Historically, the soft mode theory of ferroelectric phase transitions has been developed for the high-temperature (paraelectric) phase, where the phonon mode softens upon decreasing the temperature. In the low-temperature ferroelectric phase, a similar phonon softening occurs, also leading to a bosonic condensation of the frozen-in mode at the transition, but in this case the phonon softening occurs upon increasing the temperature. Here we present a soft mode theory of ferroelectric and displacive phase transitions by describing what happens in the low-temperature phase in terms of phonon softening and instability. A new derivation of the generalized Lyddane-Sachs-Teller (LST) relation for materials with strong anharmonic phonon damping is also presented which leads to the expression $arepsilon_{0}/arepsilon_{infty}=|omega_{LO}|^{2}/|omega_{TO}|^{2}$. The theory provides a microscopic expression for $T_c$ as a function of physical parameters, including the mode specific Gr"uneisen parameter. The theory also shows that $omega_{TO} sim (T_{c}-T)^{1/2}$, and again specifies the prefactors in terms of Gr"uneisen parameter and fundamental physical constants. Using the generalized LST relation, the softening of the TO mode leads to the divergence of $epsilon_0$ and to a polarization catastrophe at $T_c$. A quantitative microscopic form of the Curie-Weiss law is derived with prefactors that depend on microscopic physical parameters.
Soft mode theory of ferroelectric phase transitions in the low-temperature phase / L. Casella, A. Zaccone. - In: JOURNAL OF PHYSICS. CONDENSED MATTER. - ISSN 0953-8984. - 33:16(2021 Jan 13). [10.1088/1361-648X/abdb68]
Soft mode theory of ferroelectric phase transitions in the low-temperature phase
A. Zaccone
Ultimo
2021
Abstract
Historically, the soft mode theory of ferroelectric phase transitions has been developed for the high-temperature (paraelectric) phase, where the phonon mode softens upon decreasing the temperature. In the low-temperature ferroelectric phase, a similar phonon softening occurs, also leading to a bosonic condensation of the frozen-in mode at the transition, but in this case the phonon softening occurs upon increasing the temperature. Here we present a soft mode theory of ferroelectric and displacive phase transitions by describing what happens in the low-temperature phase in terms of phonon softening and instability. A new derivation of the generalized Lyddane-Sachs-Teller (LST) relation for materials with strong anharmonic phonon damping is also presented which leads to the expression $arepsilon_{0}/arepsilon_{infty}=|omega_{LO}|^{2}/|omega_{TO}|^{2}$. The theory provides a microscopic expression for $T_c$ as a function of physical parameters, including the mode specific Gr"uneisen parameter. The theory also shows that $omega_{TO} sim (T_{c}-T)^{1/2}$, and again specifies the prefactors in terms of Gr"uneisen parameter and fundamental physical constants. Using the generalized LST relation, the softening of the TO mode leads to the divergence of $epsilon_0$ and to a polarization catastrophe at $T_c$. A quantitative microscopic form of the Curie-Weiss law is derived with prefactors that depend on microscopic physical parameters.File | Dimensione | Formato | |
---|---|---|---|
main.pdf
Open Access dal 11/03/2022
Tipologia:
Post-print, accepted manuscript ecc. (versione accettata dall'editore)
Dimensione
382.67 kB
Formato
Adobe PDF
|
382.67 kB | Adobe PDF | Visualizza/Apri |
Casella_2021_J._Phys. _Condens._Matter_33_165401.pdf
accesso riservato
Tipologia:
Publisher's version/PDF
Dimensione
924.67 kB
Formato
Adobe PDF
|
924.67 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.