What question did this study set out to answer?

To formulate a mathematical framework describing how thermal agitation alters the magnetization direction of single-domain ferromagnetic particles over time.

June 1, 1963Physical Review

Thermal Fluctuations of a Single-Domain Particle

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Authors

WBWilliam Fuller BrownUniversity of Minnesota

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Implication

Theoretical analysis models magnetization orientation dynamics in single-domain ferromagnetic particles, indicating precise relaxation rates across high-energy thermal barriers.

Key Points

To formulate a mathematical framework describing how thermal agitation alters the magnetization direction of single-domain ferromagnetic particles over time.
Augmented Gilbert's equation of motion with a random-field term to formulate a Langevin-type equation for particle magnetization.
Derived a Fokker-Planck partial differential equation to track the probability density evolution of magnetization orientations using the fluctuation-dissipation theorem.
Evaluated non-equilibrium solutions under axial symmetry and high energy barriers relative to thermal energy using variational minimization and Kramers' barrier escape theory.
Demonstrated that gyroscopic terms vanish under axial symmetry, simplifying non-equilibrium orientation probability calculations into an energy minimization problem.
Calculated magnetization reversal and escape rates over large energy barriers relative to thermal energy (kT), bridging continuous diffusion and discrete relaxation models.
Defined theoretical boundaries for the validity of the discrete-orientation approximation in superparamagnetism and magnetic aftereffects.

Cite This Study

William Fuller Brown (1963) studied this question.

synapsesocial.com/papers/69d6f36bfca0359822aa8dc1 https://doi.org/10.1103/physrev.130.1677

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June 1, 1963Physical Review

Thermal Fluctuations of a Single-Domain Particle

View Full Paper

Ask AI

Bookmark

Authors

WBWilliam Fuller BrownUniversity of Minnesota

Discussion

Member takes

Implication

Theoretical analysis models magnetization orientation dynamics in single-domain ferromagnetic particles, indicating precise relaxation rates across high-energy thermal barriers.

Key Points

To formulate a mathematical framework describing how thermal agitation alters the magnetization direction of single-domain ferromagnetic particles over time.
Augmented Gilbert's equation of motion with a random-field term to formulate a Langevin-type equation for particle magnetization.
Derived a Fokker-Planck partial differential equation to track the probability density evolution of magnetization orientations using the fluctuation-dissipation theorem.
Evaluated non-equilibrium solutions under axial symmetry and high energy barriers relative to thermal energy using variational minimization and Kramers' barrier escape theory.
Demonstrated that gyroscopic terms vanish under axial symmetry, simplifying non-equilibrium orientation probability calculations into an energy minimization problem.
Calculated magnetization reversal and escape rates over large energy barriers relative to thermal energy (kT), bridging continuous diffusion and discrete relaxation models.
Defined theoretical boundaries for the validity of the discrete-orientation approximation in superparamagnetism and magnetic aftereffects.

Cite This Study

William Fuller Brown (1963) studied this question.

synapsesocial.com/papers/69d6f36bfca0359822aa8dc1 https://doi.org/10.1103/physrev.130.1677

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