Schematic showing some details about how the different measurement techniques are conducted in two-dimensional field space. A Stoner-Wohlfarth asteroid curve is also shown, with its origin shifted from the field-space origin due to internal offset fields ( and ).
(a) Schematic of the MTJ multilayer showing the relevant physical quantities that dictate the junction behavior. (b) Simplified model of the free layer, where the magnetization is determined by the two offset field components ( and ), the sample’s uniaxial anisotropy, and the external applied field . (c) Model of the pinned layer magnetization, which is assumed to be the vector sum of two forces: the applied field and the exchange biasing field .
Examples of the raw data from a circle curve (taken at 130 G; dot-dashed line) and a remnant resistance curve (solid line), along with a theoretical remnant resistance curve (dashed line). The two sets of data were taken during the same set of field sweeps.
Experimentally measured angle-dependent asteroid curve of a sample MTJ. Solid circles represent the data, while the solid line represents the best fit to the modified S-W model [Eq. (7)].
Experimental data (solid lines) and theoretical fitting results (dashed lines) for a set of three circle curves (taken at 40, 70, and 130 G) taken on a representative MTJ element. All fits are made using a single set of junction parameters.
Comparison of the measured anisotropy angles obtained from remnant resistance curves (-axis), asteroid measurements (open diamonds), and circle curve fits (open circles).
Comparison between measured transfer curves taken at different field sweep angles (solid lines), with simulated transfer curves based on the extracted circle curve parameters (dashed lines). This plot shows that the circle curve results alone can accurately predict junction behavior in arbitrary applied fields.
Plot showing the distribution of junction anisotropy angle and pinned layer direction as a function of wafer position for the twice-annealed sample. The arrows indicate the pinned layer orientation, while the length and orientation of the solid lines indicate the strength and direction of the sample anisotropy, respectively.
(a) Plot of the positional distribution of junction anisotropy angle and magnitude for the sample with standard annealing. The numbers below each line show the anisotropy angle in degrees, while the length of each line is proportional to the anisotropy strength. (b) Distribution of the extracted pinned layer direction for the same sample, as a function of wafer position.
A summary of the strengths and weaknesses of the different magnetic characterization methods.
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