Hedgehog-lattice spin texture in classical Heisenberg antiferromagnets on the breathing pyrochlore lattice

Aoyama, Kazushi; Kawamura, Hikaru

doi:10.1103/physrevb.103.014406

Cited by 39 publications

(22 citation statements)

References 128 publications

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“…Recently, the scalar chirality and the topological charge have been defined for four spins located at each vertex of the tetrahedron 37 . It has been shown by this definition that the hedgehog state realized in the tetrahedron is characterized by the topological charge of one.…”

Section: Methodsmentioning

confidence: 99%

“…This is the first theoretical discovery of the possible long-range order of the topological magnetic texture in the QC. Distinct from the topological spin textures intensively studied so far in the periodic crystals 31 – 37 , our discovery is based on the total angular momentum on the CEF-anisotropy-protected IC, which provides a new concept of topological quasicrystal .…”

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confidence: 99%

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Magnetism and topology in Tb-based icosahedral quasicrystal

Watanabe

2021

Sci Rep

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Quasicrystal (QC) possesses a unique lattice structure with rotational symmetry forbidden in conventional crystals. The electric property is far from complete understanding and it has been a long-standing issue whether the magnetic long-range order is realized in the QC. The main difficulty was lack of microscopic theory to analyze the effect of the crystalline electric field (CEF) at the rare-earth atom in QCs. Here we show the full microscopic analysis of the CEF in Tb-based QCs. We find that magnetic anisotropy arising from the CEF plays a key role in realizing unique magnetic textures on the icosahedron whose vertices Tb atoms are located at. Our analysis of the minimal model based on the magnetic anisotropy suggests that the long-range order of the hedgehog characterized by the topological charge of one is stabilized in the Tb-based QC. We also find that the whirling-moment state is characterized by unusually large topological charge of three. The magnetic textures as well as the topological states are shown to be switched by controlling compositions of the non-rare-earth elements in the ternary compounds. Our model is useful to understand the magnetism as well as the topological property in the rare-earth-based QCs and approximant crystals.

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Section: Methodsmentioning

confidence: 99%

mentioning

confidence: 99%

Magnetism and topology in Tb-based icosahedral quasicrystal

Watanabe

2021

Sci Rep

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“…In magnetic materials, the topological spin textures often appear in the form of a periodic array of the topological objects. For instance, the magnetic skyrmions appear by forming a periodic lattice called the skyrmion lattice (SkL) [48][49][50][51][52][53], and the magnetic hedgehogs (and the antihedgehogs) appear as the hedgehog lattice (HL) [25,26,[54][55][56][57][58]. These periodic structures can be represented by superpositions of multiple spin density waves, and hence, called multiple-Q spin textures.…”

Section: Introductionmentioning

confidence: 99%

Phase degree of freedom and topology in multiple-$Q$ spin textures

Shimizu,

Okumura,

Kato

et al. 2022

Preprint

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A periodic array of topological spin textures, such as skyrmions and hedgehogs, is called the multiple-Q spin texture, as it is represented by a superposition of multiple spin density waves. Depending on the way of superposition, not only the magnetic but also the topological properties are modified, leading to a variety of quantum transport and optical phenomena caused by the emergent electromagnetic fields through the Berry phase. Among others, the phase degree of freedom of the superposed waves is potentially important for such modifications, but its effect has not been fully investigated thus far. Here we perform systematic theoretical analyses of magnetic and topological properties of the multiple-Q spin textures with the phase degree of freedom in two and three dimensions. By introducing a hyperspace with an additional dimension corresponding to the phase degree of freedom, we establish a generic framework to deal with the phase shift in the multiple-Q spin textures. Using the hyperspace representation, we elaborate the complete topological phase diagrams for the superpositions of three proper screws or sinusoidal waves in two dimensions and those of four in three dimensions. In the two-dimensional case, we find that the phase shift as well as the magnetization change can yield the skyrmion lattices with the skymion number of −2, −1, 1, and 2, corresponding to the evolution of the Dirac strings connecting hedgehogs and antihedgehogs in the three-dimensional hyperspace. We show that the high skyrmion numbers ±2 appear in wider parameter regions for the sinusoidal superpositions than the screw ones. Meanwhile, in the three-dimensional case, we clarify that the topological phase diagrams include various types of the hedgehog lattices whose total number of hedgehogs and antihedgehogs ranges up to 48 in a cubic unit. Interestingly, the phase shift can generate unusual Dirac strings running on the horizontal planes perpendicular to the magnetization direction, which gives rise to unconventional pair creation of hedgehogs and antihedgehogs while increasing the magnetization in the case of the screw superpositions. We also show that the amplitude of the emergent magnetic field is maximized by fusion of hedgehogs and antihedgehogs on the horizontal Dirac strings in both proper screw and sinusoidal cases. In addition, by analyzing the numerical data in the previous studies, we demonstrate that phase shifts are indeed caused by an external magnetic field, associated with the topological transitions in the multiple-Q spin textures. Our results illuminate the topological aspects of the skyrmion and hedgehog lattices with the phase degree of freedom, which would be extended to other multiple-Q textures and useful for the exploration of topologically nontrivial magnetic phases and exotic quantum phenomena.

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“…The intriguing spin textures have been often induced by the Dzyaloshiskii-Moriya (DM) interaction, which originates from the relativistic spin-orbit coupling in the absence of spatial inversion symmetry 6,7 . As the DM interaction favors a twisted spin configuration, it can lead to topological swirling spin textures, such as a chiral soliton lattice in a one-dimensional system [8][9][10][11][12] , a skyrmion crystal (SkX) in a two-dimensional system 4,[13][14][15][16][17][18][19][20] , and a hedgehog lattice in a three-dimensional system 5,[21][22][23][24][25][26] , by combining the effect of magnetic anisotropy and external magnetic field. These nontrivial topological spin textures are promising for potential applications to next-generation spintronics devices owing to their large emergent magnetic field [27][28][29][30] .…”

Section: Introductionmentioning

confidence: 99%

Meron-antimeron crystals in noncentrosymmetric itinerant magnets on a triangular lattice

Hayami,

Yambe

2021

Preprint

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Multiple-Q magnetic states often induce nontrivial topological spin textures, such as a skyrmion and a hedgehog. We theoretically investigate yet another multiple-Q state with topological defects, a meron-antimeron crystal (MAX), represented by a periodic array of the meron and antimeron with a half-integer skyrmion number. Performing simulated annealing for an effective spin model of noncentrosymmetric itinerant magnets on a triangular lattice, we show that rectangular-shaped and triangular-shaped MAXs are stabilized by the interplay between the biquadratic interaction arising from the spin-charge coupling and the Dzyaloshinskii-Moriya interaction arising from the spin-orbit coupling. We also discuss the effect of a magnetic field on the triangular MAX, where highly anisotropic responses against a field direction are found. In particular, we show that the triangular MAX turns into the skyrmion crystal for the fields along the y and z directions, while it is replaced by another chiral state for the field along the x direction. These results would inspire further experimental investigation of the MAXs in itinerant magnets.

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Hedgehog-lattice spin texture in classical Heisenberg antiferromagnets on the breathing pyrochlore lattice

Cited by 39 publications

References 128 publications

Magnetism and topology in Tb-based icosahedral quasicrystal

Magnetism and topology in Tb-based icosahedral quasicrystal

Phase degree of freedom and topology in multiple-$Q$ spin textures

Meron-antimeron crystals in noncentrosymmetric itinerant magnets on a triangular lattice

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