Spin moiré engineering of topological magnetism and emergent electromagnetic fields

Shimizu, Kotaro; Okumura, Shun; Kato, Yasuyuki; Motome, Yukitoshi

doi:10.1103/physrevb.103.184421

Cited by 33 publications

(40 citation statements)

References 38 publications

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“…( 33) is taken on a closed surface surrounding the defect in the hyperspace. Here, Q m takes an integer, which defines the topological nature of the defects; a defect with positive (negative) Q m is a hedgehog (an antihedghog) which is regarded as a source (sink) of the emergent magnetic fields [25,57,59,79]. We find that the topological defect at √ 2 3q 0, 0, 3π 2 in Fig.…”

Section: Topological Transition In 3d Hyperspacementioning

confidence: 87%

“…In the 3D hyperspace, the spin structure composed of three proper screws may comprise a 3D topological spin structure called 3Q-HL [25,57,59,79]. It has a periodic array of topological defects called the hedgehogs and antihedgehogs, whose cores are the singular points where the spin length vanishes (see Sec.…”

Section: Hedgehogs In Hyperspacementioning

confidence: 99%

“…Following the arguments in Refs. [25,57,59,62,79], we compute the monopole charge for these defects, which is defined by…”

Section: Hedgehogs In Hyperspacementioning

confidence: 99%

“…1(a), where a SkL is given by a superposition of three proper screws and called the 3Q-SkL. As such superpositions yield superstructures as the interference patterns, the topological spin textures can be viewed as "spin moiré" [59]. Analogous to moiré fringes in optics, there are many ways to modulate the spin moiré, such as the number of superposed waves [60][61][62], the amplitudes of each spin density waves [63], and the angles between the propagating directions of the superposed waves [59].…”

Section: Introductionmentioning

confidence: 99%

“…As such superpositions yield superstructures as the interference patterns, the topological spin textures can be viewed as "spin moiré" [59]. Analogous to moiré fringes in optics, there are many ways to modulate the spin moiré, such as the number of superposed waves [60][61][62], the amplitudes of each spin density waves [63], and the angles between the propagating directions of the superposed waves [59]. Such modulations bring about various topological phases with different topological invariants and topological phase transitions between them.…”

Section: Introductionmentioning

confidence: 99%

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

Shimizu,

Okumura,

Kato

et al. 2022

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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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Section: Topological Transition In 3d Hyperspacementioning

confidence: 87%

Section: Hedgehogs In Hyperspacementioning

confidence: 99%

“…Following the arguments in Refs. [25,57,59,62,79], we compute the monopole charge for these defects, which is defined by…”

Section: Hedgehogs In Hyperspacementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Shimizu,

Okumura,

Kato

et al. 2022

Preprint

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Chiral Magnetic Phases in Moire Bilayers of Magnetic Dipoles

Tapia,

Cazor,

Mellado

2024

Advanced Physics Research

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In magnetic insulators, the sense of rotation of the magnetization is associated with novel phases of matter and exotic transport phenomena. Aimed to find new sources of chiral magnetism rooted in intrinsic fields and geometry, twisted square bilayers of magnetic dipoles with easy plane anisotropy are studied. For no twist, each lattice settles in the zig‐zag magnetic state and orders antiferromagnetically to the other layer. The moire patterns that result from the mutual rotation of the two square lattices influence such zig‐zag order, giving rise to several phases that depict non‐collinear magnetic textures with chiral motifs that break both time and inversion symmetry. For certain moire angles, helical and toroidal magnetic orders arise. Changing the vertical distance between layers can further manipulate these novel phases. It is shown that the dipolar interlayer interaction induces an emergent twist‐dependent chiral magnetic field orthogonal to the direction of the zig‐zag chains, which is responsible for the internal torques conjugated to the toroidal orders.

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Widely-sweeping magnetic field–temperature phase diagrams for skyrmion-hosting centrosymmetric tetragonal magnets

Hayami

Kato

2023

Journal of Magnetism and Magnetic Materials

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Spin moiré engineering of topological magnetism and emergent electromagnetic fields

Cited by 33 publications

References 38 publications

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

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

Chiral Magnetic Phases in Moire Bilayers of Magnetic Dipoles

Widely-sweeping magnetic field–temperature phase diagrams for skyrmion-hosting centrosymmetric tetragonal magnets

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