Relaxation approach to quantum-mechanical modeling of ferroelectric and antiferroelectric phase transitions

Abstract

Ferroelectrics and antiferroelectrics are the electric counterparts of ferromagnets and antiferromagnets. These materials undergo temperature- and electric-field-induced phase transitions that give rise to their characteristic hysteresis loops. Modeling such hysteresis loops and associated phase transitions enables both a deeper fundamental understanding and reliable property predictions for this important class of materials. To date, modeling has largely relied on classical approaches, often remaining qualitative and/or empirical. Traditional interpretation of these transitions rests on two assumptions: (i) they are activated Arrhenius-type processes and (ii) they occur well within the classical regime. Here, we demonstrate that a model can instead be built on two ''orthogonal`` assumptions: (i) the phase transitions are relaxational processes and (ii) they require a quantum mechanical treatment. Applying this model to both antiferroelectrics and ferroelectrics overcomes the limitations of traditional models and enables efficient first-principles simulations of phase transitions. Furthermore, the success of our unconventional approach highlights the significance of quantum mechanics in transitions long regarded as purely classical. We anticipate that this framework will be applicable to a broad range of phase transitions, including magnetic, elastic, multiferroic, and electronic, along with modeling of quantum tunneling, rates of chemical reactions, and others.

Figures (10)

• Figure 1: Energy per formula unit as a function of polarization for ferroelectric CsGeBr$_3$ (a) and antiferroelectric PbZrO$_3$ (d) as computed from DFT simulations. Equation of state for ferroelectric CsGeBr$_3$ (b) and antiferroelectric PbZrO$_3$ (e) obtained from their supercell energies. Black and green dots indicate metastable state and ground state, respectively. The experimental polarization as a function of electric field for CsGeBr$_3$ was reported in Ref. zhang2022ferroelectricity and for PbZrO$_3$ (f) at T = 300 K. For PbZrO$_3$, the electric field is applied along [001] pseudo-cubic direction.
• Figure 2: (a) Time evolution of polarization for antiferroelectric PbZrO$_3$ from metastable to ground state at zero Kelvin and under applied DC electric field of 400 kV/cm. (b) The hysteresis loops for PbZrO$_3$ computed from the GSR approach.
• Figure 3: (a)-(c) Time evolution of polarization from the metastable to the ground state in PbZrO$_3$ under DC electric field of 400 kv/cm using different models as given in the titles; (d)-(f) Polarization as a function of electric field in PbZrO$_3$ computed for different temperatures using the models given in the titles. The following parameters were used: $M=$ 10000$m_e$, AC field frequency $\nu=$ 0.12 THz, the integration step $\Delta t=$0.045 fs, $k_{sacale}=$ 1 for DMB Model and $k_{sacale}=$ 0.0125 for LLO, and LO models.
• Figure 4: (a)-(c) Polarization as a function of electric field in PbZrO$_3$ computed for different masses using the models given in the titles. The following parameters were used: temperature for DMB, LLO and LO Model is 1 K, 300 K and 300 K, respectively, $\nu=$ 0.12 THz, $\Delta t=$0.045 fs. $k_{sacale}=$ 1 for DMB Model and $k_{sacale}=$ 0.0125 for LLO, and LO models.
• Figure 5: (a)-(c) Polarization as a function of electric field in PbZrO$_3$ computed with intrinsic dynamics turned on or off using the DMB, LLO, and LO models, respectively. The following simulations parameters were used: $M=$ 10000$m_e$, temperature for DMB, LLO and LO Model is 1 K, 300 K and 300 K, respectively, $\nu=$ 0.93 THz, $\Delta t=$ 0.45 as. $k_{sacale}=$ 1 for DMB Model and $k_{sacale}=$ 0.0125 for LLO, and LO models.