Ferroelectric materials—definition: Which statement correctly characterizes ferroelectric substances in solid-state physics and materials engineering?

Introduction / Context:
Ferroelectric materials (e.g., BaTiO3, PbTiO3) possess a spontaneous electric polarization that can be reversed by an external electric field. Their polarization–electric field relationship shows a characteristic hysteresis loop, analogous to ferromagnetic materials in magnetism. Ferroelectrics are central to non-volatile memories, sensors, actuators, and high-K dielectrics.

Given Data / Assumptions:

• Crystalline solids exhibiting phase transitions to a non-centrosymmetric structure.
• Macroscopic spontaneous polarization exists below Curie temperature.
• External field can switch domain orientations.

Concept / Approach:

“Permanent” here means spontaneous (non-zero at zero field) but not immutable—the polarization can be reoriented by E. This distinguishes ferroelectrics from ordinary dielectrics that only polarize under applied field and lose polarization when E → 0. It also differs from anti-ferroelectrics (net polarization cancels) and paraelectrics (above Curie temperature, no spontaneous polarization).

Step-by-Step Solution:

Verification / Alternative check:

Experimental P–E loops and dielectric anomalies near Curie temperature verify ferroelectric behavior. Crystal symmetry analysis (lack of inversion center) supports spontaneous polarization.

Why Other Options Are Wrong:

• “Cannot be polarized” is the opposite of reality.
• “a_e = 0” (electronic polarizability zero) and “μ_p = 0” are physically incorrect; electronic polarizability is nonzero and μ_p concept is unrelated here.
• “Only electronic polarization with no hysteresis” describes linear dielectrics, not ferroelectrics.

Common Pitfalls:

• Confusing “permanent” with “non-switchable.” Ferroelectric polarization is switchable.

Final Answer:

have a permanent polarization