#
Mössbauer Spectroscopy of Triphylite (LiFePO_{4}) at Low Temperatures

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## Abstract

**:**

## 1. Introduction

## 2. Experimental and Computational Methods

## 3. Results and Discussion

#### 3.1. Structural and Magnetic Measurements

#### 3.2. Mössbauer Spectroscopy of LiFePO${}_{4}$

#### 3.3. Theoretical Exploration of Magnetism and Hyperfine Interactions

## 4. Conclusions and Outlook

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References and Notes

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**Figure 1.**The crystal structure of LiFePO${}_{4}$. The unit cell is indicated by blue lines. Fe coordination octahedra are also displayed. Fe atomic sites are denoted as Fe1, Fe2, Fe3, and Fe4 (there are two atoms shown for Fe1 and Fe2 atomic sites because of unit cell translation periodicity).

**Figure 2.**The XRD patterns of the LiFePO${}_{4}$ sample at room temperature. Experimental points are represented by red circles, whereas the green curve shows the fitted spectrum. Main peak indices are also given along with the peak positions (bottom part of the figure).

**Figure 3.**Temperature dependences of the ${\sigma}_{\mathrm{ZFC}}$ (zero field cooled—open circles), ${\sigma}_{\mathrm{FC}}$ (field cooled—solid circles) magnetization and inverse molar susceptibility ${\chi}_{\mathrm{m}}^{-1}$ (open triangles) of the LiFePO${}_{4}$ sample at the magnetic field 1 T.

**Figure 4.**The magnetization curves of the LiFePO${}_{4}$ sample measured at temperatures 4.2 K and 60 K.

**Figure 6.**The ${}^{57}$Fe Mössbauer spectrum of LiFePO${}_{4}$ at liquid helium temperature ($T=4.2$ K, ${B}_{\mathrm{ext}}=0$ T). The inset shows the distribution of ${B}_{\mathrm{hf}}$ at the nuclei.

**Figure 7.**The ${}^{57}$Fe Mössbauer spectrum of LiFePO${}_{4}$ at temperature $T=4.2$ K and external magnetic field ${B}_{\mathrm{ext}}=6$ T. The inset displays the distribution of ${B}_{\mathrm{eff}}$ at the ${}^{57}$Fe nuclei.

**Figure 8.**Electric field gradient (EFG) tensor principal axes for Fe1, Fe2, Fe3, and Fe4 cations (shown with their corresponding coordination octahedra; cf. Figure 1). Coloring of EFG ${V}_{\mathrm{zz}}$, ${V}_{\mathrm{yy}}$, and ${V}_{\mathrm{xx}}$ axes/vectors is illustrated for the Fe1 case and kept identical for other cations. The length of vectors corresponds to the size of ${V}_{\mathrm{zz}}$, ${V}_{\mathrm{yy}}$, and ${V}_{\mathrm{xx}}$ EFG tensor components.

**Table 1.**The hyperfine parameters determined from the ${}^{57}$Fe Mössbauer spectra in LiFePO${}_{4}$ for the three experiments performed. I stands for the intensity of spectral components. Underlined numbers represent the mean values of corresponding quantities. In the case of ${B}_{\mathrm{hf}}$ (${B}_{\mathrm{ext}}=6$ T), the value is in fact the mean value of ${B}_{\mathrm{eff}}$. Whereas for ${B}_{\mathrm{ext}}=0$ T ($T=4.2$ K), it is not necessary to consider the value as an average since the distribution width is very small.

