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論文

Spin excitations coupled with lattice and charge dynamics in La$$_{2-x}$$Sr$$_{x}$$CuO$$_{4}$$

池内 和彦*; 脇本 秀一; 藤田 全基*; 福田 竜生; 梶本 亮一; 新井 正敏*

Physical Review B, 105(1), p.014508_1 - 014508_7, 2022/01

 被引用回数:1 パーセンタイル:37.1(Materials Science, Multidisciplinary)

Spin excitations of layered copper oxide show various characteristic features, depending on the carrier concentration. In this paper, we conducted inelastic neutron-scattering measurements on La$$_{2-x}$$Sr$$_{x}$$CuO$$_{4}$$ (LSCO) with $$x$$ = 0, 0.075, 0.18, and 0.30 and La$$_{2-x}$$Sr$$_{x}$$NiO$$_{4}$$ (LSNO) with 1/3 to clarify the origin of the intensity enhancement in the excitation spectrum of LSCO at the energy ($$omega$$) of 16-19 meV [Phys. Rev. B $textbf{91}$, 224404 (2015), $textit{ibid.}$ $textbf{93}$, 094416 (2016)]. We confirmed the presence of a peak structure in the $$omega$$ dependence of the local spin susceptibility $$chi''(omega)$$ of superconducting (SC) LSCO with a peak energy of 16-19 meV where the spin excitations intersect optical phonon branches. A comparable peak structure is not observed in the insulating La$$_{2}$$CuO$$_{4}$$, LSNO, and heavily overdoped LSCO with $$x$$ = 0.30. A dome-shaped $$x$$ dependence of the integrated intensity around the peak energies is revealed for the SC phase by summarizing the present and previously reported results. Furthermore, our phonon calculation on LCO shows the existence of two optical branches at $$sim$$19 meV that could stabilize stripe alignment of carriers due to out-of-plane vibrations of Cu or O of the CuO$$_{2}$$ planes. These results indicate the interplay among spin, charge, and lattice dynamics and suggest that the intensity enhancement is associated with their composite excitations.

論文

Coexistence of two components in magnetic excitations of La$$_{2-x}$$Sr$$_{x}$$CuO$$_{4}$$ ($$x$$ = 0.10 and 0.16)

佐藤 研太朗*; 池内 和彦*; 梶本 亮一; 脇本 秀一; 新井 正敏*; 藤田 全基*

Journal of the Physical Society of Japan, 89(11), p.114703_1 - 114703_7, 2020/11

 被引用回数:4 パーセンタイル:39.42(Physics, Multidisciplinary)

To elucidate the spin dynamics of La$$_{2-x}$$Sr$$_{x}$$CuO$$_{4}$$, which couples with the charge degree of freedom, the spin excitations spanning the characteristic energy ($$E_mathrm{cross}$$ $$sim$$ 35-40 meV) are investigated for underdoped $$x$$ = 0.10 and optimally doped (OP) $$x$$ = 0.16 through inelastic neutron scattering measurements. Analysis based on a two-component picture of high-quality data clarified the possible coexistence of upright standing incommensurate (IC) excitations with gapless commensurate (C) excitations in the energy-momentum space. The IC component weakens the intensity toward $$E_mathrm{cross}$$ with increasing energy transfer ($$hbaromega$$), whereas the C component strengthens at high-$$hbaromega$$ regions. The analysis results imply that the superposition of two components with a particular intensity balance forms an hourglass-shaped excitation in appearance. Furthermore, the temperature dependence of the intensity of each component exhibits different behaviors; the IC component disappears near the pseudo-gap temperature ($$T^*$$) upon warming, whereas the C component is robust against temperature. These results suggest the itinerant electron spin nature and the localized magnetism of the parent La$$_{2}$$CuO$$_{4}$$ in IC and C excitations, respectively, similar to the spin excitations in the OP YBa$$_{2}$$Cu$$_{3}$$O$$_{6+delta}$$ and HgBa$$_{2}$$CuO$$_{4+delta}$$ with higher superconducting-transition temperatures.

