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論文

Neutron flux and energy resolution of direct-geometry disk-chopper spectrometer AMATERAS at J-PARC

楡井 真実; 古府 麻衣子; 中島 健次; 菊地 龍弥*; 河村 聖子; 村井 直樹; 原田 正英; 稲村 泰弘

Journal of Neutron Research, 26(2-3), p.75 - 82, 2024/09

We investigated neutron flux at a sample position and energy resolution of a direct-geometry disk-chopper spectrometer AMATERAS under various chopper conditions and compared them with simulations and calculations. The measured flux was comparable to other similar spectrometers with high flux. The resolution when using a pulse-shaping chopper was in close agreement with the analytical calculations, including the thickness of the disk chopper, the sample size, and the penetration depth into the detector. It is found that the chopper, placed at the intermediate distance of the primary spectrometer, works as a pulse shaper that optimizes the flux and resolution below the incident energy of 10 meV.

論文

Magnetic boson peak in classical spin glasses

古府 麻衣子; 河村 聖子; 村井 直樹; 石井 梨恵子*; 平井 大悟郎*; 有馬 寛*; 舟越 賢一*

Physical Review Research (Internet), 6(1), p.013006_1 - 013006_9, 2024/01

We revisited spin dynamics in archetypical classical spin glass systems, such as Cu$$_{1-x}$$Mn$$_{x}$$ ($$x = 0.017$$, 0.034, and 0.067) dilute alloys and iron aluminosilicate glass using a modern neutron scattering spectrometer with high neutron flux. The former is crystalline, and the latter is amorphous, where their spin glass state is well separated from magnetically ordered phases. Bose-scaled localized magnetic excitations were observed in both compounds below the spin-freezing temperature ($$T_{rm f}$$). The spectrum exhibits a maximum at low energy and a broad tail on the high-energy side. The excitation energy tends to be higher for the material with a higher $$T_{rm f}$$. Above the $$T_{rm f}$$, the spectrum considerably changes with temperature, thereby indicating the emergence of the magnetic relaxation process. The magnetic excitation in the spin glass state has much in common with the boson peak in structural glasses. We consider that the Bose-scaled broad excitation peak is an elementary excitation inherent in disordered systems.

論文

Spin gap in the weakly interacting quantum spin chain antiferromagnet KCuPO$$_{4}$$$$cdot$$H$$_{2}$$O

藤原 理賀; 萩原 雅人; 森田 克洋*; 村井 直樹; 幸田 章宏*; 岡部 博孝*; 満田 節生*

Physical Review B, 107(5), p.054435_1 - 054435_8, 2023/02

 被引用回数:0 パーセンタイル:0.00(Materials Science, Multidisciplinary)

$$S$$ = 1/2ハイゼンベルグ直線鎖反強磁性体は、最も単純なスピンモデルであるが、様々な量子多体現象のプラットフォームを提供する。この論文では、準一次元反強磁性体KCuPO$$_{4}$$$$cdot$$H$$_{2}$$Oの磁性を報告した。$$T_{rm{N}}$$ = 11.7(1)Kにおいて、格子整合な長距離反強磁性秩序が形成され、その磁気モーメントの大きさは0.31(1) $$mu_{rm{B}}$$である事がわかった。また鎖内相互作用$$J$$と鎖間相互作用$$|J'|$$の大きさはそれぞれ172Kと4.25(4)Kと見積もられ、$$|J'|$$/$$J$$の比は0.0247(3)である。中性子非弾性散乱実験により、$$T_{rm{N}}$$より高温では、一次元ハイゼンベルグ量子スピン鎖の特徴である連続体励起スペクトルが観測され、$$T_{rm{N}}$$より低温では、分散励起にスピンギャップが観測された。これらの結果は、弱く結合した$$S$$ = 1/2ハイゼンベルグスピン鎖系で観測される性質と一致する。

論文

Experimental evidence for the significance of optical phonons in thermal transport of tin monosulfide

Wu, P.*; 村井 直樹; Li, T.*; 梶本 亮一; 中村 充孝; 古府 麻衣子; 中島 健次; Xia, K.*; Peng, K.*; Zhang, Y.*; et al.

