Exchange-anisotropy-induced intrinsic distortion, structural transition, and rotational transition in skyrmion crystals

Wan, Xuejin; Hu, Yangfan; Wang, Biao

doi:10.1103/physrevb.98.174427

Cited by 8 publications

(5 citation statements)

References 39 publications

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“…Based on the continuum spin model established by Bak and Jensen [17], we write the rescaled free-energy density [30] for helimagnets with the symmetry of T point group in the following form:…”

Section: Modelmentioning

confidence: 99%

Pinning Effects of Exchange and Magnetocrystalline Anisotropies on Skyrmion Lattice

Wan

Hou

et al. 2021

Front. Phys.

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Reorientation of skyrmion crystal (SkX) with respect to crystallographic axes is believed to be insensitive to anisotropies of fourth order in spin-orbit coupling, for which sixth order terms are considered for explanation. Here, we show that this is wrong due to an oversimplified assumption that SkX possesses hexagonal symmetry. When the deformation of SkX is taken into account, fourth order anisotropies such as exchange anisotropy and magnetocrystalline anisotropy have pinning (in this work, the word ‘pinning’ refers to the reorientation effects of intrinsic anisotropy terms) effects on SkX. In particular, we reproduce some experiments of MnSi and Fe1−xCoxSi by considering the effect of fourth order magnetocrystalline anisotropy alone. We reproduce the 30∘ rotation of SkX in Cu2OSeO3 by considering the combined effects of the exchange and magnetocrystalline anisotropies. And we use the exchange anisotropy to explain the reorientation of SkX in VOSe2O5.

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Section: Modelmentioning

confidence: 99%

Pinning Effects of Exchange and Magnetocrystalline Anisotropies on Skyrmion Lattice

Wan

Hou

et al. 2021

Front. Phys.

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“…About the classification, we will talk about it later. We use the following rescaling parameters [47]…”

Section: Thermodynamic Of Emergent Crystals In Magnetic Materialsmentioning

confidence: 99%

Thermodynamics and elasticity of emergent crystals

Hu,

Wan

2019

Preprint

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Periodic field patterns of atoms and their charges/spins/orbits emerge in crystals, forming novel states of matter called emergent crystals (ECs). In recent years, they are observed in diverse systems such as skyrmion crystals in helimagnets, and periodic ripples in 2D materials. ECs essentially changes the properties of material underneath, and are deformable when subject to various effective fields. A major challenge in application is first to predict what kind of EC will appear in the system of interest, and how to quantify its "elasticity" when subject to an effective field. Here we establish the theoretical framework of thermodynamics for deformable ECs, and derive from it the linear constitutive equations when subject to the primary external field. We provide a systematic study on the ECs that may appear in helimagnets induced by the Dzyaloshinskii-Moriya interaction, and analyze their elasticity when subject to bias magnetic fields. We construct in this work the basis of emergent elasticity, a new branch studying deformable emergent crystals under effective fields.

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“…The two conditions (a) and (b) correspond to the simplest cases where the effect of an intrinsic anisotropic interaction and the effect of an anisotropic external field are considered, respectively. Condition (a) is chosen because it is previously understood [28] that a negative exchange anisotropy not only explains the intrinsic anisotropy of SkX reflected by the unequal intensities of the six Bragg spots in the SANS experiment of M nSi [1] and Cu 2 OSeO 3 [16], but also repeat the triangle-square structural transition of SkX observed in Co 8 Zn 8 M n 4 [3] and MnSi [14]. Condition (b) is chosen because a tilted bias magnetic field is probably the most convenient external field [15,[31][32][33][34] to induce a distortion of SkX, and a bias magnetic field is sometimes required to obtain a thermodynamically stable SkX [1].…”

Section: Odelmentioning

confidence: 99%

“…Practically, effects of anisotropy is not only important, but also inevitable, because presence of various kinds of anisotropic interactions are naturally permitted by the symmetry of helimagnets [26][27][28]. These intrinsic anisotropies are closely related to the intrinsic distortion of skyrmion lattice revealed by the SANS experiment in MnSi[1] and and Cu 2 OSeO 3 [16], as well as the triangular-square structural transition of SkX observed in Co 8 Zn 8 M n 4 [3] and MnSi [14].…”

mentioning

confidence: 99%

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Long-wavelength emergent phonons in Bloch skyrmion crystals distorted by exchange anisotropy and tilted magnetic fields

2019

Phys. Rev. B

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Skyrmion crystals (SkX) are periodic alignment of magnetic skyrmions, i.e., a type of topologically protected spin textures. Compared with ordinary crystals, they can be drastically deformed under anisotropic effects because they are composed of field patterns whose deformation does not cause any bond-breaking. This exotic ductility of SkX bring about great tunability of its collective excitations called emergent phonons, which are vital for magnonics application. The question is how to quantitatively determine the emergent phonons of distorted SkX. Here we systematically study the long wavelength emergent phonons of SkX distorted by (a) a negative exchange anisotropy, and (b) a tilted magnetic field. In both cases, deformation and structural transitions of SkX thoroughly influence the frequency, anisotropy of vibrational pattern and dispersion relation, and coupling between lattice vibration and in-lattice vibration for all modes. Tilted magnetic fields are very effective in tuning the emergent phonons, such that all modes except the Goldstone mode can be excited by AC magnetic fields when a tilted bias field is presented.

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Exchange-anisotropy-induced intrinsic distortion, structural transition, and rotational transition in skyrmion crystals

Cited by 8 publications

References 39 publications

Pinning Effects of Exchange and Magnetocrystalline Anisotropies on Skyrmion Lattice

Pinning Effects of Exchange and Magnetocrystalline Anisotropies on Skyrmion Lattice

Thermodynamics and elasticity of emergent crystals

Long-wavelength emergent phonons in Bloch skyrmion crystals distorted by exchange anisotropy and tilted magnetic fields

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