Magnetic Exchange Coupling Energy Calculation Using Interpolated Rotation Angles
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Solution Overview
Problem
Existing micro-magnetization analysis methods face accuracy issues when increasing the mesh size beyond 10 nm, leading to increased rotation angles of magnetization vectors, which results in decreased calculation accuracy of magnetic exchange coupling energy and field, limiting the analysis to smaller magnetic material sizes.
Innovation Solution
A method that interpolates the rotation angle between magnetization vectors using a finite volume method and integrates the magnetic field with a linearly interpolated rotation axis, allowing for accurate calculation of magnetic exchange coupling energy and field even at larger mesh sizes, such as 30 nm.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If the mesh size is increased to reduce computational resources and time, then productivity improves, but measurement precision deteriorates due to increased rotation angles of magnetization vectors
Solution Approach 1:
The invention changes the calculation parameters by introducing a rotation angle threshold (e.g., 10 degrees) to determine when to apply the improved calculation method. When the rotation angle between adjacent magnetization vectors exceeds this threshold, the patent applies a corrected formula that accounts for the larger angle, thereby maintaining calculation accuracy even with larger mesh sizes.
Solution Approach 2:
The invention replaces the standard continuous approximation method with an alternative calculation approach that specifically handles cases with larger rotation angles. Instead of relying on the assumption of small continuous variations, the patent substitutes a more robust calculation method that works accurately for both small and large rotation angles, enabling larger mesh sizes without sacrificing precision.
2Area of stationary object
If the mesh size is increased beyond 10 nm, then the analysis area that can be handled increases, but manufacturing precision deteriorates as the rotation angle between adjacent magnetization vectors exceeds acceptable limits
Solution Approach 1:
The invention modifies the calculation parameters by incorporating rotation angle thresholds (e.g., 10 degrees) that trigger the application of improved calculation formulas. This allows the system to adaptively maintain precision across different mesh sizes by switching calculation methods based on the actual rotation angles present in the model.
Solution Approach 2:
The invention introduces dynamic adaptability by allowing the calculation method to change based on the rotation angle conditions. The system dynamically selects between standard and improved calculation approaches depending on whether rotation angles remain below or exceed the threshold, enabling accurate analysis of both small and large area models.
3Device complexity
If the mesh size is increased to analyze larger magnetic material areas, then the device complexity reduces, but measurement precision deteriorates due to inaccurate magnetic exchange coupling energy calculation
Solution Approach 1:
The invention changes key calculation parameters by introducing rotation angle thresholds that determine when to apply the improved calculation method. This parameter change enables the system to maintain accuracy in magnetic exchange coupling field calculations even when using simpler, larger-mesh models with fewer elements.
Solution Approach 2:
The invention substitutes the standard calculation method with an improved approach that specifically addresses the inaccuracies introduced by larger mesh sizes. This substitution replaces the assumption of small continuous variations with a more robust method that accurately handles larger rotation angles, maintaining precision while reducing model complexity.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach enables accurate micro-magnetization analysis at larger mesh sizes, maintaining calculation accuracy and reducing computational resources and time, while allowing analysis of larger magnetic material areas.
Implementation Method 1
The magnetic exchange coupling field Hex exerts a force that originally acts between adjacent atoms
Implementation Method 2
The motion of micro-magnetization is governed by a governing equation referred to as the LLG (Landau-Lifshitz-Gilbert) equation
Data Source
AI summary
A non-transitory computer-readable recording medium stores a magnetic program causing a computer to perform an exchange coupling energy calculating process including interpolating a rotation angle between two magnetization vectors disposed at the respective centers of two adjacent elements used in a finite volume method with reference to a rotation axis perpendicular to the two magnetization vectors, and calculating a magnetic exchange coupling field by integrating a magnetic field acting as a force exerted on the two magnetization vectors with the interpolated rotation angle.