Geometric approach to optimal nonequilibrium control: Minimizing dissipation in nanomagnetic spin systems

Area of Science:

• Spintronics and Nanomagnetics
• Statistical Mechanics and Thermodynamics
• Optimal Control Theory

Background:

• Technological limits in spintronics necessitate efficient nanomagnet control.
• Optimizing complex, fluctuating nanomagnetic systems is challenging due to the need for detailed dynamical information.
• Current methods struggle with high-dimensional control parameters and energy dissipation.

Purpose of the Study:

• To derive a physically transparent metric tensor for nanomagnet control, linking protocol length to dissipation.
• To develop a numerical method for computing optimal control protocols in complex systems.
• To apply these methods to realistic nanomagnetic bit models and predict experimental outcomes.

Main Methods:

• Derivation of a metric tensor for nonequilibrium systems, enabling a geometric interpretation of control protocols.
• Implementation of geometric minimum action methods for calculating geodesics in high-dimensional control spaces.
• Application to two distinct nanomagnetic bit models: Landau-Lifshitz-Gilbert and 2D Ising models.

Main Results:

• A novel geometric framework simplifies the optimization of control protocols by relating them to path length and dissipation.
• The numerical method efficiently computes optimal control paths (geodesics) even with numerous control parameters.
• Non-trivial, experimentally testable protocols for bit erasure and reversal in nanomagnets were identified.

Conclusions:

• The geometric approach offers a powerful tool for understanding and optimizing control in complex fluctuating systems.
• This work provides a pathway towards designing ultra-low-power spintronic devices.
• The predicted protocols offer concrete, testable hypotheses for experimental validation in nanomagnet-based computing.