Magnetic field-temperature phase diagrams for multiple-$Q$ magnetic orderings: Exact steepest descent approach to long-range interacting spin systems

Kato, Yasuyuki; Motome, Yukitoshi

doi:10.48550/arxiv.2202.04407

Cited by 3 publications

(8 citation statements)

References 73 publications

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“…We here present the results of X q in the tetragonal, hexagonal, and trigonal crystal systems, where the wave vectors lie along the high symmetry lines; Q 1 is taken along the x [Fig. 2(a)] and [110] [Fig. 2(b)] axes in the tetragonal crystal system, while Q 1 is taken along the x [Fig.…”

Section: B Effective Spin Model Under Space Groupsmentioning

confidence: 99%

“…In particular, X Q1 x and X Q1 ŷ in P 6m2, P 62m, P 321, P 312, P 3m1, and P 31m crystals have a different number of independent components. The second is that the diagonal components of the in-teractions are different for all the space groups except for Q 1 [110] in P 4/mmm, P 422, P 42m, P 4m2, P 4mm, and P 4/m crystal systems, i.e., F x Q1 = F y Q1 = F z Q1 ; the difference between F x Q1 and F z Q1 (F y Q1 and F z Q1 ) is owing to an inequivalence between the in-plane and z directions, while that between F x Q1 and F y Q1 is owing to the discrete rotational symmetry around the principal axis. It is noted that in the case of Q 1 [110] in P 4/mmm, P 422, P 42m, P 4m2, P 4mm, and P 4/m crystal systems, all the space groups allow nonzero E z Q1 instead of different F x Q1 and F y Q1 .…”

Section: B Effective Spin Model Under Space Groupsmentioning

confidence: 99%

“…The second is that the diagonal components of the in-teractions are different for all the space groups except for Q 1 [110] in P 4/mmm, P 422, P 42m, P 4m2, P 4mm, and P 4/m crystal systems, i.e., F x Q1 = F y Q1 = F z Q1 ; the difference between F x Q1 and F z Q1 (F y Q1 and F z Q1 ) is owing to an inequivalence between the in-plane and z directions, while that between F x Q1 and F y Q1 is owing to the discrete rotational symmetry around the principal axis. It is noted that in the case of Q 1 [110] in P 4/mmm, P 422, P 42m, P 4m2, P 4mm, and P 4/m crystal systems, all the space groups allow nonzero E z Q1 instead of different F x Q1 and F y Q1 . The third is that the symmetric off-diagonal components, E x Q1 and E y Q1 , only appear in the trigonal crystal systems, which do not have the twofold axis along the z direction and the horizontal mirror plane [see rules (c) and (d)].…”

Section: B Effective Spin Model Under Space Groupsmentioning

confidence: 99%

“…2 but also with other {Q}. For example, the model with [110] , which are given in Table I. Then, the number of independent interactions in the model is six.…”

Section: B Effective Spin Model Under Space Groupsmentioning

confidence: 99%

“…(7) with the interactions at the two-dimensional wave vectors can be constructed from Tables I-III and Appendix B, which will give an insight into the stability of the two-dimensional multiple-Q states, such as the SkX. Similar to the case with two-dimensional wave vectors, one can construct the spin model with the interactions at three-dimensional wave vectors based on the rules (a)-(f), which leads to a minimal effective spin model to investigate an instability toward three-dimensional multiple-Q states [42,46,104,110], such as the hedgehog lattice.…”

Section: B Effective Spin Model Under Space Groupsmentioning

confidence: 99%

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Effective spin model in momentum space: Toward a systematic understanding of multiple-$Q$ instability by momentum-resolved anisotropic exchange interactions

Yambe¹,

Hayami²

2022

Preprint

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Multiple-Q magnetic states, such as a skyrmion crystal, become a source of unusual transport phenomena and dynamics. Recent theoretical and experimental studies clarify that such multiple-Q states ubiquitously appear under different crystal structures in metals and insulators. Toward a systematic understanding of the formation of the multiple-Q states in various crystal systems, in this theoretical study, we present a low-energy effective spin model with anisotropic exchange interactions in momentum space. We summarize specific six symmetry rules for nonzero symmetric and antisymmetric anisotropic exchange interactions in momentum space, which are regarded as an extension of Moriya's rule. According to the rules, we construct the effective spin model for tetragonal, hexagonal, and trigonal magnets with crystal-and momentum-dependent anisotropic exchange interactions based on magnetic representation analysis. Furthermore, we describe the origin of the effective anisotropic exchange interactions in itinerant magnets by perturbatively analyzing a multi-band periodic Anderson model with the spin-orbit coupling. We apply the effective spin model to an itinerant magnet in a P 6/mmm crystal and find various multiple-Q states with a spin scalar chirality in the ground state. Our results provide a foundation of constructing effective phenomenological spin models for any crystal systems hosting the multiple-Q states, which will stimulate further exploration of exotic multiple-Q states in materials with the spin-orbit coupling.

