#
Pressure–Temperature Phase Diagram of Multiferroic TbFe_{2.46}Ga_{0.54}(BO_{3})_{4}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

## 3. Results and Discussion

#### 3.1. Symmetry Analysis

#### 3.2. Angular-Dependent Raman Spectra

#### 3.3. Phase Transitions at Atmospheric Pressure

#### 3.4. p–T Phase Diagram

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

MDPI | Multidisciplinary Digital Publishing Institute |

FWHM | Full width at half maximum |

HH | Parallel polarisation of incident and scattered light |

HV | Cross polarisation of incident and scattered light |

## Appendix A. Calculated Intensities of Raman Modes

**Figure A1.**Calculated intensity dependence of Raman modes in the HH and HV polarisation on rotation angle in plane. The angle to z-axis is 30 degrees.

**Figure A2.**Calculated intensity dependence of Raman modes in the HH and HV polarisation on rotation angle in the plane. The angle to z-axis (vertical) is 60 degrees.

**Figure A3.**Calculated intensity dependence of Raman modes in the HH and HV polarisation on rotation angle in plane. The angle to z-axis is 90 degrees.

## Appendix B. Photos of the TbFe_{2.46}Ga_{0.54}(BO_{3})_{4} Crystal in the DAC

**Figure A5.**Sample and high-pressure sensor in the high-pressure diamond anvil cell (DAC) at different pressure–temperature conditions; 4:1 methanol–ethanol alcohol mixture as a pressure transmitting media.

