#
Isotropic Nature of the Metallic Kagome Ferromagnet Fe_{3}Sn_{2} at High Temperatures

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

## 3. Results

#### 3.1. Characterization

*****in Figure 1f.

#### 3.2. Inelastic Neutron Scattering

## 4. Discussion

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Crystal structure and characterization of Fe${}_{3}$Sn${}_{2}$. The crystallographic space group is $R\overline{3}m$ with reported lattice parameters $a=b=5.344$ Å and $c=19.845$ Å [8]. (

**a**) View along the

**a**-axis. The solid black line represents the unit cell and Fe atoms are shown as the smaller green circles and Sn atoms are shown as the larger blue circles. A single Fe site is offset from any high symmetry position ($x/a=0.4949$, $y/b=0.5051$, and $z/c=0.1134$) leading to two different Fe-Fe bond lengths in the $ab$-plane (the so-called “breathing” kagome). Two Fe-Fe bond lengths are shown, where the shorter bond is in orange, and the longer bond is in green. (

**b**) A Sn-only layer viewed along the

**c**-axis, where the Sn atoms are arranged on a honeycomb lattice. (

**c**) An Fe-Sn layer viewed along the

**c**-axis, showing the breathing kagome lattice made up of Fe atoms. The axes labels for (

**c**) are the same as in (

**b**), and the parallelogram outlined by a solid black line for both panels represents the unit cell. (

**d**) Magnetization measurements taken at 770 K (solid lines) and 600 K (dashed lines). The samples show no signs of coercivity as the sweep down in field (blue lines) coincides with the sweep up (orange lines) in field. (

**e**) Zero-field cooled (ZFC) magnetic susceptibility measurement taken in a 0.1 T applied magnetic field. The derivative (right axis) clearly shows the ferromagnetic transition at ${T}_{C}\approx 665$ K. (

**f**) Neutron powder diffraction data taken above the magnetic transition at 680 K. The data demonstrate the structure is consistent with that reported. The upper set of red tic marks denote Fe${}_{3}$Sn${}_{2}$ Bragg peak positions and the lower set denote Al Bragg peak positions coming from the sample canister. A few small impurity peaks were observed but not identified, and these are marked by the

*****symbol.

**Figure 2.**(

**a**) A three-dimensional schematic of an isotropic parabolic spin wave dispersion near $Q=0$ and energy transfer, $E=0$. The dispersion is shown as the orange surface, and dashed blue lines show the direction of constant-Q scans cutting through the dispersion surface along E. (

**b**) A two-dimensional schematic demonstrating how the experiment captures the intensity from the spin wave excitations. The orange solid line represents the dispersion, $\hslash \omega \left(q\right)=\Delta +D\left(T\right){q}^{2}$, and the surrounding blue surface represents the full-width-at-half-maximum of the spread in energy of the dispersion, $\mathsf{\Gamma}\left(q\right)$, due to thermally induced magnon-magnon interactions. Dashed blue lines are examples of constant-Q scans made in the experiment. Overlayed on these lines are the instrumental resolution ellipses, $R(Q,E)$, along $Q=0.07$ Å${}^{-1}$ and $0.11$ Å${}^{-1}$. The left panel uses the refined values for the dispersion from the actual data at $T=580$ K in the ${E}_{i}=35$ meV experiment. The right panel uses the same parameters, but increased the gap to be $0.5$ meV in order to demonstrate the sensitivity of the technique to the size of the gap. Here, the scans performed during the experiment wouldn’t be able to reach the signal of the spin waves. (

**c**) The actual data at $T=580$ K in the ${E}_{i}=35$ meV experiment. The solid orange lines are the refined fits to the data, shown as blue circles. The three constant-Q scans are vertically offset from one another for clarity.

**Figure 3.**The temperature dependence of the spin wave stiffness parameter, $D\left(T\right)$. Data from both the ${E}_{i}=13.7$ meV and ${E}_{i}=35$ meV experiments were included in the power law fit, $D\left(T\right)={D}_{0}{\left(\frac{{T}_{C}-T}{{T}_{C}}\right)}^{\nu -\beta}$, shown as the dashed line. Only the lowest four temperatures were used in the Dyson fit, $D\left(T\right)={D}_{0}\left[1-A{\left(\frac{{k}_{B}T}{4\pi {D}_{0}}\right)}^{5/2}\zeta \left(\frac{5}{2}\right)\right]$, shown as the solid line.

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**MDPI and ACS Style**

Dally, R.L.; Phelan, D.; Bishop, N.; Ghimire, N.J.; Lynn, J.W.
Isotropic Nature of the Metallic Kagome Ferromagnet Fe_{3}Sn_{2} at High Temperatures. *Crystals* **2021**, *11*, 307.
https://doi.org/10.3390/cryst11030307

**AMA Style**

Dally RL, Phelan D, Bishop N, Ghimire NJ, Lynn JW.
Isotropic Nature of the Metallic Kagome Ferromagnet Fe_{3}Sn_{2} at High Temperatures. *Crystals*. 2021; 11(3):307.
https://doi.org/10.3390/cryst11030307

**Chicago/Turabian Style**

Dally, Rebecca L., Daniel Phelan, Nicholas Bishop, Nirmal J. Ghimire, and Jeffrey W. Lynn.
2021. "Isotropic Nature of the Metallic Kagome Ferromagnet Fe_{3}Sn_{2} at High Temperatures" *Crystals* 11, no. 3: 307.
https://doi.org/10.3390/cryst11030307