Magnetic dynamics of hedgehog in icosahedral quasicrystal

Quasicrystals (QCs) possess a unique lattice structure without translational invariance, which is characterized by the rotational symmetry forbidden in periodic crystals such as the 5-fold rotation. Recent discovery of the ferromagnetic (FM) long-range order in the terbium-based QC has brought about...

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Published in	Scientific reports Vol. 12; no. 1; pp. 15514 - 8
Main Author	Watanabe, Shinji
Format	Journal Article
Language	English
Published	London Nature Publishing Group UK 15.09.2022 Nature Publishing Group Nature Portfolio
Subjects	639/766 639/766/119 639/766/119/2792 639/766/119/2792/4129 639/766/119/997 Anisotropy Crystals Electric properties Energy Humanities and Social Sciences multidisciplinary Science Science (multidisciplinary) Terbium Ultrastructure
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Abstract	Quasicrystals (QCs) possess a unique lattice structure without translational invariance, which is characterized by the rotational symmetry forbidden in periodic crystals such as the 5-fold rotation. Recent discovery of the ferromagnetic (FM) long-range order in the terbium-based QC has brought about breakthrough but the magnetic structure and dynamics remain unresolved. Here, we reveal the dynamical as well as static structure of the FM hedgehog state in the icosahedral QC. The FM hedgehog is shown to be characterized by the triple- Q state in the reciprocal-lattice q space. Dynamical structure factor is shown to exhibit highly structured q and energy dependences. We find a unique magnetic excitation mode along the 5-fold direction exhibiting the streak fine structure in the q -energy plane, which is characteristic of the hedgehog in the icosahedral QC. Non-reciprocal magnetic excitations are shown to arise from the FM hedgehog order, which emerge in the vast extent of the q -energy plane.
AbstractList	Quasicrystals (QCs) possess a unique lattice structure without translational invariance, which is characterized by the rotational symmetry forbidden in periodic crystals such as the 5-fold rotation. Recent discovery of the ferromagnetic (FM) long-range order in the terbium-based QC has brought about breakthrough but the magnetic structure and dynamics remain unresolved. Here, we reveal the dynamical as well as static structure of the FM hedgehog state in the icosahedral QC. The FM hedgehog is shown to be characterized by the triple-Q state in the reciprocal-lattice [Formula: see text] space. Dynamical structure factor is shown to exhibit highly structured [Formula: see text] and energy dependences. We find a unique magnetic excitation mode along the 5-fold direction exhibiting the streak fine structure in the [Formula: see text]-energy plane, which is characteristic of the hedgehog in the icosahedral QC. Non-reciprocal magnetic excitations are shown to arise from the FM hedgehog order, which emerge in the vast extent of the [Formula: see text]-energy plane. Quasicrystals (QCs) possess a unique lattice structure without translational invariance, which is characterized by the rotational symmetry forbidden in periodic crystals such as the 5-fold rotation. Recent discovery of the ferromagnetic (FM) long-range order in the terbium-based QC has brought about breakthrough but the magnetic structure and dynamics remain unresolved. Here, we reveal the dynamical as well as static structure of the FM hedgehog state in the icosahedral QC. The FM hedgehog is shown to be characterized by the triple- Q state in the reciprocal-lattice $${{\varvec{q}}}$$ q space. Dynamical structure factor is shown to exhibit highly structured $${{\varvec{q}}}$$ q and energy dependences. We find a unique magnetic excitation mode along the 5-fold direction exhibiting the streak fine structure in the $${{\varvec{q}}}$$ q -energy plane, which is characteristic of the hedgehog in the icosahedral QC. Non-reciprocal magnetic excitations are shown to arise from the FM hedgehog order, which emerge in the vast extent of the $${{\varvec{q}}}$$ q -energy plane. Quasicrystals (QCs) possess a unique lattice structure without translational invariance, which is characterized by the rotational symmetry forbidden in periodic crystals such as the 5-fold rotation. Recent discovery of the ferromagnetic (FM) long-range order in the terbium-based QC has brought about breakthrough but the magnetic structure and dynamics remain unresolved. Here, we reveal the dynamical as well as static structure of the FM hedgehog state in the icosahedral QC. The FM hedgehog is shown to be characterized by the triple-Q state in the reciprocal-lattice q space. Dynamical structure factor is shown to exhibit highly structured q and energy dependences. We find a unique magnetic excitation mode along the 5-fold direction exhibiting the streak fine structure in the q-energy plane, which is characteristic of the hedgehog in the icosahedral QC. Non-reciprocal magnetic excitations are shown to arise from the FM hedgehog order, which emerge in the vast extent of the q-energy plane. Abstract Quasicrystals (QCs) possess a unique lattice structure without translational invariance, which is characterized by the rotational symmetry forbidden in periodic crystals such as the 5-fold rotation. Recent discovery of the ferromagnetic (FM) long-range order in the terbium-based QC has brought about breakthrough but the magnetic structure and dynamics remain unresolved. Here, we reveal the dynamical as well as static structure of the FM hedgehog state in the icosahedral QC. The FM hedgehog is shown to be characterized by the triple-Q state in the reciprocal-lattice $${{\varvec{q}}}$$ q space. Dynamical structure factor is shown to exhibit highly structured $${{\varvec{q}}}$$ q and energy dependences. We find a unique magnetic excitation mode along the 5-fold direction exhibiting the streak fine structure in the $${{\varvec{q}}}$$ q -energy plane, which is