## References

- Vopson, M.M. Fundamentals of Multiferroic Materials and Their Possible Applications. Crit. Rev. Solid State Mater. Sci.
**2015**, 40, 223–250. [Google Scholar] [CrossRef] [Green Version] - Fiebig, M. Revival of the magnetoelectric effect. J. Phys. D Appl. Phys.
**2005**, 38, R123–R152. [Google Scholar] [CrossRef] - Eerenstein, W.; Mathur, N.D.; Scott, J.F. Multiferroic and magnetoelectric materials. Nature
**2006**, 442, 759–765. [Google Scholar] [CrossRef] [PubMed] - Hinatsu, Y.; Doi, Y.; Ito, K.; Wakeshima, M.; Alemi, A. Magnetic and calorimetric studies on rare-earth iron borates LnFe
_{3}(BO_{3})_{4}(Ln = Y, La–Nd, Sm–Ho). J. Solid State Chem.**2003**, 172, 438–445. [Google Scholar] [CrossRef] - Krylov, A.S.; Sofronova, S.N.; Gudim, I.A.; Vtyurin, A.N. Magnetoelastic interactions in Raman spectra of Ho
_{1−x}Nd_{x}Fe_{3}(BO_{3})_{4}crystals. Solid State Commun.**2013**, 174, 26–29. [Google Scholar] [CrossRef] - Krylov, A.S.; Sofronova, S.N.; Gudim, I.A.; Krylova, S.N.; Kumar, R.; Vtyurin, A.N. Manifestation of magnetoelastic interactions in Raman spectra of Ho
_{x}Nd_{1−x}Fe_{3}(BO_{3})_{4}crystals. J. Adv. Dielectr.**2018**, 8, 1850011. [Google Scholar] [CrossRef] [Green Version] - Leonyuk, N.I.; Leonyuk, L.I. Growth and characterization of RM3(BO
_{3})_{4}crystals. Prog. Cryst. Growth. Charact.**1995**, 31, 179–278. [Google Scholar] [CrossRef] - Moshkina, E.; Krylov, A.; Sofronova, S.; Gudim, I.; Temerov, V. Crystal Growth and Raman Spectroscopy Study of Sm
_{1−x}La_{x}Fe_{3}(BO_{3})_{4}Ferroborates. Cryst. Growth Des.**2016**, 16, 6915–6921. [Google Scholar] [CrossRef] - Moshkina, E.; Krylova, S.; Gudim, I.; Molokeev, M.; Temerov, V.; Pavlovskiy, M.S.; Vtyurin, A.; Krylov, A. Gallium Composition-Dependent Structural Phase Transitions in HoFe
_{3−x}Ga_{x}(BO_{3})_{4}Solid Solutions: Crystal Growth, Structure, and Raman Spectroscopy Study. Cryst. Growth Des.**2020**, 20, 1058–1069. [Google Scholar] [CrossRef] - Fausti, D.; Nugroho, A.A.; van Loosdrecht, P.H.; Klimin, S.A.; Popova, M.N.; Bezmaternykh, L.N. Raman scattering from phonons and magnons in RFe
_{3}(BO_{3})_{4}. Phys. Rev. B**2006**, 74, 024403. [Google Scholar] [CrossRef] [Green Version] - Ritter, C.; Balaev, A.; Vorotynov, A.; Petrakovskii, G.; Velikanov, D.; Temerov, V.; Gudim, I. Magnetic structure, magnetic interactions and metamagnetism in terbium iron borate TbFe
_{3}(BO_{3})_{4}: A neutron diffraction and magnetization study. J. Phys. Condens. Matter**2007**, 19, 196227. [Google Scholar] [CrossRef] - Popova, E.A.; Volkov, D.V.; Vasiliev, A.N.; Demidov, A.A.; Kolmakova, N.P.; Gudim, I.A.; Bezmaternykh, L.N.; Tristan, N.; Skourski, Y.; Büchner, B.; et al. Magnetization and specific heat of TbFe
_{3}(**B**_{O3})_{4}: Experiment and crystal-field calculations. Phys. Rev. B**2007**, 75, 224413. [Google Scholar] [CrossRef] [Green Version] - Pavlovskiy, M.S.; Shaykhutdinov, K.A.; Wu, L.S.; Ehlers, G.; Temerov, V.L.; Gudim, I.A.; Shinkorenko, A.S.; Podlesnyak, A. Observation of soft phonon mode in TbFe
_{3}(BO_{3})_{4}by inelastic neutron scattering. Phys. Rev. B**2018**, 97, 054313. [Google Scholar] [CrossRef] [Green Version] - Volkov, D.V.; Popova, E.A.; Kolmakov, N.P.; Demidov, A.A.; Tristan, N.; Skourski, Y.; Buechner, B.; Gudim, I.A.; Bezmaternykh, L.N. Magnetic properties of TbFe
_{3}(BO_{3})_{4}). JMMM**2007**, 316, e717–e720. [Google Scholar] [CrossRef] - Stanislavchuk, T.N.; Chukalina, E.P.; Bezmaternykh, L.N. Study of magnetic phase transitions and magnetic structures in a number of rare-earth ferroborates using an erbium spectroscopic probe. J. Opt. Technol.
