Topological Hall Effect from Strong to Weak Coupling

Nakazawa, Kazuki; Bibès, Manuel; Kohno, Hiroshi

doi:10.7566/jpsj.87.033705

Cited by 57 publications

(78 citation statements)

References 17 publications

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“…A. Comparison with gauge field method [20] In Ref. [20], we used the spin gauge field to derive the THC formula for the weak-coupling, diffusive regime (regions 1, 1 , 2 and 2 ) as…”

Section: Discussionmentioning

confidence: 99%

Weak coupling theory of topological Hall effect

Nakazawa

Kohno

2019

Phys. Rev. B

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Topological Hall effect (THE) caused by a noncoplanar spin texture characterized by a scalar spin chirality is often described by the Berry phase, or the associated effective magnetic field. This picture is appropriate when the coupling, M , of conduction electrons to the spin texture is strong (strong-coupling regime) and the adiabatic condition is satisfied. However, in the weak-coupling regime, where the coupling M is smaller than the electrons' scattering rate, the adiabatic condition is not satisfied and the Berry phase picture does not hold. In such a regime, the relation of the effective magnetic field to the spin texture can be "nonlocal", in contrast to the "local" relation in the strong coupling case. Focusing on the case of continuous but general spin texture, we investigate the THE in various characteristic regions in the weak-coupling regime, namely, (1) diffusive and local, (2) diffusive and nonlocal, and (3) ballistic. In the presence of spin relaxation, there arise two more regions in the "weakest-coupling" regime: (1 ) diffusive and local, and (2 ) diffusive and nonlocal. We derived the analytic expression of the topological Hall conductivity (THC) for each region, and found that the condition for the locality of the effective field is governed by transverse spin diffusion of electrons. In region 1, where the spin relaxation is negligible and the effective field is local, the THC is found to be proportional to M , instead of M 3 of the weakest-coupling regime. In the diffusive, nonlocal regions (2 and 2 ), the effective field is given by a spin chirality formed by "effective spins" that the electrons see during their diffusive motion. Applying the results to a skyrmion lattice, we found the THC decreses as the skyrmion density is increased in region 2 , reflecting the nonlocality of the effective field, and shows a maximum at the boundary to the "local" region.arXiv:1808.04543v1 [cond-mat.mes-hall]

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“…A. Comparison with gauge field method [20] In Ref. [20], we used the spin gauge field to derive the THC formula for the weak-coupling, diffusive regime (regions 1, 1 , 2 and 2 ) as…”

Section: Discussionmentioning

confidence: 99%

Weak coupling theory of topological Hall effect

Nakazawa

Kohno

2019

Phys. Rev. B

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“…Another important aspect to uncover the full potential of emergent electromagnetism is going beyond the adiabatic limit. In a recent article [82] the authors have developed a unified theory for the THE to treat adiabatic and non-adiabatic components of the spin gauge field, thereby being able to cover the range from the strong to the weak coupling regime of the electron spin following the magnetic texture.…”

Section: Current and Future Challengesmentioning

confidence: 99%

The 2020 skyrmionics roadmap

Back¹,

Cros²,

Ebert³

et al. 2020

J. Phys. D: Appl. Phys.

327

225

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The notion of non-trivial topological winding in condensed matter systems represents a major area of present-day theoretical and experimental research. Magnetic materials offer a versatile platform that is particularly amenable for the exploration of topological spin solitons in real space such as skyrmions. First identified in non-centrosymmetric bulk materials, the rapidly growing zoology of materials systems hosting skyrmions and related topological spin solitons includes bulk compounds, surfaces, thin films, heterostructures, nano-wires and nano-dots. This underscores an exceptional potential for major breakthroughs ranging from fundamental questions to applications as driven by an interdisciplinary exchange of ideas between areas in magnetism which traditionally have been pursued rather independently. The skyrmionics roadmap provides a review of the present state of the art and the wide range of research directions and strategies currently under way. These are, for instance, motivated by the identification of the fundamental structural properties of skyrmions and related textures, processes of nucleation and annihilation in the presence of non-trivial topological winding, an exceptionally efficient coupling to spin currents generating spin transfer torques at tiny current densities, as well as the capability to purposedesign broad-band spin dynamic and logic devices. arXiv:2001.00026v3 [cond-mat.str-el]

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“…Besides their potential for applications, biskyrmions are also worth being investigated from a fundamental point of view. Their nontrivial real-space topology, manifested in the topological charge of N Sk = ±2, imposes emergent electrodynamic effects: just like conventional skyrmions, biskyrmions exhibit a skyrmion Hall effect 3,8,9,67,68 and a topological Hall effect 3,10,11,[72][73][74][75][76][77][78] . In other words, under the effect of a spin-polarized current the biskyrmion and the current electrons are deflected into transverse directions.…”

Section: Discussionmentioning

confidence: 99%

Forming individual magnetic biskyrmions by merging two skyrmions in a centrosymmetric nanodisk

Göbel

Henk

Mertig

2019

Sci Rep

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When two magnetic skyrmions – whirl-like, topologically protected quasiparticles – form a bound pair, a biskyrmion state with a topological charge of N Sk = ±2 is constituted. Recently, especially the case of two partially overlapping skyrmions has brought about great research interest. Since for its formation the individual skyrmions need to posses opposite in-plane magnetizations, such a biskyrmion cannot be stabilized by the Dzyaloshinskii-Moriya-interaction (DMI), which is the interaction that typically stabilizes skyrmions in non-centrosymmetric materials and at interfaces. Here, we show that these biskyrmions can be stabilized by the dipole-dipole interaction in centrosymmetric materials in which the DMI is forbidden. Analytical considerations indicate that the bound state of a biskyrmion is energetically preferable over two individual skyrmions. As a result, when starting from two skyrmions in a micromagnetic simulation, a biskyrmion is formed upon relaxation. We propose a scheme that allows to control this biskyrmion formation in nanodisks and analyze the individual steps.

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Topological Hall Effect from Strong to Weak Coupling

Cited by 57 publications

References 17 publications

Weak coupling theory of topological Hall effect

Weak coupling theory of topological Hall effect

The 2020 skyrmionics roadmap

Forming individual magnetic biskyrmions by merging two skyrmions in a centrosymmetric nanodisk

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