論文

Al-impurity-induced magnetic excitations in heavily over-doped La$$_{1.7}$$Sr$$_{0.3}$$Cu$$_{0.95}$$Al$$_{0.05}$$O$$_{4}$$

池内 和彦*; 中島 健次; 河村 聖子; 梶本 亮一; 脇本 秀一; 鈴木 謙介*; 藤田 全基*

AIP Advances (Internet), 8(10), p.101318_1 - 101318_5, 2018/10

 被引用回数:0 パーセンタイル:0(Nanoscience & Nanotechnology)

中性子散乱実験により、Al不純物を導入した実効ホール濃度0.25の銅酸化物超伝導体、La$$_{1.7}$$Sr$$_{0.3}$$Cu$$_{0.95}$$Al$$_{0.05}$$O$$_{4}$$の巨大単結晶について、磁気励起を測定した。

論文

Detailed study of the structure of the low-energy magnetic excitations in overdoped La$$_{1.75}$$Sr$$_{0.25}$$CuO$$_{4}$$

池内 和彦*; 菊地 龍弥*; 中島 健次; 梶本 亮一; 脇本 秀一; 藤田 全基*

Physica B; Condensed Matter, 536, p.717 - 719, 2018/05

 被引用回数:2 パーセンタイル:10.5(Physics, Condensed Matter)

銅酸化物高温超伝導体の過剰ドープ領域における低エネルギーの磁気励起の構造の詳細を調べるために、我々は、La$$_{1.75}$$Sr$$_{0.25}$$CuO$$_{4}$$の中性子非弾性散乱実験を行った。過去に報告されたように、非整合な磁気相関に対応した$$Q_{rm tet}$$ = (0.5 $$pm$$ $$delta$$, 0.5)/(0.5, 0.5 $$pm$$ $$delta$$)を中心とした磁気励起を明瞭に観測した。それに加えて、$$Q_{rm tet}=(0.5, 0.5)$$を中心とした円環状の励起も観測された。円環の半径($$r$$=0.109)は、磁気相関の非整合性($$delta$$=0.118)より小さい。このことは、円環状の磁気励起は非整合な磁気相関とはその原因を異にしていることを示唆している。La$$_{2-x}$$Sr$$_{x}$$CuO$$_{4}$$の磁気励起はこのように2種類の励起を持つことが示唆される。

論文

Quantitative characterization of the nanoscale local lattice strain induced by Sr dopants in La$$_{1.92}$$Sr$$_{0.08}$$CuO$$_{4}$$

Lin, J. Q.*; Liu, X.*; Blackburn, E.*; 脇本 秀一; Ding, H.*; Islam, Z.*; Sinha, S. K.*

Physical Review Letters, 120(19), p.197001_1 - 197001_6, 2018/05

 被引用回数:2 パーセンタイル:29.56(Physics, Multidisciplinary)

X線散漫散乱の観測により、銅酸化物高温超伝導体La$$_{2-x}$$Sr$$_{x}$$CuO$$_{4}$$中の不純物Srにより生じるナノスケールの格子歪みを観測した。この結果は、これまで議論となっていた不純物による歪みの性質を明らかにしたとともに、STMで観測されているギャップの不均一性の原因ではないことを明らかにした。

論文

Fe-impurity-induced magnetic excitations in heavily over-doped La$$_{1.7}$$Sr$$_{0.3}$$Cu$$_{0.95}$$Fe$$_{0.05}$$O$$_{4}$$

池内 和彦*; 菊地 龍弥*; 中島 健次; 梶本 亮一; 脇本 秀一; 藤田 全基*

Journal of Physics; Conference Series, 969(1), p.012024_1 - 012024_5, 2018/04

 被引用回数:1 パーセンタイル:53.12

Inelastic neutron scattering experiments were performed to investigate the effect of Fe substitution on the magnetic excitation spectra in a heavily hole-doped cuprate system La$$_{1.7}$$Sr$$_{0.3}$$Cu$$_{0.95}$$Fe$$_{0.05}$$O$$_{4}$$. Well-defined low-energy magnetic excitations, associated with a static magnetic order, were observed at the incommensurate (IC) positions. The incommensurability of 0.144 (r.l.u) was larger than that of $$sim$$0.125 (r.l.u) in LSCO with $$x$$ = 0.25, suggesting an increase of incommensurability by Fe substitution. In addition to the obvious effect on IC excitations, we show the emergence of ring-shaped magnetic excitations by Fe-substitution. These results are incompatible with a simple pinning scenario of the stripe order, which is characterized by local spin correlations. The metallic aspect of the low-energy part of the magnetic excitation, which underlies high-temperature superconductivity in over-doped cuprate systems, would be enhanced/induced by Fe substitution.

