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

摘要

Optimal control of nanomagnets has become an urgent problem for the field of spintronics as technologicaltools approach thermodynamically determined limits of efficiency. In complex, fluctuating systems, such asnanomagnetic bits, finding optimal protocols is challenging, requiring detailed information about the dynamicalfluctuations of the controlled system. We provide a physically transparent derivation of a metric tensor forwhich the length of a protocol is proportional to its dissipation. This perspective simplifies nonequilibriumoptimization 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 thenumber of control parameters is large. We apply these methods to two models of nanomagnetic bits: a Landau-Lifshitz-Gilbert description of a single magnetic spin controlled by two orthogonal magnetic fields, and atwo-dimensional Ising model in which the field is spatially controlled. These calculations reveal nontrivialprotocols for bit erasure and reversal, providing important, experimentally testable predictions for ultra-low-powercomputing.