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Machine learning inspired models for Hall effects in non-collinear magnets
Authors:
Jonathan Kipp,
Fabian R. Lux,
Thorben Pürling,
Abigail Morrison,
Stefan Blügel,
Daniele Pinna,
Yuriy Mokrousov
Abstract:
The anomalous Hall effect has been front and center in solid state research and material science for over a century now, and the complex transport phenomena in nontrivial magnetic textures have gained an increasing amount of attention, both in theoretical and experimental studies. However, a clear path forward to capturing the influence of magnetization dynamics on anomalous Hall effect even in sm…
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The anomalous Hall effect has been front and center in solid state research and material science for over a century now, and the complex transport phenomena in nontrivial magnetic textures have gained an increasing amount of attention, both in theoretical and experimental studies. However, a clear path forward to capturing the influence of magnetization dynamics on anomalous Hall effect even in smallest frustrated magnets or spatially extended magnetic textures is still intensively sought after. In this work, we present an expansion of the anomalous Hall tensor into symmetrically invariant objects, encoding the magnetic configuration up to arbitrary power of spin. We show that these symmetric invariants can be utilized in conjunction with advanced regularization techniques in order to build models for the electric transport in magnetic textures which are, on one hand, complete with respect to the point group symmetry of the underlying lattice, and on the other hand, depend on a minimal number of order parameters only. Here, using a four-band tight-binding model on a honeycomb lattice, we demonstrate that the developed method can be used to address the importance and properties of higher-order contributions to transverse transport. The efficiency and breadth enabled by this method provides an ideal systematic approach to tackle the inherent complexity of response properties of noncollinear magnets, paving the way to the exploration of electric transport in intrinsically frustrated magnets as well as large-scale magnetic textures.
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Submitted 5 January, 2024;
originally announced January 2024.
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Chiral response of spin spiral-states as the origin of chiral transport fingerprints of spin textures
Authors:
Jonathan Kipp,
Fabian R. Lux,
Yuriy Mokrousov
Abstract:
The transport properties of non-trivial spin textures are coming under closer scrutiny as the amount of experimental data and theoretical simulations is increasing. To extend the commonly accepted yet simplifying and approximate picture of transport effects taking place in systems with spatially varying magnetization, it is important to understand the transport properties of building blocks for sp…
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The transport properties of non-trivial spin textures are coming under closer scrutiny as the amount of experimental data and theoretical simulations is increasing. To extend the commonly accepted yet simplifying and approximate picture of transport effects taking place in systems with spatially varying magnetization, it is important to understand the transport properties of building blocks for spin textures $-$ the homochiral spin-spiral states. In this work, by referring to phenomenological symmetry arguments based on the gradient expansion, and explicit calculations within the Kubo framework, we study the transport properties of various types of spin-spirals in a two-dimensional model with strong spin-orbit interaction. In particular, we focus on the contributions to the magnetoconductivity, the planar Hall effect and the anomalous Hall effect, which are sensitive to the sense of chirality of the spiral states. We analyze the emergence, symmetry, and microscopic properties of the resulting chiral magnetoconductivity, chiral planar Hall effect, and chiral Hall effect in terms of spin-spiral propagation direction, cone angle, spiral pitch, and disorder strength. Our findings suggest that the presence of spin-spiral states in magnets can be readily detected in various types of magnetotransport setups. Moreover, the sizable magnitude of chiral contributions to the conductivity of skyrmions estimated from homochiral spirals implies that chiral, as opposed to topological, magnetotransport can play a prominent role for the detection of non-trivial spin textures.
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Submitted 1 December, 2021;
originally announced December 2021.
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The chiral Hall effect in canted ferromagnets and antiferromagnets
Authors:
J. Kipp,
K. Samanta,
F. R. Lux,
M. Merte,
J. -P. Hanke,
M. Redies,
F. Freimuth,
S. Blügel,
M. Ležaić,
Y. Mokrousov
Abstract:
The anomalous Hall effect has been indispensable in our understanding of numerous magnetic phenomena. This concerns both ferromagnetic materials, as well as diverse classes of antiferromagnets, where in addition to the anomalous and crystal Hall effects, the topological Hall effect in non-coplanar antiferromagnets has been a subject of intensive research in the past decades. Here, we uncover a new…
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The anomalous Hall effect has been indispensable in our understanding of numerous magnetic phenomena. This concerns both ferromagnetic materials, as well as diverse classes of antiferromagnets, where in addition to the anomalous and crystal Hall effects, the topological Hall effect in non-coplanar antiferromagnets has been a subject of intensive research in the past decades. Here, we uncover a new flavour of the anomalous Hall effect in canted spin systems. Using advanced theoretical tools we demonstrate that upon canting, the anomalous Hall effect acquires a contribution which is sensitive to the sense of imprinted vector chirality among spins. We explore the origins and basic properties of corresponding chiral Hall effect, and closely tie it to the symmetry properties of the system. Our findings suggest that the chiral Hall effect and corresponding chiral magneto-optical effects emerge as novel versatile tools in characterizing an interplay of structure and chirality in complex magnets, as well as in tracking their chiral dynamics and fluctuations.
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Submitted 1 April, 2021; v1 submitted 3 July, 2020;
originally announced July 2020.