# Micromagnetic Simulations of Chaotic Ferromagnetic Nanofiber Networks

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Simulations

_{S}= 1700 × 10

^{3}A/m, exchange constant A = 21 × 10

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

_{1}= 48 × 10

^{3}J/m

^{3}. The Gilbert damping constant was set to α = 0.5 (equivalent to a quasi-static case).

^{−11}J/m, magnetic polarization at saturation J

_{s}= 1 T, and the Gilbert damping constant α = 0.01.

## 3. Results and Discussion

_{x}) and along the z-axis (M

_{z}).

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Magnetization reversal process in sample NF1 for an external magnetic field along 45° from “lower left” to “upper right” orientation. From Blachowicz et al. [29].

**Figure 2.**Thickness dependence of (

**a**) the longitudinal and (

**b**) the transverse hysteresis loops, simulated for sample NF1 under an angle of 0°.

**Figure 3.**Thickness dependence of (

**a**) the longitudinal and (

**b**) the transverse hysteresis loops, simulated for sample NF1 under an angle of 45° (see Figure 1).

**Figure 4.**Thickness dependence of (

**a**) the longitudinal and (

**b**) the transverse hysteresis loops, simulated for a sample NF1 under an angle of 90°.

**Figure 5.**Angle dependence of (

**a**) the longitudinal and (

**b**) the transverse hysteresis loops, simulated for sample NF1 with a thickness of 120 nm.

**Figure 6.**Thickness dependence of (

**a**) the longitudinal and (

**b**) the transverse hysteresis loops, simulated for sample NF2 under an angle of 0°.

**Figure 7.**Thickness dependence of (

**a**) the longitudinal and (

**b**) the transverse hysteresis loops, simulated for sample NF2 under an angle of 45°.

**Figure 8.**Thickness dependence of (

**a**) the longitudinal and (

**b**) the transverse hysteresis loops, simulated for sample NF2 under an angle of 90°.

**Figure 9.**Angle dependence of (

**a**) the longitudinal and (

**b**) the transverse hysteresis loops, simulated for sample NF2 with a thickness of 120 nm.

**Figure 10.**Angle dependence of the longitudinal and transverse hysteresis loops simulated for sample NF2 with a thickness of 120 nm.

**Figure 11.**Influence of neighboring fibers in different distances on the magnetization reversal process, simulated for an angle of 45° and a thickness of 120 nm. (

**a**) two neighboring fibers NF2, (

**b**) three neighboring fibers NF2, (

**c**) five neighboring fibers NF2, and (

**d**) two adjacent fibers NF1.

**Figure 12.**(

**a**) Definition of the axes, magnetization components, (

**b**) M

_{x}, and (

**c**) M

_{z}in the non-random case of 0° possible deviation of the fiber orientation from the z-orientation.

**Figure 13.**Fiber orientations used in the simulations for random angle ranges, depicted in steps of 10°: (

**a**) 10°, (

**b**) 20°, (

**c**) 30°, (

**d**) 40°, (

**e**) 50°, (

**f**) 60°, (

**g**) 70°, (

**h**) 80°, and (

**i**) 90°.

**Figure 14.**Hysteresis loops, simulated for an external magnetic field sweep along the x-axis and random angle ranges, depicted in steps of 10°: (

**a**) 10°, (

**b**) 20°, (

**c**) 30°, (

**d**) 40°, (

**e**) 50°, (

**f**) 60°, (

**g**) 70°, (

**h**) 80°, and (

**i**) 90°.

**Figure 15.**Hysteresis loops, simulated for an external magnetic field sweep along the z-axis and random angle ranges, depicted in steps of 10°: (

**a**) 10°, (

**b**) 20°, (

**c**) 30°, (

**d**) 40°, (

**e**) 50°, (

**f**) 60°, (

**g**) 70°, (

**h**) 80°, and (

**i**) 90°.

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**MDPI and ACS Style**

Blachowicz, T.; Döpke, C.; Ehrmann, A. Micromagnetic Simulations of Chaotic Ferromagnetic Nanofiber Networks. *Nanomaterials* **2020**, *10*, 738.
https://doi.org/10.3390/nano10040738

**AMA Style**

Blachowicz T, Döpke C, Ehrmann A. Micromagnetic Simulations of Chaotic Ferromagnetic Nanofiber Networks. *Nanomaterials*. 2020; 10(4):738.
https://doi.org/10.3390/nano10040738

**Chicago/Turabian Style**

Blachowicz, Tomasz, Christoph Döpke, and Andrea Ehrmann. 2020. "Micromagnetic Simulations of Chaotic Ferromagnetic Nanofiber Networks" *Nanomaterials* 10, no. 4: 738.
https://doi.org/10.3390/nano10040738