New Journal of Physics (Internet), 25(1), p.013032_1 - 013032_11, 2023/01

 被引用回数:0 パーセンタイル:0.00(Physics, Multidisciplinary)

The understanding of the lattice dynamics is essential for engineering the thermal transport properties in quantum materials. Based on the canonical point of view, acoustic phonons are believed to be the principal thermal carriers in heat flow. Here, in this work, optical phonons are elucidated to play a pivotal role in determining the lattice thermal conductivity in thermoelectric material SnS by using the state-of-the-art inelastic neutron scattering technique combined with first-principles calculations. Additionally, in contrast to acoustic phonons, optical phonons are observed to exhibit pronounced softening and broadening with temperature. Our observations not only shed light on the significance of the optical phonons in thermal transport but also provide a vital clue to suppress the propagation of optical phonons to optimize the thermoelectric performance of SnS.

論文

Partial breakdown of translation symmetry at a structural quantum critical point associated with a ferroelectric soft mode

石井 悠衣*; 山本 有梨沙*; 佐藤 直大*; 南部 雄亮*; 河村 聖子; 村井 直樹; 尾原 幸治*; 河口 彰吾*; 森 孝雄*; 森 茂生*

Physical Review B, 106(13), p.134111_1 - 134111_7, 2022/10

 被引用回数:0 パーセンタイル:0.00(Materials Science, Multidisciplinary)

We report that complete suppression of a phonon-driven structural phase transition causes partial breakdown of a three-dimensional translation symmetry in a well-defined sublattice. This state is revealed for a dielectric compound, Ba$$_{1-x}$$Sr$$_x$$Al$$_2$$O$$_4$$, that comprises an AlO$$_4$$ network incorporated into a hexagonal Ba(Sr) sublattice. Pair distribution function analyses and inelastic neutron scattering experiments provide clear-cut evidence of the AlO$$_4$$ network forming a continuum of Al-O short-range correlations similar to glasses, whereas the Ba(Sr) sublattice preserves the original translational symmetry. This glassy network significantly dampens the phonon spectrum and transforms it into the broad one resembling those typically observed in glass materials.

論文

Anisotropic magnon damping by zero-temperature quantum fluctuations in ferromagnetic CrGeTe$$_{3}$$

Chen, L.*; Mao, C.*; Chung, J.-H.*; Stone, M. B.*; Kolesnikov, A. I.*; Wang, X.*; 村井 直樹; Gao, B.*; Delaire, O.*; Dai, P.*

Nature Communications (Internet), 13, p.4037_1 - 4037_7, 2022/07

 被引用回数:14 パーセンタイル:76.75(Multidisciplinary Sciences)

Spin and lattice are two fundamental degrees of freedom in a solid, and their fluctuations about the equilibrium values in a magnetic ordered crystalline lattice form quasiparticles termed magnons (spin waves) and phonons (lattice waves), respectively. In most materials with strong spin-lattice coupling (SLC), the interaction of spin and lattice induces energy gaps in the spin wave dispersion at the nominal intersections of magnon and phonon modes. Here we use neutron scattering to show that in the two-dimensional (2D) van der Waals honeycomb lattice ferromagnetic CrGeTe$$_{3}$$, spin waves propagating within the 2D plane exhibit an anomalous dispersion, damping, and breakdown of quasiparticle conservation, while magnons along the c axis behave as expected for a local moment ferromagnet. These results indicate the presence of dynamical SLC arising from the zero-temperature quantum fluctuations in CrGeTe$$_{3}$$, suggesting that the observed in-plane spin waves are mixed spin and lattice quasiparticles fundamentally different from pure magnons and phonons.

論文

Recent update of AMATERAS; A Cold-neutron disk-chopper spectrometer

中島 健次; 河村 聖子; 古府 麻衣子; 村井 直樹; 稲村 泰弘; 菊地 龍弥*; 若井 大介*

JPS Conference Proceedings (Internet), 33, p.011089_1 - 011089_7, 2021/03

J-PARCに設置されている冷中性子ディスクチョッパー型分光器AMATERASの近況について報告する。最後に報告を行った2017年以降、新たな検出器の増設、散乱真空槽の真空系の更新作業(継続中)等を行っている。また、分解能について再調査を実施した。この他、2018年、2019年のJ-PARCの1MW試験時に試験測定も行った。今後の高度化計画についても触れる。

論文

Field-tuned magnetic structure and phase diagram of the honeycomb magnet YbCl$$_3$$

Hao, Y. Q.*; Wo, H. L.*; Gu, Y. M.*; Zhang, X. W.*; Gu, Y. Q.*; Zheng, S. Y.*; Zhao, Y.*; Xu, G. Y.*; Lynn, J. W.*; 中島 健次; et al.