論文

日本原子力研究開発機構における研究開発の現状

大井川 宏之; 脇本 秀一

電気評論, 103(2), p.50 - 65, 2018/02

日本原子力研究開発機構は、わが国唯一の総合的な原子力の研究開発機関として、原子力による新しい科学技術や産業の創出を目指して基礎研究、応用研究からプロジェクト研究開発に至るまで幅広い研究開発を行ってきた。平成29年3月には、施設の集約化・重点化、安全確保、バックエンド対策を三位一体とした「施設中長期計画」、研究開発成果の社会還元とイノベーション創出につなげるための基本的な取り組み方針である「イノベーション創出戦略」、国際協力を実施するにあたっての指針となる「国際戦略」を策定・公表し、より一層の成果創出に向けた取り組みを開始したところである。本稿では、機構における平成29年度の研究開発の主な成果を中心に、現状と今後の展望を紹介する。

論文

Observation of momentum-dependent charge excitations in hole-doped cuprates using resonant inelastic X-ray scattering at the oxygen $$K$$ edge

石井 賢司*; 遠山 貴巳*; 浅野 駿*; 佐藤 研太朗*; 藤田 全基*; 脇本 秀一; 筒井 健二*; 曽田 繁利*; 宮脇 淳*; 丹羽 秀治*; et al.

Physical Review B, 96(11), p.115148_1 - 115148_8, 2017/09

AA2017-0402.pdf:0.81MB

 被引用回数:28 パーセンタイル:78.15(Materials Science, Multidisciplinary)

We investigate electronic excitations in La$$_{2-x}$$(Br,Sr)$$_x$$CuO$$_4$$ using resonant inelastic X-ray scattering (RIXS) at the oxygen $$K$$ edge. We observed momentum-dependent spectral weight below 1 eV, which is consistent with theoretical calculation of the dynamical charge structure factor on oxygen orbitals in a three-band Hubbard model. Our results confirm that the momentum-dependent charge excitations exist on the order of the transfer energy ($$t$$), and the broad spectral line shape indicates damped and incoherent character of the charge excitations at the energy range in the doped Mott insulators.

論文

Scaling of memories and crossover in glassy magnets

Samarakoon, A. M.*; 高橋 満*; Zhang, D.*; Yang, J.*; 片山 尚幸*; Sinclair, R.*; Zhou, H. D.*; Diallo, S. O.*; Ehlers, G.*; Tennant, D. A.*; et al.

Scientific Reports (Internet), 7(1), p.12053_1 - 12053_8, 2017/09

AA2017-0448.pdf:3.45MB

 被引用回数:6 パーセンタイル:46.38(Multidisciplinary Sciences)

Glassiness is ubiquitous and diverse in characteristics in nature. Understanding their differences and classification remains a major scientific challenge. Here, we show that scaling of magnetic memories with time can be used to classify magnetic glassy materials into two distinct classes. The systems studied are high temperature superconductor-related materials, spin-orbit Mott insulators, frustrated magnets, and dilute magnetic alloys. Our bulk magnetization measurements reveal that most densely populated magnets exhibit similar memory behavior characterized by a relaxation exponent of $$1-n$$ $$approx$$ $$0.6$$(1). This exponent is different from $$1-n$$ $$approx$$ $$1/3$$ of dilute magnetic alloys that was ascribed to their hierarchical and fractal energy landscape, and is also different from $$1-n=1$$ of the conventional Debye relaxation expected for a spin solid, a state with long range order.

論文

Observation of magnetoelastic effects in a quasi-one-dimensional spiral magnet

Wang, C.*; Daiwei, Y.*; Liu, X.*; Chen, R.*; Du, X.*; Hu, B.*; Wang, L.*; 飯田 一樹*; 蒲沢 和也*; 脇本 秀一; et al.

Physical Review B, 96(8), p.085111_1 - 085111_5, 2017/08

AA2017-0274.pdf:1.02MB

 被引用回数:7 パーセンタイル:35.8(Materials Science, Multidisciplinary)

This paper presents a systematic study of spin and lattice dynamics in the quasi-one-dimensional spiral magnet CuBr$$_2$$, using Raman scattering in conjunction with infrared and neutron spectroscopy. Along with the development of spin correlations upon cooling, we observe a rich set of broad Raman bands at energies that correspond to phonon-dispersion energies near the one-dimensional magnetic wave vector. The low-energy bands further exhibit a distinct intensity maximum at the spiral magnetic ordering temperature.

