Lett. 73, 1861 (1994) 10.1103/PhysRevLett.73.1861.
W. Zhong, D. Vanderbilt, and K. M. Rabe, First-principles theory of ferroelectric phase transitions for perovskites: The case of (Equation presented), Phys. Rev. B 52, 6301 (1995) 10.1103/PhysRevB.52.6301.
S. Tinte, M. G. Stachiotti, M. Sepliarsky, R. L. Migoni, and C. O. Rodriguez, Atomistic modelling of (Equation presented) based on first-principles calculations, J. Phys. Condens. Matter 11, 9679 (1999) 10.1088/0953-8984/11/48/325.
J. M. Vielma and G. Schneider, Shell model of (Equation presented) derived from ab-initio total energy calculations, J. Appl. Phys. 114, 174108 (2013) 10.1063/1.4827475.
Y. Qi, S. Liu, I. Grinberg, and A. M. Rappe, Atomistic description for temperature-driven phase transitions in (Equation presented), Phys. Rev. B 94, 134308 (2016) 10.1103/PhysRevB.94.134308.
S. Tinte, J. Íñiguez, K. M. Rabe, and D. Vanderbilt, Quantitative analysis of the first-principles effective Hamiltonian approach to ferroelectric perovskites, Phys. Rev. B 67, 064106 (2003) 10.1103/PhysRevB.67.064106.
B. G. Dick and A. W. Overhauser, Theory of the dielectric constants of alkali halide crystals, Phys. Rev. 112, 90 (1958) 10.1103/PhysRev.112.90.
G. V. Gibbs, R. T. Downs, D. F. Cox, N. L. Ross, C. T. Prewitt, K. M. Rosso, T. Lippmann, and A. Kirfel, Bonded interactions and the crystal chemistry of minerals: A review, Z. Krist. Cryst. Mater. 223, 01 (2008) 10.1524/zkri.2008.0002.
R. He, H. Wu, L. Zhang, X. Wang, F. Fu, S. Liu, and Z. Zhong, Structural phase transitions in (Equation presented) from deep potential molecular dynamics, Phys. Rev. B 105, 064104 (2022) 10.1103/PhysRevB.105.064104.
L. Gigli, M. Veit, M. Kotiuga, G. Pizzi, N. Marzari, and M. Ceriotti, Thermodynamics and dielectric response of (Equation presented) by data-driven modeling, npj Comput. Mater. 8, 209 (2022) 10.1038/s41524-022-00845-0.
N. Xu, Y. Shi, Y. He, and Q. Shao, A deep-learning potential for crystalline and amorphous Li-Si alloys, J. Phys. Chem. C 124, 16278 (2020) 10.1021/acs.jpcc.0c03333.
L. Zhang, M. Chen, X. Wu, H. Wang, W. E., and R. Car, Deep neural network for the dielectric response of insulators, Phys. Rev. B 102, 041121 (R) (2020) 10.1103/PhysRevB.102.041121.
J. C. Wojdeł, P. Hermet, M. P. Ljungberg, P. Ghosez, and J. Íñiguez, First-principles model potentials for lattice-dynamical studies: General methodology and example of application to ferroic perovskite oxides, J. Phys.: Condens. Matter 25, 305401 (2013) 10.1088/0953-8984/25/30/305401.
P. Zubko, J. C. Wojdeł, M. Hadjimichael, S. Fernandez-Pena, A. Sené, I. Luk'yanchuk, J.-M. Triscone, and J. Íñiguez, Negative capacitance in multidomain ferroelectric superlattices, Nature (London) 534, 524 (2016) 10.1038/nature17659.
M. A. Pereira Gonçalves, C. Escorihuela-Sayalero, P. Garca-Fernández, J. Junquera, and J. Íñiguez, Theoretical guidelines to create and tune electric skyrmion bubbles, Sci. Adv. 5, eaau7023 (2019) 10.1126/sciadv.aau7023.
H. Aramberri, N. S. Fedorova, and J. Íñiguez, Ferroelectric/paraelectric superlattices for energy storage, Sci. Adv. 8, eabn4880 (2022) 10.1126/sciadv.abn4880.
