Observation of soft phonon mode in ${\mathrm{TbFe}}_{3}{({\mathrm{BO}}_{3})}_{4}$ by inelastic neutron scattering

Observation of soft phonon mode in ${TbFe}_{3} {({BO}_{3})}_{4}$ by inelastic neutron scattering

M. S. Pavlovskiy, K. A. Shaykhutdinov, L. S. Wu, G. Ehlers, V. L. Temerov, I. A. Gudim, A. S. Shinkorenko, and A. Podlesnyak

Phys. Rev. B 97, 054313 – Published 28 February 2018

Abstract

The phonon dispersion in terbium iron borate ${TbFe}_{3} {({BO}_{3})}_{4}$ has been measured by inelastic neutron scattering in a temperature range $180 < T < 350$ K through the displacive structural transition at $T_{S} = 192.5$ K and studied by ab initio calculations. Significant, but not complete, softening of the transverse acoustic (TA) branch has been observed at the corner of the Brillouin zone ( $Λ$ point) at temperatures $T ⪆ T_{S}$ , in full agreement with theoretical calculations. The TA soft mode undergoes considerable broadening at the $Λ$ point near the transition temperature that can be attributed to the anharmonic interference between transverse acoustic and optical modes.

Received 16 November 2017
Revised 23 January 2018

DOI:https://doi.org/10.1103/PhysRevB.97.054313

Physics Subject Headings (PhySH)

Lattice dynamics Phase transitions

Inelastic neutron scattering

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

M. S. Pavlovskiy¹, K. A. Shaykhutdinov¹, L. S. Wu², G. Ehlers³, V. L. Temerov¹, I. A. Gudim¹, A. S. Shinkorenko¹, and A. Podlesnyak^2,*

¹Kirensky Institute of Physics, Federal Research Center, Krasnoyarsk 660036, Russia
²Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
³Neutron Technologies Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA

^*Corresponding author: podlesnyakaa@ornl.gov

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Vol. 97, Iss. 5 — 1 February 2018

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Figure 1
Top: Schematic crystal structure of ${TbFe}_{3} {({BO}_{3})}_{4}$ . (a) The helicoidal chains of edge-sharing ${FeO}_{6}$ octahedra with threefold symmetry. Tb and B atoms are omitted for clarity. (b) The ${FeO}_{6}$ octahedra interconnected by two kinds of ${BO}_{3}$ triangles (green) and $R O_{6}$ distorted prisms (violet). Bottom: (c) Brillouin zone with symmetry points and axes of the trigonal $R 32$ symmetry group.
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Figure 2
Theoretically calculated phonon spectrum along high-symmetry directions of the first Brillouin zone of ${TbFe}_{3} {({BO}_{3})}_{4}$ in the $R 32$ structure (the $Λ_{1}$ point is between $P_{1}$ and $Q_{1}$ ). Imaginary frequencies of the unstable modes are shown in the real negative frequency range. The acoustic branches are marked in red. The right side of the figure shows the partial phonon density of states of the constituent elements: terbium, yellow; iron, blue; oxygen, green; boron, pink.
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Figure 3
Temperature dependence of the specific heat of ${TbFe}_{3} {({BO}_{3})}_{4}$ . The arrows show the antiferromagnetic $T_{N} = 37.4 (1)$ K and structural $T_{S} = 192.5 (1)$ K transition temperatures.
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Figure 4
Reciprocal $(H 0 L)$ map of ${TbFe}_{3} {({BO}_{3})}_{4}$ measured on CNCS at $T = 180$ K (a) and 350 K (b). Data are elastic scattering only, integrated over the energy transfer range $\pm 0.5$ meV. The dotted lines represent the intersection of the Brillouin zone with the $K = 0$ plane for the high-temperature structure. The inset shows the symmetry points of the Brillouin zone with the $R 32$ structure. Axis values are in reciprocal lattice units (r.l.u.). Note that not all weak reflections are clear visible due to instrumental constraints.
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Figure 5
Color maps of the inelastic neutron scattering spectra measured in ${TbFe}_{3} {(^{11} {BO}_{3})}_{4}$ single crystal at $T =$ 350 (a), 250 (b), 198 (c) and 180 K (d), showing the acoustic phonon dispersion along the $Γ \to Λ$ direction, where lower and higher energy branches are assigned to two transverse acoustic (TA) and longitudinal acoustic (LA) modes, respectively. The integration depth along the $K$ and $L$ directions is $\pm 0.1$ r.l.u.
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Figure 6
(a) INS spectra of the soft phonon mode at the $Λ$ point at different temperatures, obtained by integration in a $q$ range $H, K, L < 0.1$ r.l.u. The solid curves are fits to the data by a damped harmonic oscillator model (2). The elastic line was fitted by a Gaussian function. (b) Comparison between experimentally observed (green, 350 K; blue, 250 K; black, 198 K) and calculated (red line) TA phonon dispersion along the $Γ \to Λ$ crystal orientation, at different temperatures.
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Physical Review B

covering condensed matter and materials physics

Observation of soft phonon mode in ${TbFe}_{3} {({BO}_{3})}_{4}$ by inelastic neutron scattering

M. S. Pavlovskiy, K. A. Shaykhutdinov, L. S. Wu, G. Ehlers, V. L. Temerov, I. A. Gudim, A. S. Shinkorenko, and A. Podlesnyak

Phys. Rev. B 97, 054313 – Published 28 February 2018

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Physical Review B

covering condensed matter and materials physics

Observation of soft phonon mode in TbFe3(BO3)4 by inelastic neutron scattering

M. S. Pavlovskiy, K. A. Shaykhutdinov, L. S. Wu, G. Ehlers, V. L. Temerov, I. A. Gudim, A. S. Shinkorenko, and A. Podlesnyak

Phys. Rev. B 97, 054313 – Published 28 February 2018

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Observation of soft phonon mode in ${TbFe}_{3} {({BO}_{3})}_{4}$ by inelastic neutron scattering