論文

日本原子力研究開発機構における研究開発の現状

大井川 宏之; 脇本 秀一

電気評論, 102(2), p.46 - 61, 2017/02

日本原子力研究開発機構は、平成27年度から国立研究開発法人の指定を受け、第3期中長期計画を開始し、わが国唯一の総合的原子力研究開発機関として、原子力による新しい科学技術や産業の創出を目指して基礎研究、応用研究からプロジェクト開発的研究に至るまで幅広い研究開発を行ってきた。特に、科学的技術的専門性を最大限に活用して、東京電力福島第一原子力発電所事故からの復旧・復興に向けた取り組み、原子力安全研究、核燃料サイクル技術の確立を目指した研究開発、放射性廃棄物処理に関わる研究等を重点的に実施すべき業務として進めてきた。平成28年4月に量子ビーム応用研究の一部および核融合研究開発を量子科学技術研究開発機構へ移管し、核分裂エネルギー関連分野を中心に原子力機構の業務の重点化を図り、効率的・効果的な組織運営を開始したところである。本稿では原子力機構における平成28年度の研究開発の主な成果を中心に、現状と今後の展望を紹介する。

報告書

JAEAプロジェクト研究「機能物質の構造と電子物性」「銅酸化物高温超伝導体のスピン・格子ダイナミクスの研究」合同研究会講演集

梶本 亮一; 中島 健次; 脇本 秀一

JAEA-Review 2016-018, 84 Pages, 2016/08

JAEA-Review-2016-018.pdf:20.69MB

J-PARCセンター物質・生命科学ディビジョンでは、物質・生命科学実験施設内の原子力機構が管理する中性子実験装置を主に利用した研究プロジェクト「JAEAプロジェクト研究」を実施している。そのうち2012年度-2014年度まで実施された「機能物質の構造と電子物性」と、2015年度から開始された「超伝導体におけるスピン・格子ダイナミクスの研究」の2つのプロジェクト研究の合同研究会が、2016年3月22日-23日に東北大学金属材料研究所において開催された。本報告書は上記研究会の講演要旨および講演で使用された発表資料を収録したものである。

論文

Neutron scattering study of spin fluctuations in La$$_{2-x}$$Sr$$_{x}$$CuO$$_{4}$$ by four-dimensional mapping of neutron cross-sections using the 4SEASONS chopper spectrometer

脇本 秀一; 池内 和彦*; 新井 正敏; 藤田 全基*; 梶本 亮一; 川村 奨*; 松浦 直人*; 中島 健次; 山田 和芳*

JPS Conference Proceedings (Internet), 8, p.034013_1 - 034013_6, 2015/09

Previous neutron results of La$$_{2-x}$$Sr$$_{x}$$CuO$$_{4}$$ (LSCO) by TOF measurements revealed that magnetic dynamical structure factor has a maximum at $$sim$$ 18 meV. To clarify the origin of the maximum, we carried out 4 dimensional mapping of dynamical structure factor $$S(Q, omega)$$ to see details of both magnons and phonons. We found that $$x$$ = 0 shows ordinary spin waves while $$x$$ = 0.08 shows a maximum at $$sim$$ 18 meV where $$Q$$-independent phonon branch crosses. This imply that in superconducting compositions phonon may also indirectly related to the superconductivity.

論文

High-energy magnetic excitations in overdoped La$$_{2-x}$$Sr$$_{x}$$CuO$$_{4}$$ studied by neutron and resonant inelastic X-ray scattering

脇本 秀一; 石井 賢司; 木村 宏之*; 藤田 全基*; Dellea, G.*; Kummer, K.*; Braicovich, L.*; Ghiringhelli, G.*; Debeer-Schmitt, L. M.*; Granroth, G.*

Physical Review B, 91(18), p.184513_1 - 184513_7, 2015/05

 被引用回数:27 パーセンタイル:73.87(Materials Science, Multidisciplinary)

