# Magnetization Reversal in Concave Iron Nano-Superellipses

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

_{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 cubic magnetocrystalline anisotropy constant [37]. The Gilbert damping constant was 0.5 (quasistatic case), the crystalline orientation was set to constant, with the easy cubic anisotropy axes along 0° and 90° corresponding to epitaxially grown nanostructures. This is in contrast to a previous investigation of square iron nanodots with arbitrary anisotropy orientation per cell [11], to enable investigating the effect of an epitaxial growth in addition to the modification of the sample shape, and thus the shape anisotropy.

_{L}) and transversal magnetization components (M

_{T}) were calculated, and screenshots were taken during the magnetization-reversal processes. The hysteresis loops and six snapshots of the magnetization-reversal process per simulation are depicted in Supplementary Information.

## 3. Results and Discussion

_{C}and reversibility fields H

_{rev}in the angular range of 0°−90°. Values in Figure 6a,c and Figure 6b,d were equal, depicted against the angles of the external magnetic field or the sample number. In most cases, 45° showed the highest coercive field, indicating that this orientation corresponds to an easy axis [41,42,43]. Deviations from this behaviour, as shown in Figure 6c by comparing 0° and 45° for Samples SE10 and SE20, can be attributed to the previously discussed high symmetry of the 0° orientation, which may suppress magnetization reversal, since no rotational direction is favoured by geometry or external magnetic field.

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Sketches of some shapes under examination: (

**a**) SE0; (

**b**) SE20; (

**c**) SE40; (

**d**) SE60; and (

**e**) SE90; (

**f**) definition of angles in this study.

**Figure 2.**(

**a**,

**c**,

**e**) Hysteresis loops and (

**b**,

**d**,

**f**) snapshots of the magnetization reversal from positive to negative saturation and back, simulated for SE0 at angles defined in the graphs.

**Figure 3.**(

**a**,

**c**,

**e**) Hysteresis loops and (

**b**,

**d**,

**f**) snapshots of magnetization reversal from positive to negative saturation and back, simulated for Sample SE20 at angles defined in the graphs.

**Figure 4.**(

**a**,

**c**) Hysteresis loops and (

**b**,

**d**) snapshots of magnetization reversal from positive to negative saturation and back, simulated for SE30 at angles defined in the graphs.

**Figure 5.**(

**a**,

**c**,

**e**) Hysteresis loops and (

**b**,

**d**,

**f**) snapshots of magnetization reversal from positive to negative saturation and back, simulated for SE50 at angles defined in the graphs.

**Figure 6.**(

**a**,

**c**) Coercive fields and (

**b**,

**d**) reversibility fields as function of (

**a**,

**b**) the angle of the external magnetic field or (

**c**,

**d**) the sample number, respectively.

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Öncü, E.; Ehrmann, A.
Magnetization Reversal in Concave Iron Nano-Superellipses. *Condens. Matter* **2021**, *6*, 17.
https://doi.org/10.3390/condmat6020017

**AMA Style**

Öncü E, Ehrmann A.
Magnetization Reversal in Concave Iron Nano-Superellipses. *Condensed Matter*. 2021; 6(2):17.
https://doi.org/10.3390/condmat6020017

**Chicago/Turabian Style**

Öncü, Emre, and Andrea Ehrmann.
2021. "Magnetization Reversal in Concave Iron Nano-Superellipses" *Condensed Matter* 6, no. 2: 17.
https://doi.org/10.3390/condmat6020017