Ising-like models for stacking faults in a free electron metal

Area of Science:

• Condensed Matter Physics
• Materials Science
• Computational Materials Science

Background:

• Calculating stacking fault energies in materials like magnesium is complex due to long-range electronic screening.
• The axial next nearest neighbour Ising (ANNNI) model is a theoretical tool for studying magnetic and structural properties.
• Previous applications of the ANNNI model faced challenges with convergence and accuracy in systems with free electron gases.

Purpose of the Study:

• To extend the ANNNI model to include a general number of spin interactions.
• To accurately calculate stacking fault energies in magnesium using the extended model.
• To compare the performance of density functional theory (DFT) and generalized pseudopotential theory (GPT) for this calculation.

Main Methods:

• Development of an extended axial next nearest neighbour Ising (ANNNI) model.
• Application of high-precision density functional theory (DFT) calculations.
• Utilisation of generalized pseudopotential theory (GPT) with analytic, long-ranged, oscillating pair potentials.

Main Results:

• The standard ANNNI model requires higher-order terms for reasonable accuracy in stacking fault energy calculations.
• The extended ANNNI model exhibited slow convergence in DFT due to the free electron gas, leading to consistency issues.
• Generalized pseudopotential theory (GPT) demonstrated convergence and internal consistency comparable to DFT bandstructure methods without precision loss.
• GPT accurately calculated stacking fault energies in magnesium, with oscillations in model parameters effectively damped without introducing error.

Conclusions:

• The extended ANNNI model, particularly when implemented with GPT, provides an accurate and consistent method for calculating stacking fault energies in magnesium.
• GPT overcomes the convergence and internal consistency challenges encountered with DFT implementations of the ANNNI model in this system.
• The improved performance of GPT is attributed to its ability to handle the long-ranged interactions and damping of oscillations inherent in the electronic structure.