Experimental test of Landauer's principle in single-bit operations on nanomagnetic memory bits

Abstract

Minimizing energy dissipation has emerged as the key challenge in continuing to scale the performance of digital computers. The question of whether there exists a fundamental lower limit to the energy required for digital operations is therefore of great interest. A well-known theoretical result put forward by Landauer states that any irreversible single-bit operation on a physical memory element in contact with a heat bath at a temperature T requires at least k B T ln(2) of heat be dissipated from the memory into the environment, where k B is the Boltzmann constant. We report an experimental investigation of the intrinsic energy loss of an adiabatic single-bit reset operation using nanoscale magnetic memory bits, by far the most ubiquitous digital storage technology in use today. Through sensitive, high-precision magnetometry measurements, we observed that the amount of dissipated energy in this process is consistent (within 2 SDs of experimental uncertainty) with the Landauer limit. This result reinforces the connection between "information thermodynamics" and physical systems and also provides a foundation for the development of practical information processing technologies that approach the fundamental limit of energy dissipation. The significance of the result includes insightful direction for future development of information technology.

Keywords: Energy Dissipation; Information thermodynamics; Landauer Erasure; Minimum Energy; Nanomagnetic memory.

Fig. 1. Thermodynamics background.

(A) Description of single-bit reset by time sequence. Before the erasure, the memory stores information in state 0 or 1; after the reset, the memory stores information in state 0 in accordance with the unit probability. (B) Timing diagram for the external magnetic fields applied during the restore-to-one process. H_x is applied along the magnetic hard axis to remove the uniaxial anisotropy barrier, whereas H_y is applied along the easy axis to force the magnetization into the 1 state. Illustrations are provided of the magnetization of the nanomagnet at the beginning and end of each stage and of the direction of the applied field in the x-y plane.

Fig. 2. The magneto-optic Kerr microscopy experimental set up.

(A) Schematic of the experimental MOKE setup. (B) SEM images of the sample. The circle represents the approximate size of the probe laser spot. (C) MFM images of individual single-domain nanomagnets.

Fig. 3. The experimental m-H hysteresis loops of nanomagnets during the reset operation.

(A and B) The m_y-H_y loop (easy axis) (A) and the m_x-H_x loop (hard axis) (B). The indicated stages correspond to the timing diagram shown in Fig. 1B.

Fig. 4. Experimental results for total energy dissipation.

(A) The temperature dependence of energy dissipation during single-bit reset. Triangles represent experimental data obtained from integrating and subtracting hysteresis loops similar to the example shown in Fig. 3. The red line is the best fit to the experimental data. The black squares represent the Landauer limit, k_BT ln(2). (B) The experimentally determined energy dissipation during the reset operation. Different bars from 1 to 5 represent separate experimental runs to measure energy dissipation. The values in the table indicate estimated relative SD of the measurements of average dot area (Area), average dot thickness (Thickness), applied magnetic field (H_calib), saturation magnetization (M_S), residual remanence due to “tilt” effect (Lithography), and the run-to-run variation (Trials), respectively. The total experimental error was determined from the root-mean-square value for all of the variables in the table. The dotted line represents the Landauer limit, k_BT ln(2) for T = 300 K.