Dielectric hysteresis: does it require AC cycling? Dielectric hysteresis refers to a loop in the polarization–electric field (P–E) relationship. Under which type of excitation is hysteresis observed in practice?

Introduction / Context:
Dielectric (ferroelectric) hysteresis is the path-dependent relationship between polarization P and applied electric field E, producing a closed loop when the field is cycled. This behavior is fundamental for nonvolatile memories, capacitors with voltage-dependent capacitance, and electroceramic actuators.

Given Data / Assumptions:

• We consider materials exhibiting nonlinear, history-dependent polarization (e.g., ferroelectrics like BaTiO3).
• “Observed hysteresis” means tracing a closed P–E loop.
• Field is varied cyclically through positive and negative values.

Concept / Approach:
A static dc field sets a single operating point on the P–E curve; without changing the field, there is no loop—just a point (possibly with remanent polarization if the field is then removed). Hysteresis is revealed when E is swept through a cycle (typically sinusoidal or triangular), i.e., an ac or time-varying field, so that polarization follows a different path on increasing and decreasing E, forming the loop.

Step-by-Step Solution:
Apply dc only: polarization shifts to a steady value; no loop is traced.Apply cyclic (ac) field: increase and decrease E across coercive values.Observe remanence and coercive field leading to a closed P–E loop—this is hysteresis.Hence, hysteresis is practically observed with ac (time-varying) excitation.

Verification / Alternative check:
Standard Sawyer–Tower circuits drive samples with an alternating waveform to record P–E loops; commercial ferroelectric testers use ac cycling to characterize hysteresis.

Why Other Options Are Wrong:
dc: A constant field does not trace a loop. Both ac and dc: Misleading; the loop requires cycling. None: Contradicts well-known ferroelectric behavior. Only pulsed above breakdown: Unrelated to the fundamental requirement of cyclic excitation.

Common Pitfalls:
Confusing remanent polarization (measured after dc poling) with hysteresis loop measurement, which requires varying the field.

Final Answer:
ac