Spectrum Type | T | ${\mathit{B}}_{\mathbf{ext}}$ | ${\mathit{B}}_{\mathbf{hf}}$ | $\mathbf{IS}$ | $\mathbf{QS}$ | I | $\mathit{\Gamma}$ | ${\mathit{V}}_{\mathbf{zz}}$ | $\mathit{\eta}$ | $\mathit{\varphi}$ | $\mathit{\vartheta}$ | $\mathbf{\Delta}{\mathit{B}}_{\mathbf{eff}}$ |
---|---|---|---|---|---|---|---|---|---|---|---|---|

(K) | (T) | (T) | (mm/s) | (mm/s) | (%) | (mm/s) | (10${}^{21}$ V/m${}^{2}$) | (${}^{\circ}$) | (${}^{\circ}$) | (T) | ||

D | 60 | 0 | – | 1.33(2) | 3.01(2) | 100 | 0.30(1) | – | – | – | – | – |

O | 4.2 | 0 | 12.4(2) | 1.35(2) | 3.05(2) | 100 | 0.29(1) | 16.7 | 0.77(1) | 0 | 0 | ∼0.3 |

O | 4.2 | 6 | 12.7(2) | 1.35(2) | 3.04(2) | 100 | 0.29(1) | 16.7 | 0.78(1) | ∼143 | ∼13 | ∼6 |

**Table 2.**Results of density functional theory (DFT) calculations for the three antiferromagnetic (AF) configurations. The first column indicates the AF configuration. $\Delta {E}_{\mathrm{AF}}$ is the unit cell total energy relative to the lowest energy configuration. ${B}_{\mathrm{hf}}$ covers the contact (isotropic) interaction only.

Order | $\mathbf{\Delta}{\mathit{E}}_{\mathbf{AF}}$ (meV) | ${\mathit{V}}_{\mathbf{zz}}$ (10${}^{21}$ V/m${}^{2}$) | $\phantom{\rule{1.em}{0ex}}\mathit{\eta}$ | ${\mathit{B}}_{\mathbf{hf}}$ (T) |
---|---|---|---|---|

AF1 | 35.9 | 14.2 | 0.61 | 32.7 |

AF2 | 00.0 | 14.1 | 0.63 | 32.8 |

AF3 | 65.1 | 13.1 | 0.55 | 31.4 |

**Table 3.**Results of easy/hard magnetization direction calculations with the spin-orbit coupling (SOC) taken into account. The first column indicates the direction with which Fe ion MMs are collinear. $\Delta {E}_{\mathrm{eh}}$ is the unit cell total energy relative to the easy direction case. ${B}_{\mathrm{hf}}$ also includes orbital and spin dipolar contributions.

MM $\left|\right|$ | $\mathbf{\Delta}{\mathit{E}}_{\mathbf{eh}}$ (meV) | ${\mathit{V}}_{\mathbf{zz}}$ (10${}^{21}$ V/m${}^{2}$) | $\phantom{\rule{1.em}{0ex}}\mathit{\eta}$ | ${\mathit{m}}_{\mathbf{l}}$ (${\mathit{\mu}}_{\mathit{b}}$) | ${\mathit{B}}_{\mathbf{hf}}$ (T) |
---|---|---|---|---|---|

[100] | 4.55 | 14.0 | 0.65 | 0.08 | 30.5 |

[010] | 0.00 | 14.1 | 0.63 | 0.11 | 11.7 |

[001] | 9.19 | 14.1 | 0.62 | 0.03 | 43.3 |

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**MDPI and ACS Style**

Kmječ, T.; Kohout, J.; Dopita, M.; Veverka, M.; Kuriplach, J.
Mössbauer Spectroscopy of Triphylite (LiFePO_{4}) at Low Temperatures. *Condens. Matter* **2019**, *4*, 86.
https://doi.org/10.3390/condmat4040086

**AMA Style**

Kmječ T, Kohout J, Dopita M, Veverka M, Kuriplach J.
Mössbauer Spectroscopy of Triphylite (LiFePO_{4}) at Low Temperatures. *Condensed Matter*. 2019; 4(4):86.
https://doi.org/10.3390/condmat4040086

**Chicago/Turabian Style**

Kmječ, Tomáš, Jaroslav Kohout, Milan Dopita, Miroslav Veverka, and Jan Kuriplach.
2019. "Mössbauer Spectroscopy of Triphylite (LiFePO_{4}) at Low Temperatures" *Condensed Matter* 4, no. 4: 86.
https://doi.org/10.3390/condmat4040086