**2007**, 74, 139–143. [Google Scholar] [CrossRef] - Gnatchenko, S.L.; Kachur, I.S.; Piryatinskaya, V.G.; Bedarev, V.A.; Pashchenko, M.I. Spectroscopic and magnetooptical investigations of spin-reorientation phase transition in TbFe
_{3}(BO_{3})_{4}. Low Temp. Phys.**2011**, 37, 693–698. [Google Scholar] [CrossRef] - Szaller, D.; Kocsis, V.; Bordács, S.; Fehér, T.; Rõõm, T.; Nagel, U.; Engelkamp, H.; Ohgushi, K.; Kézsmárki, I. Magnetic resonances of multiferroic TbFe
_{3}(BO_{3})_{4}. Phys. Rev. B**2017**, 95, 024427. [Google Scholar] [CrossRef] [Green Version] - Krylova, S.; Gudim, I.; Aleksandrovsky, A.; Vtyurin, A.; Krylov, A. Electronic band structures of NdFe
_{3}(BO_{3})_{4}and NdGa3(BO_{3})_{4}crystals: Ab initio calculations. Ferroelectrics**2021**, 575, 11–17. [Google Scholar] [CrossRef] - Krylova, S.N.; Aleksandrovsky, A.S.; Roginskii, E.M.; Krylov, A.A.; Gudim, I.A.; Vtyurin, A.N. Optical properties of the HoGa3(BO
_{3})_{4}crystal: Experiment and ab initio calculation. Ferroelectrics**2020**, 559, 135–140. [Google Scholar] [CrossRef] - Klimin, S.A.; Fausti, D.; Meetsma, A.; Bezmaternykh, L.N.; Van Loosdrecht, P.H.M.; Palstra, T.T.M. Evidence for differentiation in the iron-helicoidal chain in GdFe
_{3}(BO_{3})_{4}. Acta Cryst. B**2005**, 61, 481–485. [Google Scholar] [CrossRef] [Green Version] - Krylov, A.S.; Gudim, I.A.; Krylova, S.N.; Krylov, A.A.; Vtyurin, A.N. Structural phase transition in TbFe
_{2.5}Ga_{0.5}(BO_{3})_{4}single crystal. Ferroelectrics**2020**, 559, 128–134. [Google Scholar] [CrossRef] - Moshkina, E.; Gudim, I.; Temerov, V.; Krylov, A. Temperature-dependent absorption lines observation in Raman spectra of SmFe
_{3}(BO_{3})_{4}ferroborate. J. Raman Spectrosc.**2018**, 49, 1732–1735. [Google Scholar] [CrossRef] - Popova, M.N.; Stanislavchuk, T.N.; Malkin, B.Z.; Bezmaternykh, L.N. Phase transitions and crystal-field and exchange interactions in TbFe
_{3}(BO_{3})_{4}as seen via optical spectroscopy. J. Phys. Condens. Matter**2012**, 24, 196002. [Google Scholar] [CrossRef] - Peschanskii, A.V.; Yeremenko, A.V.; Fomin, V.I.; Bezmaternykh, L.N.; Gudim, I.A. Raman scattering under structural and magnetic phase transitions in terbium ferroborate. Low Temp. Phys.
**2014**, 40, 171–178. [Google Scholar] [CrossRef] - Adem, U.; Wang, L.; Fausti, D.; Schottenhamel, W.; van Loosdrecht, P.H.M.; Vasiliev, A.; Bezmaternykh, L.N.; Büchner, B.; Hess, C.; Klingeler, R. Magnetodielectric and magnetoelastic coupling in TbFe
_{3}(BO_{3})_{4}. Phys. Rev. B**2010**, 82, 064406. [Google Scholar] [CrossRef] [Green Version] - Bedarev, V.; Pashchenko, M.; Merenkov, D.; Savina, Y.; Pashchenko, V.; Gnatchenko, S.; Bezmaternykh, L.; Temerov, V. The Faraday effect in TbFe
_{3}(BO_{3})_{4}and TbAl_{3}(BO_{3})_{4}borates. J. Magnet. Magnet. Mater.**2014**, 362, 150–153. [Google Scholar] [CrossRef] - Krylov, A.S.; Gudim, I.A.; Nemtsev, I.; Krylova, S.N.; Shabanov, A.V.; Krylov, A.A. Raman study of HoFe
_{3}(BO_{3})_{4}at simultaneously high pressure and high temperature: p–T phase diagram. J. Raman Spectrosc.**2017**, 48, 1406–1410. [Google Scholar] [CrossRef] - Krylov, A.; Pavlovskiy, M.; Kitaev, Y.; Gudim, I.; Andryshin, N.; Vtyurin, A.; Jiang, Q.; Krylova, S. Phase transitions and p–T phase diagram of the multiferroic TbFe
_{3}(BO_{3})_{4}crystal. J. Raman Spectrosc.**2022**. [Google Scholar] [CrossRef] - Datchi, F.; Dewaele, A.; Loubeyre, P.; Letoullec, R.; Godec, Y.L.; Canny, B. Optical pressure sensors for high-pressure–high-temperature studies in a diamond anvil cell. High Press. Res.
