Debye formulas for a relaxing system with memory

Area of Science:

• Statistical physics
• Condensed matter physics
• Magnetism

Background:

• Rate equations are fundamental in statistical physics.
• Previous models have not incorporated memory effects.
• Understanding system dynamics with memory is crucial.

Purpose of the Study:

• To introduce and analyze an integro-differential rate equation with memory.
• To investigate the impact of memory on the ac susceptibility of magnetic systems.
• To explore frequency-induced diamagnetism as a potential experimental signature.

Main Methods:

• Derivation of a modified Debye formula for a single-domain magnetic particle model.
• Analysis of an integro-differential rate equation incorporating memory time (Θ).
• Numerical calculations to support theoretical predictions.

Main Results:

• The in-phase component of ac susceptibility becomes negative at high frequencies (ω).
• The system exhibits frequency-induced diamagnetism due to memory effects.
• Ferromagnetic coupling enhances memory effects, while antiferromagnetic coupling suppresses them.

Conclusions:

• The introduction of memory into rate equations leads to novel phenomena like frequency-induced diamagnetism.
• Frequency-induced diamagnetism serves as a potential experimental indicator of correlated noise.
• Memory effects significantly alter magnetic system responses, with coupling type playing a key role.