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Section: B Effective Spin Model Under Space Groupsmentioning

confidence: 99%

Section: B Effective Spin Model Under Space Groupsmentioning

confidence: 99%

Section: B Effective Spin Model Under Space Groupsmentioning

confidence: 99%

“…2 but also with other {Q}. For example, the model with [110] , which are given in Table I. Then, the number of independent interactions in the model is six.…”

Section: B Effective Spin Model Under Space Groupsmentioning

confidence: 99%

Section: B Effective Spin Model Under Space Groupsmentioning

confidence: 99%

See 3 more Smart Citations

Effective spin model in momentum space: Toward a systematic understanding of multiple-$Q$ instability by momentum-resolved anisotropic exchange interactions

Yambe¹,

Hayami²

2022

Preprint

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Helicity locking of square skyrmion crystal in a centrosymmetric lattice system without vertical mirror symmetry

Hayami,

Yambe

2022

Preprint

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We theoretically investigate the stability of a square skyrmion crystal (SkX) in a centrosymmetric tetragonal lattice structure with the emphasis on the role of the magnetic anisotropy arising from the absence of vertical mirror symmetry. Our analysis is based on an effective bilinear and biquadratic model in momentum space, which is a canonical model for itinerant magnets in a weak-coupling regime. By performing the simulated annealing for the model on the two-dimensional square lattice, we find that the off-diagonal spin component in the interaction, which becomes nonzero when the vertical mirror symmetry is broken, gives rise to the square SkX with a definite helicity in an external magnetic field. We show that the helicity of the centrosymmetric SkXs is determined by the competition between the off-diagonal and diagonal anisotropic interactions, the latter of which appears in the discrete fourfold-rotational lattice structure. Furthermore, we discuss helicitydependent physical phenomena by introducing odd-parity multipoles, where electric (magnetic) and electric (magnetic) toroidal multipoles are sources of an antisymmetric spin polarization and an Edelstein effect (a magnetoelectric effect). We also discuss the stability of the SkXs with different helicities in a magnetic field rotation. Our results provide a way of engineering the helicity-locked SkXs by the symmetric anisotropic interaction in centrosymmetric magnets, which is distinct from that by the antisymmetric Dzyaloshinskii-Moriya interaction in noncentrosymmetric magnets.

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Multifarious skyrmion phases on a trilayer triangular lattice

Hayami

2022

Preprint

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The instability toward a magnetic skyrmion crystal in centrosymmetric trilayer magnets is investigated based on a spin model with layer-dependent Dzayloshinskii-Moriya interaction. We find various types of skyrmion crystal phases with different skyrmion numbers in a low-temperature phase diagram by performing the simulated annealing. In addition to the Néel skyrmion crystal phase that is expected to emerge in the presence of the polar-type Dzayloshinskii-Moriya interaction, we obtain the skyrmion crystal phases characteristics of the layered system: the twisted surface skyrmion crystal, anti-skyrmion crystal, and high-topological-number skyrmion crystal phases. The rich magnetic phases are brought about by the synergy among the layer-dependent Dzayloshinskii-Moriya interaction, interlayer exchange interaction, and an external magnetic field. Our results indicate that the layer degree of freedom at the surface and heterostructures provides a good platform to engineer and design the topological spin textures.

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Magnetic field-temperature phase diagrams for multiple-$Q$ magnetic orderings: Exact steepest descent approach to long-range interacting spin systems

Cited by 3 publications

References 73 publications

Effective spin model in momentum space: Toward a systematic understanding of multiple-$Q$ instability by momentum-resolved anisotropic exchange interactions

Effective spin model in momentum space: Toward a systematic understanding of multiple-$Q$ instability by momentum-resolved anisotropic exchange interactions

Helicity locking of square skyrmion crystal in a centrosymmetric lattice system without vertical mirror symmetry

Multifarious skyrmion phases on a trilayer triangular lattice

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