M. Torrent, F. Jollet, F. Bottin, G. Zérah, and X. Gonze, Implementation of the projector augmented-wave method in the abinit code: Application to the study of iron under pressure, Comput. Mater. Sci. 42, 337 (2008) 10.1016/j.commatsci.2007.07.020.
X. Gonze, A brief introduction to the abinit software package, Z. Krist. Cryst. Mater. 220, 558 (2005) 10.1524/zkri.220.5.558.65066.
J. P. Perdew, A. Ruzsinszky, G. I. Csonka, O. A. Vydrov, G. E. Scuseria, L. A. Constantin, X. Zhou, and K. Burke, Restoring the density-gradient expansion for exchange in solids and surfaces, Phys. Rev. Lett. 100, 136406 (2008) 10.1103/PhysRevLett.100.136406.
J. Laflamme Janssen, Y. Gillet, S. Poncé, A. Martin, M. Torrent, and X. Gonze, Precise effective masses from density functional perturbation theory, Phys. Rev. B 93, 205147 (2016) 10.1103/PhysRevB.93.205147.
X. Gonze, First-principles responses of solids to atomic displacements and homogeneous electric fields: Implementation of a conjugate-gradient algorithm, Phys. Rev. B 55, 10337 (1997) 10.1103/PhysRevB.55.10337.
X. Gonze and C. Lee, Dynamical matrices, Born effective charges, dielectric permittivity tensors, and interatomic force constants from density-functional perturbation theory, Phys. Rev. B 55, 10355 (1997) 10.1103/PhysRevB.55.10355.
C. Escorihuela-Sayalero, J. C. Wojdeł, and J. Íñiguez, Efficient systematic scheme to construct second-principles lattice dynamical models, Phys. Rev. B 95, 094115 (2017) 10.1103/PhysRevB.95.094115.
See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevB.108.134117 for all the anharmonic terms of bounded model; total energy and pressure change with time steps; phonon dispersion for rhombohedral phase of BTO from bounded model; and polarization and lattice constants changes with temperature from unbounded model.
G. H. Kwei, A. C. Lawson, S. J. L. Billinge, and S. W. Cheong, Structures of the ferroelectric phases of barium titanate, J. Phys. Chem. C 97, 2368 (1993) 10.1021/j100112a043.
B. J. Campbell, H. T. Stokes, D. E. Tanner, and D. M. Hatch, isodisplace: A web-based tool for exploring structural distortions, J. Appl. Crystallogr. 39, 607 (2006) 10.1107/S0021889806014075.
A. Togo, L. Chaput, T. Tadano, and I. Tanaka, Implementation strategies in phonopy and phono3py, J. Phys. Condens. Matter 35, 353001 (2023) 10.1088/1361-648X/acd831.
A. Togo, First-principles phonon calculations with phonopy and phono3py, J. Phys. Soc. Jpn. 92, 012001 (2022) 10.7566/JPSJ.92.012001.
F. Mayer, M. N. Popov, D. M. Evans, S. Krohns, M. Deluca, and J. Spitaler, Improved description of the potential energy surface in (Equation presented) by anharmonic phonon coupling, Phys. Rev. B 106, 064108 (2022) 10.1103/PhysRevB.106.064108.
A. Paul, J. Sun, J. P. Perdew, and U. V. Waghmare, Accuracy of first-principles interatomic interactions and predictions of ferroelectric phase transitions in perovskite oxides: Energy functional and effective Hamiltonian, Phys. Rev. B 95, 054111 (2017) 10.1103/PhysRevB.95.054111.
G. A. Samara, Pressure and temperature dependences of the dielectric properties of the perovskites (Equation presented) and (Equation presented), Phys. Rev. 151, 378 (1966) 10.1103/PhysRev.151.378.
R. E. Cohen, Origin of ferroelectricity in perovskite oxides, Nature (London) 358, 136 (1992) 10.1038/358136a0.
O. Trithaveesak, J. Schubert, and C. Buchal, Ferroelectric properties of epitaxial (Equation presented) thin films and heterostructures on different substrates, J. Appl. Phys. 98, 114101 (2005) 10.1063/1.2135891.