characteristic of the hedgehog in the icosahedral QC. Non-reciprocal magnetic excitations are shown to arise from the FM hedgehog order, which emerge in the vast extent of the $${{\varvec{q}}}$$ q -energy plane. Quasicrystals (QCs) possess a unique lattice structure without translational invariance, which is characterized by the rotational symmetry forbidden in periodic crystals such as the 5-fold rotation. Recent discovery of the ferromagnetic (FM) long-range order in the terbium-based QC has brought about breakthrough but the magnetic structure and dynamics remain unresolved. Here, we reveal the dynamical as well as static structure of the FM hedgehog state in the icosahedral QC. The FM hedgehog is shown to be characterized by the triple-Q state in the reciprocal-lattice [Formula: see text] space. Dynamical structure factor is shown to exhibit highly structured [Formula: see text] and energy dependences. We find a unique magnetic excitation mode along the 5-fold direction exhibiting the streak fine structure in the [Formula: see text]-energy plane, which is characteristic of the hedgehog in the icosahedral QC. Non-reciprocal magnetic excitations are shown to arise from the FM hedgehog order, which emerge in the vast extent of the [Formula: see text]-energy plane.Quasicrystals (QCs) possess a unique lattice structure without translational invariance, which is characterized by the rotational symmetry forbidden in periodic crystals such as the 5-fold rotation. Recent discovery of the ferromagnetic (FM) long-range order in the terbium-based QC has brought about breakthrough but the magnetic structure and dynamics remain unresolved. Here, we reveal the dynamical as well as static structure of the FM hedgehog state in the icosahedral QC. The FM hedgehog is shown to be characterized by the triple-Q state in the reciprocal-lattice [Formula: see text] space. Dynamical structure factor is shown to exhibit highly structured [Formula: see text] and energy dependences. We find a unique magnetic excitation mode along the 5-fold direction exhibiting the streak fine structure in the [Formula: see text]-energy plane, which is characteristic of the hedgehog in the icosahedral QC. Non-reciprocal magnetic excitations are shown to arise from the FM hedgehog order, which emerge in the vast extent of the [Formula: see text]-energy plane. Quasicrystals (QCs) possess a unique lattice structure without translational invariance, which is characterized by the rotational symmetry forbidden in periodic crystals such as the 5-fold rotation. Recent discovery of the ferromagnetic (FM) long-range order in the terbium-based QC has brought about breakthrough but the magnetic structure and dynamics remain unresolved. Here, we reveal the dynamical as well as static structure of the FM hedgehog state in the icosahedral QC. The FM hedgehog is shown to be characterized by the triple- Q state in the reciprocal-lattice q space. Dynamical structure factor is shown to exhibit highly structured q and energy dependences. We find a unique magnetic excitation mode along the 5-fold direction exhibiting the streak fine structure in the q -energy plane, which is characteristic of the hedgehog in the icosahedral QC. Non-reciprocal magnetic excitations are shown to arise from the FM hedgehog order, which emerge in the vast extent of the q -energy plane. Quasicrystals (QCs) possess a unique lattice structure without translational invariance, which is characterized by the rotational symmetry forbidden in periodic crystals such as the 5-fold rotation. Recent discovery of the ferromagnetic (FM) long-range order in the terbium-based QC has brought about breakthrough but the magnetic structure and dynamics remain unresolved. Here, we reveal the dynamical as well as static structure of the FM hedgehog state in the icosahedral QC. The FM hedgehog is shown to be characterized by the triple- Q state in the reciprocal-lattice \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\varvec{q}}}$$\end{document} q space. Dynamical structure factor is shown to exhibit highly structured \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\varvec{q}}}$$\end{document} q and energy dependences. We find a unique magnetic excitation mode along the 5-fold direction exhibiting the streak fine structure in the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\varvec{q}}}$$\end{document} q -energy plane, which is characteristic of the hedgehog in the icosahedral QC. Non-reciprocal magnetic excitations are shown to arise from the FM hedgehog order, which emerge in the vast extent of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\varvec{q}}}$$\end{document} q -energy plane.
ArticleNumber	15514
Author	Watanabe, Shinji
Author_xml	– sequence: 1 givenname: Shinji surname: Watanabe fullname: Watanabe, Shinji email: swata@mns.kyutech.ac.jp organization: Department of Basic Sciences, Kyushu Institute of Technology
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CitedBy_id	crossref_primary_10_1380_ejssnt_2023_036 crossref_primary_10_1380_vss_66_277 crossref_primary_10_1038_s41598_023_41292_1 crossref_primary_10_1103_PhysRevB_109_184404
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Snippet	Quasicrystals (QCs) possess a unique lattice structure without translational invariance, which is characterized by the rotational symmetry forbidden in... Abstract Quasicrystals (QCs) possess a unique lattice structure without translational invariance, which is characterized by the rotational symmetry forbidden...
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SubjectTerms	639/766 639/766/119 639/766/119/2792 639/766/119/2792/4129 639/766/119/997 Anisotropy Crystals Electric properties Energy Humanities and Social Sciences multidisciplinary Science Science (multidisciplinary) Terbium Ultrastructure
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Title	Magnetic dynamics of hedgehog in icosahedral quasicrystal
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