Science China; Physics, Mechanics & Astronomy, 64(3), p.237411_1 - 237411_6, 2021/03

 被引用回数:11 パーセンタイル:69.18(Physics, Multidisciplinary)

We report thermodynamic and neutron diffraction measurements on the magnetic ordering properties of the honeycomb lattice magnet YbCl$$_3$$. We find YbCl$$_3$$ exhibits a N${'e}$el type long-range magnetic order at the wavevector (0, 0, 0) below T$$_N$$ = 600 mK. This magnetic order is associated with a small sharp peak in heat capacity and most magnetic entropy release occurs above the magnetic ordering temperature. The magnetic moment lies in-plane, parallel to the monoclinic a-axis, whose magnitude m$$_{rm Yb}$$ = 0.86(3) $$mu_B$$ is considerably smaller than the expected fully ordered moment of 2.24 $$mu_B$$ for the doublet crystal-field ground state. The magnetic ordering moment gradually increases with increasing magnetic field perpendicular to the ab-plane, reaching a maximum value of 1.6(2) $$mu_B$$ at 4 T, before it is completely suppressed above $$sim$$9 T. These results indicate the presence of strong quantum fluctuations in YbCl$$_3$$.

論文

$$q$$=0 long-range magnetic order in centennialite CaCu$$_{3}$$(OD)$$_{6}$$Cl$$_{2}$$ $$cdot$$ 0.6D$$_{2}$$O; A Spin-$$frac{1}{2}$$ perfect kagome antiferromagnet with $$J_{1}$$-$$J_{2}$$-$$J_{d}$$

飯田 一樹*; 吉田 紘行*; 中尾 朗子*; Jeschke, H. O.*; Iqbal, Y.*; 中島 健次; 河村 聖子; 宗像 孝司*; 稲村 泰弘; 村井 直樹; et al.

Physical Review B, 101(22), p.220408_1 - 220408_6, 2020/06

 被引用回数:25 パーセンタイル:79.61(Materials Science, Multidisciplinary)

鉱物センテニアライトCaCu$$_{3}$$(OD)$$_{6}$$Cl$$_{2}$$ $$cdot$$ 0.6D$$_{2}$$Oの結晶構造と磁気構造をシンクロトロンX線回折と中性子回折測定に密度汎関数理論(DFT)と疑似フェルミオン汎関数繰り込み群(PFFRG)の計算を組み合わせることで調べた。CaCu$$_{3}$$(OD)$$_{6}$$Cl$$_{2}$$ $$cdot$$ 0.6D$$_{2}$$OではCu$$^{2+}$$イオンは反強磁性$$J_{1}$$と幾何学的に完全なカゴメネットワークを形成する。Cu$$^{2+}$$とCa$$^{2+}$$イオン間のサイト間無秩序は見つからなかった。CaCu$$_{3}$$(OD)$$_{6}$$Cl$$_{2}$$ $$cdot$$ 0.6D$$_{2}$$Oは$$T$$$$_{rm N}$$=7.2K以下で磁気秩序を示し、負のベクトルスピンキラリティーを持つ$$q$$=0の磁気構造が現れる。0.3Kでの秩序モーメントは0.58(2)$$mu$$Bに抑えられている。我々のDFT計算では、この系が量子臨界点の近くにあり、$$J_{1}$$-$$J_{2}$$-$$J_{d}$$カゴメ反強磁性体の優れた実現であることを示唆している。

論文

Horizontal line nodes in Sr$$_2$$RuO$$_4$$ proved by spin resonance

飯田 一樹*; 古府 麻衣子; 鈴木 雄大*; 村井 直樹; 河村 聖子; 梶本 亮一; 稲村 泰弘; 石角 元志*; 長谷川 舜介*; 益田 隆嗣*; et al.