We have performed neutron inelastic scattering and resonant inelastic X-ray scattering (RIXS) at the Cu-$$L_3$$ edge to study high-energy magnetic excitations at energy transfers of more than 100 meV for overdoped La$$_{2-x}$$Sr$$_{x}$$CuO$$_{4}$$ with $$x$$ = 0.25 ($$T_c$$ = 15 K) and $$x$$ = 0.30 (nonsuperconducting) using identical single-crystal samples for the two techniques. Our results indicate consistency between neutron inelastic scattering and RIXS, and elucidate the entire magnetic excitation in the $$(pi, pi)$$ direction by the complementary use of two probes. The paramagnon along $$(pi, 0)$$ agrees well with the LCO spin-wave dispersion, while the paramagnon in the $$(pi, pi)$$ direction probed by RIXS appears to be less dispersive.

論文

Influence of electron doping on magnetic order in CeRu$$_2$$Al$$_{10}$$

小林 理気*; 金子 耕士; 斉藤 耕太郎*; Mignot, J.-M.*; Andr$'e$, G.*; Robert, J.*; 脇本 秀一; 松田 雅昌*; Chi, S.*; 芳賀 芳範; et al.

Journal of the Physical Society of Japan, 83(10), p.104707_1 - 104707_5, 2014/10

 被引用回数:16 パーセンタイル:68.66(Physics, Multidisciplinary)

The effect of electron doping by the substitution of Rh for Ru on unconventional magnetic order in CeRu$$_2$$Al$$_{10}$$ was investigated via neutron powder diffraction. In Ce(Ru$$_{1-x}$$Rh$$_x$$)$$_2$$Al$$_{10}$$ with $$x$$ = 0.05, 0.12, 0.2, reorientation of the ordered moment from the $$c$$- to the $$a$$-axis takes place in all samples, while the ordering vector $$q$$ = (0 1 0) remains unchanged within this concentration range. The moment reorientation is accompanied by an enhancement in its size by a factor of 2.4, from $${mu}$$=0.43 $${mu}_B$$ at $$x$$ = 0 to $${mu}$$=1.06, 1.04, and 1.02 $${mu}_B$$ for $$x$$ = 0.05, 0.12 and 0.2, respectively. The continuous decrease in N$'e$el temperature $$T_0$$($$T_N$$), despite an abrupt increase in $${mu}$$, underlines the strong anisotropy in the exchange interaction in CeRu$$_2$$Al$$_{10}$$, and the fact that this anisotropy is easily suppressed by electron doping.

論文

Anisotropic magnetic form factor in a detwinned single crystal of BaFe$$_2$$As$$_2$$

樹神 克明; 石角 元志*; 脇本 秀一; 木方 邦宏*; Lee, C.-H.*; 伊豫 彰*; 永崎 洋*; 社本 真一

Physical Review B, 90(14), p.144510_1 - 144510_5, 2014/10

 被引用回数:1 パーセンタイル:4.7(Materials Science, Multidisciplinary)

We have performed neutron diffraction measurements at 12K on a single crystal of BaFe$$_2$$As$$_2$$, which serves as the parent compound of iron-based superconductor. To investigate the in-plane anisotropy of the magnetic form factor in the antiferromagnetic phase, the single crystal was detwinned. The magnetic structure factor and magnetic form factor are well explained by the spin densities comprising $$3d_{yz}$$ electrons with a fraction of approximately 40% and electrons in the other four $$3d$$ orbitals each with a fraction of approximately 15%. It is a direct observation of the largely anisotropic spin density relative to the small orthorhombic lattice distortion, $$(a-b)/(a+b)$$ $$sim$$ 0.3%.

論文

Anharmonic Pr guest modes in Pr(Os$$_{1-x}$$Ru$$_x$$)$$_4$$Sb$$_{12}$$ investigated by inelastic X-ray scattering

筒井 智嗣; 金子 耕士; 宮崎 亮一*; 東中 隆二*; 青木 勇二*; 小林 理気*; 脇本 秀一; Baron, A. Q. R.*; 菅原 仁*; 佐藤 英行*