**2007**, 27, 447–463. [Google Scholar] [CrossRef] - Rashchenko, S.V.; Kurnosov, A.; Dubrovinsky, L.; Litasov, K.D. Revised calibration of the Sm:SrB4O7 pressure sensor using the Sm-doped yttrium-aluminum garnet primary pressure scale. J. Appl. Phys.
**2015**, 117, 145902. [Google Scholar] [CrossRef] - Orobengoa, D.; Capillas, C.; Aroyo, M.I.; Perez-Mato, J.M. AMPLIMODES: Symmetry-mode analysis on the Bilbao Crystallographic Server. J. Appl. Crystallogr.
**2009**, 42, 820–833. [Google Scholar] [CrossRef] - Perez-Mato, J.M.; Orobengoa, D.; Aroyo, M.I. Mode crystallography of distorted structures. Acta Crystallogr. Sect. A
**2010**, 66, 558–590. [Google Scholar] [CrossRef] [Green Version] - Choi, Y.; Kim, K.; Lim, S.Y.; Kim, J.; Park, J.M.; Kim, J.H.; Lee, Z.; Cheong, H. Complete determination of the crystallographic orientation of ReX2 (X = S, Se) by polarized Raman spectroscopy. Nanoscale Horiz.
**2020**, 5, 308–315. [Google Scholar] [CrossRef] [Green Version] - Peticolas, W.L.; Nafie, L.; Stein, P.; Fanconi, B. Quantum Theory of the Intensities of Molecular Vibrational Spectra. J. Chem. Phys.
**1970**, 52, 1576–1584. [Google Scholar] [CrossRef] - Chang, Y.; He, S.; Sun, M.; Xiao, A.; Zhao, J.; Ma, L.; Qiu, W. Angle-Resolved Intensity of In-Axis/Off-Axis Polarized Micro-Raman Spectroscopy for Monocrystalline Silicon. J. Spectrosc.
**2021**, 2860007. [Google Scholar] [CrossRef] - Aroyo, M.I. (Ed.) International Tables for Crystollography. Vol. A. Space Group Symmetry, 6th ed.; Wiley: Hoboken, NJ, USA, 2016. [Google Scholar]
- Litvin, D.B. Magnetic space-group types. Acta Crystallogr. Sect. A
**2001**, 57, 729–730. [Google Scholar] [CrossRef] [Green Version] - Wills, A. Magnetic structures and their determination using group theory. J. Phys. IV France
**2001**, 11, Pr9-133–Pr9-158. [Google Scholar] [CrossRef] - Litvin, D. Magnetic Group Tables: 1-, 2-, and 3-Dimensional Magnetic Subperiodic Groups and Magnetic Space Groups; International Union of Crystallography: Chester, UK, 2013. [Google Scholar] [CrossRef]
- Cracknell, A.P. Space-Group Selection Rules for Magnetic Crystals. Prog. Theoret. Phys.
**1967**, 38, 1252–1269. [Google Scholar] [CrossRef] [Green Version] - Shubnikov, A.V.; Belov, N. Colored Symmetry, 6th ed.; Pergamon Press: Oxford, UK, 1964. [Google Scholar]
- Krylov, A.; Vtyurin, A.; Gudim, I.; Nemtsev, I.; Krylova, S. Phase diagram and soft modes behaviour TbFe
_{3−X}GaX(BO_{3})_{4}solid solutions with huntite structures. Opt. Spectrosc.**2022**, 130, 84–91. [Google Scholar] - Salje, E.K.; Bismayer, U. Hard mode spectroscopy: The concept and applications. Phase Transit.
**1997**, 63, 1–75. [Google Scholar] [CrossRef] - Bismayer, U. Hard Mode Spectroscopy of Phase Transitions. Rev. Mineral. Geochem.
**2000**, 39, 265–283. [Google Scholar] [CrossRef] - Bismayer, U. Hard mode Raman spectroscopy and its application to ferroelastic and ferroelectric phase transitions. Phase Transit.
**1990**, 27, 211–267. [Google Scholar] [CrossRef] - Salje, E.K.H. Hard mode Spectroscopy: Experimental studies of structural phase transitions. Phase Transit.
**1992**, 37, 83–110. [Google Scholar] [CrossRef] - Piermarini, G.J.; Block, S.; Barnett, J.D.; Forman, R.A. Calibration of the pressure dependence of the R1 ruby fluorescence line to 195 kbar. J. Appl. Phys.
**1975**, 46, 2774–2780. [Google Scholar] [CrossRef] - Ragan, D.D.; Gustavsen, R.; Schiferl, D. Calibration of the ruby R1 and R2 fluorescence shifts as a function of temperature from 0 to 600 K. J. Appl. Phys.
**1992**, 72, 5539–5544. [Google Scholar] [CrossRef] [Green Version]