Journal of the Physical Society of Japan, 89(5), p.053702_1 - 053702_5, 2020/05

 被引用回数:20 パーセンタイル:78.58(Physics, Multidisciplinary)

We investigated the low-energy incommensurate (IC) magnetic fluctuations in Sr$$_2$$RuO$$_4$$ by the high-resolution inelastic neutron scattering measurements and random phase approximation (RPA) calculations. We observed a spin resonance with energy of $$hbar omega_{rm res}0.56$$ meV centered at a characteristic wavevector $$Q_{rm res}=(0.3,0.3,0.5)$$. The resonance energy corresponds well to the superconducting gap 2$$Delta$$ = 0.56 meV estimated by the tunneling spectroscopy. The spin resonance shows the $$L$$ modulation with a maximum at around $$L = 0.5$$. The $$L$$ modulated intensity of the spin resonance and our RPA calculations indicate that the superconducting gaps regarding the quasi-one-dimensional $$alpha$$ and $$beta$$ sheets at the Fermi surfaces have the horizontal line nodes. These results may set a strong constraint on the pairing symmetry of Sr$$_2$$RuO$$_4$$. We also discuss the implications on possible superconducting order parameters.

論文

Lattice dynamics in FeSe via inelastic X-ray scattering and first-principles calculations

村井 直樹; 福田 竜生; 中島 正道*; 河村 光晶*; 石川 大介*; 田島 節子*; Baron, A. Q. R.*

Physical Review B, 101(3), p.035126_1 - 035126_6, 2020/01

 被引用回数:7 パーセンタイル:38.96(Materials Science, Multidisciplinary)

非弾性X線散乱を用いたFeSe超伝導体のフォノン研究について報告する。実験的に決定したフォノン分散と非磁性相の密度汎関数理論(DFT)とを比較を行うと、両所の間には顕著な不一致が見られた。FeSeは磁気秩序を示さないにもかかわらず、スピン偏極DFTを用いることによって初めて実験結果は再現される。この解析は、強いスピン揺らぎを内在した常時性状態における近似を与える。

論文

Experimental investigation of the suppressed superconducting gap and double-resonance mode in Ba$$_{1-x}$$K$$_{x}$$Fe$$_{2}$$As$$_{2}$$

出田 真一郎*; 村井 直樹; 中島 正道*; 梶本 亮一; 田中 清尚*

Physical Review B, 100(23), p.235135_1 - 235135_7, 2019/12

 被引用回数:3 パーセンタイル:14.55(Materials Science, Multidisciplinary)

Ba$$_{1-x}$$K$$_{x}$$Fe$$_{2}$$As$$_{2}$$ has an exotic physical property where that the C$$_{2}$$-SDW phase suddenly changes to the C$$_{4}$$-magnetic phase and superconductivity is suppressed within a narrow composition range around x = 0.25. We have investigated the doping dependence of the electronic structure of Ba$$_{1-x}$$K$$_{x}$$Fe$$_{2}$$As$$_{2}$$ using angle-resolved photoemission spectroscopy (ARPES) and found an anomaly in the superconducting (SC) gap structure only for x = 0.25 in both the hole and electron Fermi surfaces (FSs). We also propose that the mechanism of a newly observed double-resonance peak by inelastic neutron scattering is understandable by the SC gap obtained by ARPES. Our discovery reveals the important relationship between the C$$_{4}$$- magnetic phase and superconductivity, and provides an opportunity to survey the underlying relationship between the SC gap and resonance mode in the hole-doped iron-based superconductor.

論文

Coexisting spin resonance and long-range magnetic order of Eu in EuRbFe$$_{4}$$As$$_{4}$$

飯田 一樹*; 永井 佑紀; 石田 茂之*; 石角 元志*; 村井 直樹; Christianson, A. D.*; 吉田 紘行*; 稲村 泰弘; 中村 博樹; 中尾 朗子*; et al.

Physical Review B, 100(1), p.014506_1 - 014506_8, 2019/07

 被引用回数:37 パーセンタイル:84.59(Materials Science, Multidisciplinary)

パルス中性子散乱実験による鉄系超伝導体EuRbFe$$_{4}$$As$$_{4}$$のスピン揺らぎ、磁気構造の測定を行い、同物質における超伝導体対称性などの議論を行った。

論文

Study on use of superconducting magnet and first inelastic neutron scattering experiment under magnetic field at 4SEASONS spectrometer

梶本 亮一; 石角 元志*; 吉良 弘*; 金子 耕士; 中村 充孝; 蒲沢 和也*; 稲村 泰弘; 池内 和彦*; 飯田 一樹*; 村井 直樹; et al.

