Direct Observation of the Statics and Dynamics of Emergent Magnetic Monopoles in a Chiral Magnet

N. Kanazawa, A. Kitaori, J. S. White, V. Ukleev, H. M. Rønnow, A. Tsukazaki, M. Ichikawa, M. Kawasaki, and Y. Tokura

Phys. Rev. Lett. 125, 137202 – Published 25 September 2020

Abstract

In the three-dimensional (3D) Heisenberg model, topological point defects known as spin hedgehogs behave as emergent magnetic monopoles, i.e., quantized sources and sinks of gauge fields that couple strongly to conduction electrons, and cause unconventional transport responses such as the gigantic Hall effect. We observe a dramatic change in the Hall effect upon the transformation of a spin hedgehog crystal in a chiral magnet MnGe through combined measurements of magnetotransport and small-angle neutron scattering (SANS). At low temperatures, well-defined SANS peaks and a negative Hall signal are each consistent with expectations for a static hedgehog lattice. In contrast, a positive Hall signal takes over when the hedgehog lattice fluctuates at higher temperatures, with a diffuse SANS signal observed upon decomposition of the hedgehog lattice. Our approach provides a simple way to both distinguish and disentangle the roles of static and dynamic emergent monopoles on the augmented Hall motion of conduction electrons.

Received 21 April 2020
Accepted 24 August 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.137202

Physics Subject Headings (PhySH)

Anomalous Hall effect Skyrmions Topological Hall effect

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

N. Kanazawa ^1,*, A. Kitaori^1,*, J. S. White ^2,*, V. Ukleev ², H. M. Rønnow³, A. Tsukazaki⁴, M. Ichikawa¹, M. Kawasaki^1,5, and Y. Tokura^1,5,6

¹Department of Applied Physics, University of Tokyo, Tokyo 113-8656, Japan
²Laboratory for Neutron Scattering and Imaging (LNS), Paul Scherrer Institute (PSI), CH-5232 Villigen, Switzerland
³Laboratory for Quantum Magnetism (LQM), Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
⁴Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan
⁵RIKEN Center for Emergent Matter Science (CEMS), Wako 351-0198, Japan
⁶Tokyo College, University of Tokyo, Tokyo 113-8656, Japan

^*These three authors equally contributed to this work.

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Issue

Vol. 125, Iss. 13 — 25 September 2020

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Images

Figure 1
(a),(b) Schematic illustrations of hedgehog and antihedgehog spin structures (a) and their monopolelike EMF distributions (b). (c) A pair of hedgehog (yellow dot) and antihedgehog (green dot) in the ferromagnetic background (red arrows). The magnetic line defect (blue arrows) appears between the pair, where the negative EMF emerges as indicated by the blue region. (d) The bridging skyrmionic structure between the pair in cross section. (e) Cubic hedgehog lattice (HL) state in MnGe. Reddish and bluish arrows indicate spins with positive and negative $z$ components, respectively. (f) EMF distribution of the HL at zero magnetic field. Reddish and bluish regions represent EMF with positive and negative $z$ components, respectively. (g) Expected neutron scattering intensity map for the MnGe thick film with the two chiral crystalline domains. Red dots represent magnetic reflections. White and black dots represent directions of $⟨ 100 ⟩$ crystalline axes of right- and left-handed domains, respectively.
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Figure 2
(a)–(f) Representative SANS patterns (left panels) and their schematic illustrations (right panels) at zero (a)–(c) and finite (d)–(f) magnetic fields. The view is along the film normal direction. (g)–(l), Magnetic-field dependence of positions and area sizes of magnetic Bragg satellites at various temperatures. The position and area size are described as the angle $θ$ between $q_{i}$ and the film normal [inset of (i)] and the product of half widths of the elliptical intensity distribution along its long and short axes, respectively. The inset of (l) shows an enlargement of the main panel. The horizontal dotted lines at $θ = 54 °$ represent the angle which corresponds to a $q$ -vector alignment of spots with the original orthogonal $⟨ 100 ⟩$ axes, while vertical dotted lines indicate critical fields for HL transformation ( $H_{t}$ ) and ferromagnetic transition ( $H_{c}$ ).
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Figure 3
(a)–(c) Magnetic-field dependence of magnetization along [111] in the thick ( $3 μ m$ ) epitaxial (111) film at various temperatures. Inset of (c) shows scanning electron microscope (SEM) image of a MnGe single crystal. (d)–(f) Magnetic-field dependence of Hall resistivity $ρ_{y x}$ and the estimated contribution from conventional Hall response $ρ_{y x}^{est}$ in the single crystal at various temperatures.
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Figure 4
(a) Magnetic-field dependence of $ρ_{y x}^{T}$ in the single crystal, obtained at various temperatures. Data at adjacent temperatures are shifted vertically for clarity. Black triangles indicate the magnetic fields $H_{p}$ at the tops of positive peak structures. (b) Color map of $ρ_{y x}^{T}$ and scatter plot of SANS pattern type along with critical fields $H_{p}$ and $H_{c}$ . A different color marker as shown in the middle panels of (b) indicates each different category of pattern classified according to the directions and diffuseness of the scattering spots. The bottom panels are the distributions of hedgehogs (yellow dots), antihedgehogs (green dots) and emergent magnetic field (reddish and bluish regions) in the respective magnetic unit cells of the cubic (bottom left) and rhombohedral (bottom right) HL.
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