**Figure 1.**Full Raman spectra transformation with temperature of TbFe${}_{2.46}$Ga${}_{0.54}$(BO${}_{3}$)${}_{4}$. Color code: black—$R32$ phase, red—$P{3}_{1}21$ phase.

**Figure 2.**Raman spectra transformation with temperature of TbFe${}_{2.46}$Ga${}_{0.54}$(BO${}_{3}$)${}_{4}$ in the mid-wavenumber region. Color code: black—$R32$ phase, red—$P{3}_{1}21$ phase.

**Figure 4.**(

**a**–

**f**) Temperature dependencies of Raman line positions (black color) and halfwidths (red color). The dashed line denotes the temperature of structural phase transition 33 K.

**Figure 5.**Raman spectra transformation with pressure of TbFe${}_{2.46}$Ga${}_{0.54}$(BO${}_{3}$)${}_{4}$ at 296 K. Color code: black—$R32$ phase, red—$P{3}_{1}21$ phase.

**Figure 6.**p–T phase diagram of TbFe${}_{2.46}$Ga${}_{0.54}$(BO${}_{3}$)${}_{4}$ crystal. Color code: orange—phase $R32$, dark cyan—phase $P{3}_{1}21$, black—phase boundary.

${\mathit{A}}_{1}$ | E(x) | E(y) | ||||||
---|---|---|---|---|---|---|---|---|

a | 0 | 0 | c | 0 | 0 | 0 | −c | −d |

0 | a | 0 | 0 | −c | d | −c | 0 | 0 |

0 | 0 | b | 0 | d | 0 | −d | 0 | 0 |

**Table 2.**Dependence of the peak position of the vibrational mode on the angle of rotation. Back scattering geometry at 296 K ($R32$ phase) in TbFe${}_{2.46}$Ga${}_{0.54}$(BO${}_{3}$)${}_{4}$ crystal.

Raman Shift, cm${}^{-1}$ | HH | HV | Irred. Repres. |
---|---|---|---|

93 | E | ||

181 | A${}_{1}$ | ||

199 | A${}_{1}$ | ||

448 | E | ||

482 | A${}_{1}$ | ||

736 | E | ||

961 | E | ||

991 | A${}_{1}$ | ||

1237 | E | ||

1413 | E |

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**MDPI and ACS Style**

Krylov, A.; Krylova, S.; Gudim, I.; Kitaev, Y.; Golovkina, E.; Zhang, H.; Vtyurin, A.
Pressure–Temperature Phase Diagram of Multiferroic TbFe_{2.46}Ga_{0.54}(BO_{3})_{4}. *Magnetochemistry* **2022**, *8*, 59.
https://doi.org/10.3390/magnetochemistry8060059

**AMA Style**

Krylov A, Krylova S, Gudim I, Kitaev Y, Golovkina E, Zhang H, Vtyurin A.
Pressure–Temperature Phase Diagram of Multiferroic TbFe_{2.46}Ga_{0.54}(BO_{3})_{4}. *Magnetochemistry*. 2022; 8(6):59.
https://doi.org/10.3390/magnetochemistry8060059

**Chicago/Turabian Style**

Krylov, Alexander, Svetlana Krylova, Irina Gudim, Yuri Kitaev, Elena Golovkina, Haibo Zhang, and Alexander Vtyurin.
2022. "Pressure–Temperature Phase Diagram of Multiferroic TbFe_{2.46}Ga_{0.54}(BO_{3})_{4}" *Magnetochemistry* 8, no. 6: 59.
https://doi.org/10.3390/magnetochemistry8060059