Physica B; Condensed Matter, 556, p.26 - 30, 2019/03

BB2018-0570.pdf:2.17MB

 被引用回数:2 パーセンタイル:9.38(Physics, Condensed Matter)

Magnets are important for studying magnetism and are commonly used as sample environment devices of neutron scattering instruments. However, the use of magnets was prevented at the time-of-flight direct-geometry neutron spectrometer 4SEASONS in Materials and Life Science Experimental Facility (MLF) at J-PARC, because the instrument is surrounded by iron components, and it is equipped with a piece of equipment operated with magnetic bearings. In the present work, we investigate the influence of stray magnetic fields from a superconducting magnet which is shared among neutron scattering instruments in MLF. Based on the investigation, we modified 4SEASONS such that it can be used with the magnet. Finally, we successfully performed the first inelastic neutron scattering experiments with applied magnetic fields using this sample environment.

論文

Quantum magnetisms in uniform triangular lattices Li$$_{2}$$$$A$$Mo$$_{3}$$O$$_{8}$$ ($$A$$ = In, Sc)

飯田 一樹*; 吉田 紘行*; 岡部 博孝*; 片山 尚幸*; 石井 裕人*; 幸田 章宏*; 稲村 泰弘; 村井 直樹; 石角 元志*; 門野 良典*; et al.

Scientific Reports (Internet), 9(1), p.1826_1 - 1826_9, 2019/02

 被引用回数:12 パーセンタイル:64.27(Multidisciplinary Sciences)

Molecular based spin-1/2 triangular lattice systems have attracted research interest. Li$$_2$$$$A$$Mo$$_3$$O$$_8$$ ($$A$$ = In or Sc) is such a compound where spin-1/2 Mo$$_3$$O$$_{13}$$ clusters in place of Mo ions form the uniform triangular lattice. Here, we report exotic magnetisms in Li$$_2$$InMo$$_3$$O$$_8$$ and Li$$_2$$ScMo$$_3$$O$$_8$$ investigated by muon spin rotation ($$mu$$SR) and inelastic neutron scattering (INS) spectroscopies. Li$$_2$$InMo$$_3$$O$$_8$$ exhibits spin wave excitation which is quantitatively described by the nearest neighbor anisotropic Heisenberg model based on the 120$$^{circ}$$ spin structure. In contrast, Li$$_2$$ScMo$$_3$$O$$_8$$ undergoes short-range magnetic order below 4 K with quantum-spin-liquid-like magnetic fluctuations down to the base temperature. Origin of the different ground states is discussed in terms of anisotropies of crystal structures and magnetic interactions.

論文

Status report of the chopper spectrometer 4SEASONS

梶本 亮一; 中村 充孝; 稲村 泰弘; 蒲沢 和也*; 池内 和彦*; 飯田 一樹*; 石角 元志*; 村井 直樹; 吉良 弘*; 中谷 健; et al.

Journal of Physics; Conference Series, 1021(1), p.012030_1 - 012030_6, 2018/06

BB2016-1727.pdf:0.39MB

 被引用回数:3 パーセンタイル:87.45(Nuclear Science & Technology)

4SEASONS is a medium-resolution thermal neutron chopper spectrometer in the Materials and Life Science Experimental Facility (MLF) at J-PARC. Although 4SEASONS is routinely used for many experiments by internal and external users, upgrading and maintenance work is still underway. This paper reviews the recent improvements of the instrument.

論文

Effect of electron correlations on spin excitation bandwidth in Ba$$_{0.75}$$K$$_{0.25}$$Fe$$_{2}$$As$$_{2}$$ as seen via time-of-flight inelastic neutron scattering

村井 直樹; 鈴木 雄大*; 出田 真一郎*; 中島 正道*; 田中 清尚*; 池田 浩章*; 梶本 亮一

Physical Review B, 97(24), p.241112_1 - 241112_6, 2018/06

 被引用回数:6 パーセンタイル:28.27(Materials Science, Multidisciplinary)

非弾性中性子散乱による鉄系超伝導体Ba$$_{0.75}$$K$$_{0.25}$$Fe$$_{2}$$As$$_{2}$$の磁気励起測定を行い、約200meV程度のバンド幅を持つスピン波的分散を観測した。測定されたスペクトルは、同一試料に対する角度分解光電子分光測定により得られた電子バンドの繰り込み因子を考慮し、密度汎関数理論により構築された5軌道ハバード模型に乱雑位相近似を適応する事で再現される。これらの結果は電子バンドの繰り込みという形でしばしば現れる所謂、電子相関効果の観測が非弾性中性子散乱によっても可能であることを示すものである。

論文

Elastic and dynamical structural properties of La and Mn-doped SrTiO$$_{3}$$ studied by neutron scattering and their relation with thermal conductivities

梶本 亮一; 中村 充孝; 村井 直樹; 社本 真一; 本田 孝志*; 池田 一貴*; 大友 季哉*; 畑 博人*; 江藤 貴弘*; 野田 正亮*; et al.

