# Micromagnetic Simulation of Vortex Development in Magnetic Bi-Material Bow-Tie Structures

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Results and Discussion

_{L}is defined as parallel to the external magnetic field, while the transverse magnetization component M

_{T}depicts the hysteresis curve perpendicular to it.

## 3. Materials and Methods

_{S,Fe}= 1700 × 10

^{3}A/m (M

_{S,Py}= 796 × 10

^{3}A/m), exchange constant A

_{Fe}= 21 × 10

^{−12}J/m (A

_{Py}= 10.5 × 10

^{−12}J/m), magneto-crystalline anisotropy constant K

_{1,Fe}= 48 × 10

^{3}J/m

^{3}(K

_{1,Py}= 0.5 × 10

^{3}J/m

^{3}). Along the borders, these values were averaged between the values of the single materials.

^{3}for the whole sample. Simulations were typically performed in the range between ± 200 mT in steps of 0.4 mT; if minor loops were found, the field ranges were correspondingly increased to investigate proper full hysteresis loops. All simulations are started from a fully saturated state of the magnetization along the corresponding angle.

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Sketch of the bow-tie structure under examination consisting of iron (

**black**) and permalloy (

**green**) as well as orientation of the external magnetic field angles.

**Figure 2.**Snapshots of the magnetization reversal process and hysteresis loops of pure iron nanoparticles, simulated for an external field orientation of 45°, for a thickness of (

**a,b**) 15 nm or (

**c,d**) 30 nm, respectively. In all graphs, the longitudinal magnetization M

_{L}is detected parallel to the magnetic field, while the transverse magnetization M

_{T}is perpendicular to it.

**Figure 3.**Snapshots of the magnetization reversal process and hysteresis loops of pure permalloy nanoparticles, simulated for an external field orientation of 30°, for a thickness of (

**a,b**) 15 nm or (

**c,d**) 30 nm, respectively.

**Figure 4.**(

**a**) Snapshots of the magnetization reversal process and (

**b**) hysteresis loops of bow-tie nanoparticles, simulated for an external field orientation of 30° and a thickness of 15 nm.

**Figure 5.**(

**a**) Snapshots of the magnetization reversal process and (

**b**) hysteresis loops of bow-tie nanoparticles, simulated for an external field orientation of 30° and a thickness of 30 nm.

**Figure 6.**(

**a**) Snapshots of the magnetization reversal process and (

**b**) hysteresis loops of bow-tie nanoparticles, simulated for an external field orientation of 45° and a thickness of 15 nm.

**Figure 7.**(

**a**) Snapshots of the magnetization reversal process and (

**b**) hysteresis loops of bow-tie nanoparticles, simulated for an external field orientation of 45° and a thickness of 30 nm.

**Figure 8.**(

**a**) Snapshots of the magnetization reversal process and (

**b**) hysteresis loops of bow-tie nanoparticles, simulated for an external field orientation of 60° and a thickness of 15 nm.

**Figure 9.**(

**a**) Snapshots of the magnetization reversal process and (

**b**) hysteresis loops of bow-tie nanoparticles, simulated for an external field orientation of 60° and a thickness of 30 nm.

**Figure 10.**Single-material bow tie structures (

**a**) as layout and (

**b**) produced with an edge length of 200 nm with negative resist AR-N.

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**MDPI and ACS Style**

Sudsom, D.; Juhász Junger, I.; Döpke, C.; Blachowicz, T.; Hahn, L.; Ehrmann, A. Micromagnetic Simulation of Vortex Development in Magnetic Bi-Material Bow-Tie Structures. *Condens. Matter* **2020**, *5*, 5.
https://doi.org/10.3390/condmat5010005

**AMA Style**

Sudsom D, Juhász Junger I, Döpke C, Blachowicz T, Hahn L, Ehrmann A. Micromagnetic Simulation of Vortex Development in Magnetic Bi-Material Bow-Tie Structures. *Condensed Matter*. 2020; 5(1):5.
https://doi.org/10.3390/condmat5010005

**Chicago/Turabian Style**

Sudsom, Devika, Irén Juhász Junger, Christoph Döpke, Tomasz Blachowicz, Lothar Hahn, and Andrea Ehrmann. 2020. "Micromagnetic Simulation of Vortex Development in Magnetic Bi-Material Bow-Tie Structures" *Condensed Matter* 5, no. 1: 5.
https://doi.org/10.3390/condmat5010005