Mumax3 Script for Micromagnetic Simulation of Hybrid Py Nanodot and CoPd Matrix Structure with Variable Vertical Positioning

Abstract

This repository contains a Mumax³ simulation script designed to model the magnetic behavior of a hybrid nanostructured system consisting of a Permalloy (Py) nanodot embedded into a circular anti-dot vacancy within a Cobalt-Palladium (CoPd) matrix. The script systematically investigates the ground-state magnetization profiles and relaxation processes of the Py nanodot as a function of its vertical displacement ($Z$-shift) relative to the CoPd layer under a varying out-of-plane external magnetic field.

Technical Details & System Geometry

• Software Framework: Mumax³ (Micro-magnetic simulation software).

• Simulation Grid: 160 x 160 x 31 cells with a cell size of 2.5 x 2.5 x 1.0 nm.

• Boundary Conditions: Periodic Boundary Conditions (PBC) applied in the X and Y directions (SetPBC(2, 2, 0)).

• Materials Modeled:

  • Region 1 (Py Nanodot): Diameter 50 nm, thickness 3 nm. Soft magnetic material parameters: M_s = 810 kA/m, A_ex = 10.5 pJ/m, alpha = 0.1.

  • Region 2 (CoPd Matrix with Anti-dot): Matrix thickness 31 nm containing a circular anti-dot defect of diameter 60 nm where the Py dot is positioned. Hard magnetic material with Perpendicular Magnetic Anisotropy (PMA): M_s = 1 MA/m, A_ex = 20 pJ/m, K_u1 = 700 kJ/m³ along the Z-axis, alpha = 0.2.

Simulation Protocol

1. Geometry and Material Initialization: Defines the complementary geometry of the CoPd matrix layer and the shifting Py nanodot.

2. Parametric Sweep over Vertical Shift ($Z$-Shift): The script executes a loop iterating the vertical alignment step-by-step to study how the physical overlap or depth of the Py dot inside the matrix affects its magnetic configuration.

3. Demagnetization/Relaxation Sequence: * An external perpendicular magnetic field (B_ext) is applied along the Z-axis, decreasing cubically from 1.2 T down to <span clas

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