Scientific Reports (Internet), 8(1), p.9651_1 - 9651_8, 2018/06

 被引用回数:6 パーセンタイル:45.68(Multidisciplinary Sciences)

The electron-doped SrTiO$$_{3}$$ exhibits good thermoelectric properties, which makes this material a promising candidate of an n-type oxide thermoelectric device. Recent studies indicated that only a few percent co-doping of La and Mn in SrTiO$$_{3}$$ substantially reduces the thermal conductivity, thereby greatly improving the thermoelectric figure of merit at room temperature. Our time-of-flight neutron scattering studies revealed that by doping both La and Mn into SrTiO$$_{3}$$, the inelastic scattering spectrum shows a momentum-independent increase in the low-energy spectral weight approximately below 10 meV. The increase in the low-energy spectral weight exhibits a clear correlation with thermal conductivity. The correlation is attributed to dynamical and local structural fluctuations caused by the Jahn-Teller instability in Mn$$^{3+}$$ ions coupled with the incipient ferroelectric nature of SrTiO$$_{3}$$, as the origin of the low thermal conductivity.

論文

Spin resonance in the new-structure-type iron-based superconductor CaKFe$$_{4}$$As$$_{4}$$

飯田 一樹*; 石角 元志*; 永井 佑紀; 吉田 紘行*; Christianson, A. D.*; 村井 直樹; 川島 健司*; 吉田 良行*; 永崎 洋*; 伊豫 彰*

Journal of the Physical Society of Japan, 86(9), p.093703_1 - 093703_4, 2017/09

 被引用回数:26 パーセンタイル:80.06(Physics, Multidisciplinary)

The dynamical spin susceptibility in the new-structure iron-based superconductor CaKFe$$_{4}$$As$$_{4}$$ was investigated by a combination of inelastic neutron scattering (INS) measurements and random phase approximation (RPA) calculations. Powder INS measurements show that the spin resonance at Q$$_{rm res}$$ = 1.17(1) ${AA}$ vector in the tetragonal notation, evolves below Tc. The characteristic energy of the spin resonance E$$_{rm res}$$ = 12.5 meV is smaller than twice the size of the superconducting gap (2$$Delta$$). The broad energy feature of the dynamical susceptibility of the spin resonance can be explained by the RPA calculations which take into account the different superconducting gaps on the different Fermi surfaces. Our INS and PRA studies demonstrated that the superconducting pairing nature in CaKFe$$_{4}$$As$$_{4}$$ is the s$$pm$$ symmetry.

論文

Effect of magnetism on lattice dynamics in SrFe$$_2$$As$$_2$$ using high-resolution inelastic X-ray scattering

村井 直樹*; 福田 竜生; 小林 達也*; 中島 正道*; 内山 裕士*; 石川 大介*; 筒井 智嗣*; 中村 博樹; 町田 昌彦; 宮坂 茂樹*; et al.

Physical Review B, 93(2), p.020301_1 - 020301_5, 2016/01

 被引用回数:7 パーセンタイル:32.63(Materials Science, Multidisciplinary)

Phonon spectra of detwinned SrFe$$_2$$As$$_2$$ crystals, as measured by inelastic X-ray scattering, show clear anisotropyaccompanying the magnetostructural transition at 200 K. We model the mode splitting using magnetic DFT calculations, including a phenomenological reduction in force-constant anisotropy that can be attributed to magnetic fluctuations. This serves as a starting point for a general model of phonons in this material applicable to both the antiferromagnetically ordered phase and the paramagnetic phase. Using this model, the measured splitting in the magnetic phase below T$$_N$$, and the measured phonon linewidth, we set a lower bound on the mean magnetic fluctuation frequency above T$$_N$$ at 210 K.

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