# Micromagnetic Simulation of Round Ferromagnetic Nanodots with Varying Roughness and Symmetry

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

^{3}which works on GPUs [34].

_{S,Fe}= 1700 × 10

^{3}A/m as magnetization at saturation, A

_{Fe}= 21 × 10

^{−12}J/m as exchange constant and K

_{1,Fe}= 48 × 10

^{3}J/m

^{3}as magneto-crystalline anisotropy constant [35]. The Gilbert damping constant was chosen with a value of α = 0.5 to represent the quasistatic case.

^{3}unless mentioned differently.

_{L}) and transversal magnetization components (M

_{T}), spatially resolved screenshots were taken to investigate the magnetic states and magnetization reversal processes. The simulations were performed at angles θ of the external magnetic field from 0° to 90° at intervals of 15°.

## 3. Results and Discussion

^{3}. This curve again looks quantitatively different from the former curves. Comparing it with both curves simulated with the (92 × 92) mask without edge thinning, it can be stated that no large difference is visible between cell sizes of (5 nm)

^{3}and (2 nm)

^{3}, but reducing the edge roughness quantitatively (not qualitatively) changes the hysteresis loops.

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Sketches of the five cases under examination: (

**a**) case 1; (

**b**) case 2; (

**c**) case 3; (

**d**) case 4; and (

**e**) case 5; (

**f**) definition of angles in this study. The colour of the snapshots depends on the orientation of the magnetization: red = magnetization pointing to the right, blue = magnetization pointing to the left, white = magnetization pointing from top to bottom or vice versa.

**Figure 2.**(

**a**,

**c**,

**e**) Hysteresis loops and (

**b**,

**d**,

**f**) snapshots of the magnetization reversal from positive to negative saturation and back for case 1, simulated for the angles θ depicted in the graphs.

**Figure 3.**(

**a**) Hysteresis loops, simulated for case 1 at θ = 0° with different random orientations of anisotropy axes and different edge definitions; (

**b**) comparison between different cells sizes and edge constructions; (

**c**) comparison between different simulation ΔH; (

**d**) snapshots for the magnetization reversal with “smoothed” edges.

**Figure 4.**(

**a**,

**c**) Hysteresis loops and (

**b**,

**d**) snapshots of the magnetization reversal from positive to negative saturation and back for case 2, simulated for the angles depicted in the graphs.

**Figure 5.**(

**a**,

**c**,

**e**) Hysteresis loops and (

**b**,

**d**,

**f**) snapshots of the magnetization reversal from positive to negative saturation and back for case 3, simulated for the angles depicted in the graphs.

**Figure 6.**(

**a**) Hysteresis loop and (

**b**) snapshots of the magnetization reversal from positive to negative saturation and back for case 4, simulated for θ = 60°.

**Figure 7.**(

**a**,

**c**,

**e**) Hysteresis loops and (

**b**,

**d**,

**f**) snapshots of the magnetization reversal from positive to negative saturation and back for case 5, simulated for the angles depicted in the graphs.

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**MDPI and ACS Style**

Steinmetz, P.; Ehrmann, A.
Micromagnetic Simulation of Round Ferromagnetic Nanodots with Varying Roughness and Symmetry. *Condens. Matter* **2021**, *6*, 19.
https://doi.org/10.3390/condmat6020019

**AMA Style**

Steinmetz P, Ehrmann A.
Micromagnetic Simulation of Round Ferromagnetic Nanodots with Varying Roughness and Symmetry. *Condensed Matter*. 2021; 6(2):19.
https://doi.org/10.3390/condmat6020019

**Chicago/Turabian Style**

Steinmetz, Pia, and Andrea Ehrmann.
2021. "Micromagnetic Simulation of Round Ferromagnetic Nanodots with Varying Roughness and Symmetry" *Condensed Matter* 6, no. 2: 19.
https://doi.org/10.3390/condmat6020019