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

TL;DR

This paper introduces a geometric framework and numerical methods for optimizing control protocols in nanomagnetic systems to minimize energy dissipation, with applications to spintronics and ultra-low power computing.

Contribution

It develops a new geometric approach to quantify dissipation in nanomagnetic control and provides numerical tools for finding optimal protocols in complex systems.

Findings

Derived a metric tensor linking protocol length to dissipation.

Applied methods to models of nanomagnetic bits, revealing nontrivial optimal protocols.

Predicted experimentally testable protocols for energy-efficient bit operations.

Abstract

Optimal control of nanomagnets has become an urgent problem for the field of spintronics as technological tools approach thermodynamically determined limits of efficiency. In complex, fluctuating systems, like nanomagnetic bits, finding optimal protocols is challenging, requiring detailed information about the dynamical fluctuations of the controlled system. We provide a new, physically transparent derivation of a metric tensor for which the length of a protocol is proportional to its dissipation. This perspective simplifies nonequilibrium optimization problems by recasting them in a geometric language. We then describe a numerical method, an instance of geometric minimum action methods, that enables computation of geodesics even when the number of control parameters is large. We apply these methods to two models of nanomagnetic bits: a simple Landau-Lifshitz-Gilbert description of a single magnetic spin controlled by two orthogonal magnetic fields and a two dimensional Ising model in which the field is spatially controlled. These calculations reveal nontrivial protocols for bit erasure and reversal, providing important, experimentally testable predictions for ultra-low power computing.