JPS Conference Proceedings (Internet), 3, p.011060_1 - 011060_5, 2014/06

We have investigated the Ru/Os concentration dependence of the Pr guest mode in Pr(Os$$_{1-x}$$Ru$$_x$$)$$_4$$Sb$$_{12}$$ and its variation with temperature. The Pr guest mode at 3.2 meV in PrOs$$_4$$Sb$$_{12}$$ at the N point linearly shifts to a higher energy with the substitution of Ru into the Os site. The energy of the Pr guest mode decreases with decreasing temperature for all compositions, indicating the presence of an anharmonic potential at the Pr site. The slope of the temperature dependence of the guest mode energy is steeper for pure PrOs$$_4$$Sb$$_{12}$$ than for the other Pr(Os$$_{1-x}$$Ru$$_x$$)$$_4$$Sb$$_{12}$$ compounds we measured. The present results imply the importance of the transition metal in determining anharmonicity in Pr(Os$$_{1-x}$$Ru$$_x$$)$$_4$$Sb$$_{12}$$.

論文

Role of magnetic chirality in polarization flip upon a commensurate-incommensurate magnetic phase transition in YMn$$_{2}$$O$$_{5}$$

脇本 秀一; 木村 宏之*; 坂本 勇馬*; 福永 守*; 野田 幸男*; 武田 全康; 加倉井 和久

Physical Review B, 88(14), p.140403_1 - 140403_5, 2013/10

 被引用回数:18 パーセンタイル:61.1(Materials Science, Multidisciplinary)

We have performed simultaneous measurements of magnetic chirality by using polarized neutrons and electric polarization along the $$b$$-axis of single crystals of YMn$$^{4+}$$(Mn$$_{1-x}$$Ga$$_{x}$$)$$^{3+}$$O$$_{5}$$ with $$x=0.047$$ and $$0.12$$, in which nonmagnetic Ga-ions dilute Mn$$^{3+}$$ spins. Measurements conducted under zero field heating after various field-cooling conditions evidence that the magnetic chirality of Mn$$^{4+}$$ cycloidal spins plays a dominant role in the incommensurate magnetic (ICM) phase, whereas the magnetic exchange striction by the Mn$$^{4+}$$-Mn$$^{3+}$$ chain plays a dominant role in the commensurate magnetic (CM) phase. The polarization of YMn$$_{2}$$O$$_{5}$$ flips upon CM to ICM phase transition because the ferroelectricity driven by the magnetic chirality and the exchange striction provides opposite directions of polarization.

論文

三軸分光器を用いた偏極中性子散乱

脇本 秀一

波紋, 23(3), p.230 - 237, 2013/08

物質による中性子の散乱には核散乱と磁気散乱がある。通常、非偏極中性子を用いた実験ではこれらの区別は厳密には不可能であるが、偏極中性子を用いることで、これらの区別、物質内のスピンの配列、磁気モーメントの大きさに関する情報を得ることが可能である。さらにはスピンヘリカル構造などの複雑な磁気構造の詳細について知ることができる。本論文では、三軸分光器における偏極中性子利用について概観する。

論文

Powder neutron diffraction study of HoCoGa$$_{5}$$

小林 理気; 金子 耕士; 脇本 秀一; Chi, S.*; 眞田 直幸*; 綿貫 竜太*; 鈴木 和也*

Journal of the Korean Physical Society, 63(3), p.337 - 340, 2013/08

 被引用回数:3 パーセンタイル:33.81(Physics, Multidisciplinary)

We have studied the magnetic structure of HoCoGa$$_5$$ which shows successive magnetic phase transition at $$T_{N1}$$ = 9.6 K and $$T_{N2}$$ = 7.5 K by using powder neutron diffraction. The data indicates magnetic reflection peaks with propagation vector $$q_L$$ = (1/2 0 0.35) at $$T_{N2} < T < T_{N1}$$ (AFIC phase), and then the propagation vector changes to $$q_{C}$$ = (1/2 0 1/2) below $$T_{N2}$$ (AFC phase). In addition, the temperature dependence of magnetic reflection intensity shows temperature hysteresis at $$T_{N2}$$. These results suggest that the transition at $$T_{N2}$$ is an incommensurate to commensurate first order transition. From our analysis, we have decided that the magnetic structure at 3.5 K is collinear antiferromagnetic one with propagation vector $$q_C$$, and magnitude of magnetic moment is 8.6(2) $$mu_B$$ along the $$c$$-axis. This structure is same as TbCoGa$$_5$$ which is proposed existence of component separated magnetic order due to the competition between magnetic and quadrupolar interactions.

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