Research ArticleMATERIALS SCIENCE

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

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Science Advances  11 Mar 2016:
Vol. 2, no. 3, e1501492
DOI: 10.1126/sciadv.1501492
  • 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. Hx is applied along the magnetic hard axis to remove the uniaxial anisotropy barrier, whereas Hy 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 my-Hy loop (easy axis) (A) and the mx-Hx 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, kBT 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 (Hcalib), saturation magnetization (MS), 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, kBT ln(2) for T = 300 K.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/2/3/e1501492/DC1

    Fig. S1. The temperature dependence of the magnetization curves as measured by MOKE on both the easy and hard axes.

    Fig. S2. m-H loops of the total magnetic moment of the full sample.

    Fig. S3. (A) Hard axis m-H curves corresponding to stage 1 of the Landauer erasure protocol with various sample tilt angles.

    Fig. S4. (A) The simulated energy dissipation at 0 K by varying the maximum fields (Hx, max and Hy, max) field.

    Video S1. The comprehensive hysteresis loops during the complete erasure process.

    References (1416)

  • Supplementary Materials

    This PDF file includes:

    • Fig. S1. The temperature dependence of the magnetization curves as measured by MOKE on both the easy and hard axes.
    • Fig. S2. m-H loops of the total magnetic moment of the full sample.
    • Fig. S3. (A) Hard axis m-H curves corresponding to stage 1 of the Landauer erasure protocol with various sample tilt angles.
    • Fig. S4. (A) The simulated energy dissipation at 0 K by varying the maximum fields (Hx, max and Hy, max) field.
    • Legend for video S1
    • References (14–16)

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    Other Supplementary Material for this manuscript includes the following:

    • Video S1 (.avi format). The comprehensive hysteresis loops during the complete erasure process.

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