Exploring the Thermodynamic Limits of Computation in Integrated Systems: Magnetic Memory, Nanomagnetic Logic, and the Landauer Limit

Abstract

Nanomagnetic memory and logic circuits are attractive integrated platforms for studying the fundamental thermodynamic limits of computation. Using the stochastic Landau-Lifshitz-Gilbert equation, we show by direct calculation that the amount of energy dissipated during nanomagnet erasure approaches Landauer's thermodynamic limit of kTln(2) with high precision when the external magnetic fields are applied slowly. In addition, we find that nanomagnet systems behave according to generalized formulations of Landauer's principle that hold for small systems and generic logic operations. In all cases, the results are independent of the anisotropy energy of the nanomagnet. Lastly, we apply our computational approach to a nanomagnet majority logic gate, where we find that dissipationless, reversible computation can be achieved when the magnetic fields are applied in the appropriate order.

Quantum Landauer erasure with a molecular nanomagnet

“…2b-comparable to that proposed previously for classical magnets 6 . In step 1, the magnetic field H y is ramped up to 2 T, the spin states mix and the bit is erased.…”

“…The performance of our spin register in terms of energy-time cost is orders of magnitude better than existing memory devices to date. The result shows that thermodynamics sets a limit on the energy cost of certain quantum operations and illustrates a way to enhance classical computations by using a quantum system.While a computation performed with an ideal binary logic gate (for example, NOT) has no lower energy dissipation limit [5][6][7] , one carried out in a memory device does. The reason is that in the former the bit is merely displaced isentropically in the space of states, whereas in the latter the minimal operation, called Landauer erasure, entails resetting the memory irrespective of its initial state.…”

“…While a computation performed with an ideal binary logic gate (for example, NOT) has no lower energy dissipation limit [5][6][7] , one carried out in a memory device does. The reason is that in the former the bit is merely displaced isentropically in the space of states, whereas in the latter the minimal operation, called Landauer erasure, entails resetting the memory irrespective of its initial state.…”

“…χ z is proportional to the derivative of the magnetization ∂M/∂H and is a function of the temperature T, the frequency ω/2π of the a.c.-field H a.c. and the magnetic field vector H. The magnetization and work can be derived by integrating χ ′ z once and twice with respect to the d.c. magnetic field, respectively. The work W obtained in this manner quantifies the entropy produced during the erasure and measures how reversible the reset operation is 4,6 .…”

Magnetic State of Multilayered Synthetic Antiferromagnets during Soliton Nucleation and Propagation for Vertical Data Transfer

“…[ 3 ] The nonvolatility of this technology, [ 1 ] its potential ultra-low power consumption, [ 4 ] the possibility to address data using spin-transfer-torque [ 5 ] or the spin-Hall effect, [ 6 ] the robustness of some designs against data transfer errors caused by thermal fl uctuations, [ 7 ] and the high speeds of data transfer [ 8 ] have identifi ed NML as a promising candidate for future computing technologies. One of the main unresolved challenges for NMLbased technology is data transfer in the vertical direction, a necessary step toward 3D spintronic systems.…”